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Neural-PDE-Solver

PDE: Partial Differentiable Equation

Neural Operators: Learning nonlinear mappings between function spaces.

Contributed by Chunyang Zhang.

1. Survey
2. Model
2.1 PINN 2.2 DeepONet
2.3 Fourier Operator 2.4 Graph Network
2.5 Green Function 2.6 Finite Element
2.7 Convolution 2.8 AutoEncoder
2.9 Neural Operator 2.10 Machine Learning
2.11 Identification 2.12 Inverse Design
2.13 Neural ODE 2.14 Large Model
3. Mechanism
3.1 Benchmark 3.2 Investigation
3.3 Domain Adaptation 3.4 Loss Function
3.5 Sampling 3.6 Mesh
3.7 Decomposition 3.8 Disentangle
3.9 Solver 3.10 AutoML
3.11 Neural Implicit Flow 3.12 Uncertainty Quantification
3.13 Generative Model 3.14 Transformer
3.15 Theory 3.16 Gaussian Process
3.17 Variation 3.18 Bayesian
3.19 Latent Space 3.20 Lagrangian
3.21 Multi Scale 3.22 Multi Fidelity
3.23 Multi Grid 3.24 Active Learning
3.25 Multi Task
4. Applications
4.1 Optimization 4.2 Fluid
4.3 Cybernetics 4.4 Climate
4.5 Mechanics 4.6 Robotics
4.7 Physics 4.8 Image
4.9 Chemistry 4.10 Materials
4.11 Molecules 4.12 Energy
4.13 Quantum 4.14 Game Theory
4.15 Industry 4.16 Economics
4.17 Reconstruction 4.18 Electromagnetism
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    Khemraj Shukla, Ameya D.Jagtap, and George Em Karniadakis.

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    Xiangyu Yang and Zhen Wang.

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    Amirhossein Arzani, Kevin W.Cassel, and Roshan M.D'Souza.

  21. A-PINN: Auxiliary physics informed neural networks for forward and inverse problems of nonlinear integro-differential equations. JCP, 2022. paper

    Lei Yuan, Yiqing Ni, Xiangyun Deng, and Shuo Hao.

  22. A mixed formulation for physics-informed neural networks as a potential solver for engineering problems in heterogeneous domains: Comparison with finite element method. CMAME, 2022. paper

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  23. Physics-informed neural networks combined with polynomial interpolation to solve nonlinear partial differential equations. Computers & Mathematics with Applications, 2023. paper

    Siping Tang, Xinlong Feng, Wei Wu, and Hui Xu.

  24. A novel sequential method to train physics informed neural networks for Allen Cahn and Cahn Hilliard equations. CMAME, 2022. paper

    Revanth Mattey and Susanta Ghosh.

  25. RPINNs: Rectified-physics informed neural networks for solving stationary partial differential equations. Computers and Fluids, 2022. paper

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  29. Anisotropic, sparse and interpretable physics-informed neural networks for PDEs. arXiv, 2022. paper

    Amuthan A. Ramabathiran and Prabhu Ramachandran.

  30. Fast neural network based solving of partial differential equations. arXiv, 2022. paper

    Jaroslaw Rzepecki, Daniel Bates, and Chris Doran.

  31. Discontinuity computing using physics-informed neural network. arXiv, 2022. paper

    Li Liu, Shengping Liu, Hui Xie, Fansheng Xiong, Tengchao Yu, Mengjuan Xiao, Lufeng Liu, and Heng Yong.

  32. Learning differentiable solvers for systems with hard constraints. arXiv, 2022. paper

    Geoffrey Négiar, Michael W. Mahoney, and Aditi S. Krishnapriyan.

  33. Momentum diminishes the effect of spectral bias in physics-informed neural networks. arXiv, 2022. paper

    Ghazal Farhani, Alexander Kazachek, and Boyu Wang.

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    Jiawei Guo, Yanzhong Yao, Han Wang, and Tongxiang Gu.

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    Siddharth Rout.

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    Ziya Uddin, Sai Ganga, Rishi Asthana, and Wubshet Ibrahim.

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    Akarsh Pokkunuru, Pedram Rooshenas, Thilo Strauss, Anuj Abhishek, and Taufiquar Khan.

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  52. NSGA-PINN: A multi-objective optimization method for physics-informed neural network training. arXiv, 2023. paper

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    S Chandra Mouli, Muhammad Ashraful Alam, and Bruno Ribeiro.

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    Haoyang Zheng, Yao Huang, Ziyang Huang, Wenrui Hao, and Guang Lin.

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    Aleksandr Dekhovich, Marcel H.F. Sluiter, David M.J. Tax, and Miguel A. Bessa.

  58. Global convergence of deep Galerkin and PINNs methods for solving partial differential equations. arXiv, 2023. paper

    Francisco Eiras, Adel Bibi, Rudy Bunel, Krishnamurthy Dj Dvijotham, Philip Torr, and M. Pawan Kumar.

  59. Provably correct physics-informed neural networks. arXiv, 2023. paper

    Deqing Jiang, Justin Sirignano, and Samuel N. Cohen.

  60. Predictive limitations of physics-informed neural networks in vortex shedding. arXiv, 2023. paper

    Pi-Yueh Chuang and Lorena A. Barba.

  61. Residual-based error bound for physics-informed neural networks. arXiv, 2023. paper

    Shuheng Liu, Xiyue Huang, and Pavlos Protopapas.

  62. Automatic boundary fitting framework of boundary dependent physics-informed neural network solving partial differential equation with complex boundary conditions. CMAME, 2023. paper

    Yuchen Xie, Yu Ma, and Yahui Wang.

  63. Solving a class of multi-scale elliptic PDEs by means of Fourier-based mixed physics informed neural networks. arXiv, 2023. paper

    Xi'an Li, Jinran Wu, Zhi-Qin John Xu, and You-Gan Wang.

  64. Separable physics informed neural networks. arXiv, 2023. paper

    Junwoo Cho, Seungtae Nam, Hyunmo Yang, Seok-Bae Yun, Youngjoon Hong, and Eunbyung Park.

  65. Achieving high accuracy with PINNs via energy natural gradient descent. ICML, 2023. paper

    Johannes Müller and Marius Zeinhofer.

  66. Gradient descent finds the global optima of two-layer physics-informed neural networks. ICML, 2023. paper

    Yihang Gao, Yiqi Gu, and Michael Ng.

  67. Residual-based attention in physics-informed neural networks. CMAME, 2024. paper

    Sokratis J. Anagnostopoulos, Juan Diego Toscano, Nikolaos Stergiopulos, and George Em Karniadakis.

  68. Auxiliary-tasks learning for physics-informed neural network-based partial differential equations solving. arXiv, 2023. paper

    Junjun Yan, Xinhai Chen, Zhichao Wang, Enqiang Zhou, and Jie Liu.

  69. Tackling the curse of dimensionality with physics-informed neural networks. arXiv, 2023. paper

    Zheyuan Hu, Khemraj Shukla, George Em Karniadakis, and Kenji Kawaguchi.

  70. Solving PDEs on spheres with physics-informed convolutional neural networks. arXiv, 2023. paper

    Guanhang Lei, Zhen Lei, Lei Shi, Chenyu Zeng, and Dingxuan Zhou.

  71. Solving PDEs on spheres with physics-informed convolutional neural networks. arXiv, 2023. paper

    Guanhang Lei, Zhen Lei, Lei Shi, Chenyu Zeng, and Dingxuan Zhou.

  72. Tensor-compressed back-propagation-free training for (physics-informed) neural networks. arXiv, 2023. paper

    Yequan Zhao, Xinling Yu, Zhixiong Chen, Ziyue Liu, Sijia Liu, and Zheng Zhang.

  73. How to select physics-informed neural networks in the absence of ground truth: A pareto front-based strategy. ICML, 2023. paper

    Zhao Wei, Jian Cheng Wong, Nicholas Wei Yong Sung, Abhishek Gupta, Chin Chun Ooi, Pao-Hsiung Chiu, My Ha Dao, and Yew-Soon Ong.

  74. A gradient-enhanced physics-informed neural network (gPINN) scheme for the coupled non-fickian/non-fourierian diffusion-thermoelasticity analysis: A novel gPINN structure. EAAI, 2023. paper

    Katayoun Eshkofti and Seyed Mahmoud Hosseini.

  75. Learning only on boundaries: A physics-informed neural operator for solving parametric partial differential equations in complex geometries. arXiv, 2023. paper

    Zhiwei Fang, Sifan Wang, and Paris Perdikaris.

  76. Exact and soft boundary conditions in physics-informed neural networks for the variable coefficient poisson equation. arXiv, 2023. paper

    Sebastian Barschkis.

  77. Investigating the ability of PINNs to solve burgers’ PDE near finite-time blowup. arXiv, 2023. paper

    Dibyakanti Kumar and Anirbit Mukherjee.

  78. Correcting model misspecification in physics-informed neural networks (PINNs). CMAME, 2024. paper

    Zongren Zou, Xuhui Meng, and George Em Karniadakis.

  79. On residual minimization for PDEs: Failure of PINN, modified equation, and implicit bias. arXiv, 2023. paper

    Tao Luo and Qixuan Zhou.

  80. Operator learning enhanced physics-informed neural networks for solving partial differential equations characterized by sharp solutions. arXiv, 2023. paper

    Bin Lin, Zhiping Mao, Zhicheng Wang, and George Em Karniadakis.

  81. PINNs-TF2: Fast and user-friendly physics-informed neural networks in TensorFlow V2. NIPS, 2023. paper

    Reza Akbarian Bafghi and Maziar Raissi.

  82. Filtered partial differential equations: A robust surrogate constraint in physics-informed deep learning framework. arXiv, 2023. paper

    Dashan Zhang, Yuntian Chen, and Shiyi Chen.

  83. Enhanced physics-informed neural networks with domain scaling and residual correction methods for multi-frequency elliptic problems. arXiv, 2023. paper

    Deok-Kyu Jang, Hyea Hyun Kim, and Kyungsoo Kim.

  84. Physics-informed neural networks for transformed geometries and manifolds. arXiv, 2023. paper

    Samuel Burbulla.

    Zheyuan Hu, Zhouhao Yang, Yezhen Wang, George Em Karniadakis, and Kenji Kawaguchi.

  85. Neuro-PINN: A hybrid framework for efficient nonlinear projection equation solutions. The International Journal for Numerical Methods in Engineering, 2023. paper

    Dawen Wu and Abdel Lisser.

  86. Exactly conservative physics-informed neural networks and deep operator networks for dynamical systems. arXiv, 2023. paper

    Elsa Cardoso-Bihlo and Alex Bihlo.

  87. Semi-analytic PINN methods for boundary layer problems in a rectangular domain. arXiv, 2023. paper

    Gungmin Gie, Youngjoon Hong, Chang-Yeol Jung, and Tselmuun Munkhjin.

  88. PICL: Physics informed contrastive learning for partial differential equations. arXiv, 2024. paper

    Cooper Lorsung and Amir Barati Farimani.

  89. Fourier warm start for physics-informed neural networks. EAAI, 2024. paper

    Ge Jin, Jian Cheng Wong, Abhishek Gupta, Shipeng Li, and Yew-Soon Ong.

  90. Preconditioning for physics-informed neural networks. ICML, 2024. paper

    Songming Liu, Chang Su, Jiachen Yao, Zhongkai Hao, Hang Su, Youjia Wu, and Jun Zhu.

  91. RBF-PINN: Non-Fourier positional embedding in physics-informed neural networks. arXiv, 2024. paper

    Chengxi Zeng, Tilo Burghardt, and Alberto M Gambaruto.

  92. Training dynamics in physics-informed neural networks with feature mapping. arXiv, 2024. paper

    Chengxi Zeng, Tilo Burghardt, and Alberto M Gambaruto.

  93. Score-based physics-informed neural networks for high-dimensional Fokker-Planck equations. arXiv, 2024. paper

    Zheyuan Hu, Zhongqiang Zhang, George Em Karniadakis, and Kenji Kawaguchi.

  94. Investigation of compressor cascade flow using physics-informed neural networks with adaptive learning strategy. AIAA Journal, 2024. paper

    Zhihui Li, Francesco Montomoli, and Sanjiv Sharma.

  95. Exact enforcement of temporal continuity in sequential physics-informed neural networks. arXiv, 2024. paper

    Pratanu Roy and Stephen Castonguay.

  96. Multiple scattering simulation via physics-informed neural networks. arXiv, 2024. paper

    Siddharth Nair, Timothy F. Walsh, Greg Pickrell, and Fabio Semperlotti.

  97. Toward a better understanding of Fourier neural operators: Analysis and improvement from a spectral perspective. arXiv, 2024. paper

    Shaoxiang Qin, Fuyuan Lyu, Wenhui Peng, Dingyang Geng, Ju Wang, Naiping Gao, Xue Liu, and Liangzhu Leon Wang.

  98. Anti-derivatives approximator for enhancing physics-informed neural networks. CMAME, 2024. paper

    Jeongsu Lee.

  99. GMC-PINNs: A new general Monte Carlo PINNs methodfor solving fractional partial differential equations on irregular domains. arXiv, 2024. paper

    Shupeng Wang and George Em Karniadakis.

  100. CEENs: Causality-enforced evolutional networks for solving time-dependent partial differential equations. CMAME, 2024. paper

    Jeahan Jung, Heechang Kim, Hyomin Shin, and Minseok Choi.

  101. PTPI-DL-ROMs: Pre-trained physics-informed deep learning-based reduced order models for nonlinear parametrized PDEs. arXiv, 2024. paper

    Simone Brivio, Stefania Fresca, and Andrea Manzoni.

  102. Closed-form symbolic solutions: A new perspective on solving partial differential equations. arXiv, 2024. paper

    Shu Wei, Yanjie Li, Lina Yu, Min Wu, Weijun Li, Meilan Hao, Wenqiang Li, Jingyi Liu, and Yusong Deng.

  103. RoPINN: Region optimized physics-informed neural networks. arXiv, 2024. paper

    Haixu Wu, Huakun Luo, Yuezhou Ma, Jianmin Wang, and Mingsheng Long.

  104. Interface PINNs (I-PINNs): A physics-informed neural networks framework for interface problems. CMAME, 2024. paper

    Antareep Kumar Sarma, Sumanta Roy, Chandrasekhar Annavarapu, Pratanu Roy, and Shriram Jagannathan.

  105. Parameterized physics-informed neural networks for parameterized PDEs. ICML, 2024. paper

    Woojin Cho, Minju Jo, Haksoo Lim, Kookjin Lee, Dongeun Lee, Sanghyun Hong, and Noseong Park.

  1. Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators. NMI, 2021. paper

    Lu Lu, Pengzhan Jin, Guofei Pang, Zhongqiang Zhang, and George Em Karniadakis.

  2. Learning the solution operator of parametric partial differential equations with physics-informed DeepONets. SA, 2021. paper

    Wang Sifan, Hanwen Wang, and Paris Perdikaris.

  3. Deep transfer operator learning for partial differential equations under conditional shift. NMI, 2022. paper

    Somdatta Goswami, Katiana Kontolati, Michael D. Shields, and George Em Karniadakis.

  4. Variable-input deep operator networks. arXiv, 2022. paper

    Michael Prasthofer, Tim De Ryck, and Siddhartha Mishra.

  5. MIONet: Learning multiple-input operators via tensor product. arXiv, 2022. paper

    Jeremy Yu, Lu Lu, Xuhui Meng, and George Em Karniadakis.

  6. Long-time integration of parametric evolution equations with physics-informed DeepONets. arXiv, 2021. paper

    Sifan Wang and Paris Perdikaris.

  7. Improved architectures and training algorithms for deep operator networks. Journal of Scientific Computing, 2022. paper

    Sifan Wang, Hanwen Wang, and Paris Perdikaris.

  8. SVD perspectives for augmenting DeepONet flexibility and interpretability. arXiv, 2022. paper

    Simone Venturi and Tiernan Casey.

  9. Accelerated replica exchange stochastic gradient Langevin diffusion enhanced Bayesian DeepONet for solving noisy parametric PDEs. arXiv, 2021. paper

    Guang Lin, Christian Moya, and Zecheng Zhang.

  10. Bi-fidelity modeling of uncertain and partially unknown systems using DeepONet. arXiv, 2022. paper

    Subhayan De, Matthew Reynolds, Malik Hassanaly, Ryan N. King, and Alireza Doostan.

  11. MultiAuto-DeepONet: A multi-resolution autoencoder DeepONet for nonlinear dimension reduction, uncertainty quantification and operator learning of forward and inverse stochastic problems. arXiv, 2022. paper

    Jiahao Zhang, Shiqi Zhang, and Guang Lin.

  12. Transfer learning enhanced DeepONet for long-time prediction of evolution equations. AAAI, 2023. paper

    Wuzhe Xu, Yulong Lu, and Li Wang.

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    Jaewan Park, Shashank Kushwaha, Junyan He, Seid Koric, Diab Abueidda, and Iwona Jasiuk.

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  20. DON-LSTM: Multi-resolution learning with DeepONets and long short-term memory neural networks. arXiv, 2023. paper

    Katarzyna Michałowska, Somdatta Goswami, George Em Karniadakis, and Signe Riemer-Sørensen.

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  22. Derivative-enhanced deep operator network. arXiv, 2024. paper

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  1. Fourier neural operator for parametric partial differential equations. ICLR, 2021. paper

    Zongyi Li, Nikola Borislavov Kovachki, Kamyar Azizzadenesheli, Burigede liu, Kaushik Bhattacharya, Andrew Stuart, and Anima Anandkumar.

  2. On universal approximation and error bounds for Fourier neural operators. JMLR, 2021. paper

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  3. HyperFNO: Improving the generalization behavior of Fourier neural operators. NIPS, 2022. paper

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  4. Neural operator: Graph kernel network for partial Differential equations. arXiv, 2020. paper

    Zongyi Li, Nikola Kovachki, Kamyar Azizzadenesheli, Burigede Liu, Kaushik Bhattacharya, Andrew Stuart, and Anima Anandkumar.

  5. Fourier neural operator with learned deformations for PDEs on general geometries. arXiv, 2022. paper

    Zongyi Li, Daniel Zhengyu Huang, Burigede Liu, and Anima Anandkumar.

  6. Multipole graph neural operator for parametric partial differential equations. NIPS, 2020. paper

    Zongyi Li, Nikola Kovachki, Kamyar Azizzadenesheli, Burigede Liu, Kaushik Bhattacharya, Andrew Stuart, and Anima Anandkumar.

  7. Fast sampling of diffusion models via operator learning. ICML, 2023. paper

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  8. Factorized Fourier neural operators. ICLR, 2023. paper

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    Michael Rotman, Amit Dekel, Ran Ilan Ber, Lior Wolf, and Yaron Oz.

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    Haitao Lin, Lirong Wu, Yongjie Xu, Yufei Huang, Siyuan Li, Guojiang Zhao, Stan Z, and Li Cari.

  14. Incremental spectral learning Fourier neural operator. arXiv, 2022. paper

    Jiawei Zhao, Robert Joseph George, Yifei Zhang, Zongyi Li, and Anima Anandkumar.

  15. Fourier continuation for exact derivative computation in physics-informed neural operators. arXiv, 2022. paper

    Haydn Maust, Zongyi Li, Yixuan Wang, Daniel Leibovici, Oscar Bruno, Thomas Hou, and Anima Anandkumar.

  16. Non-equispaced Fourier neural solvers for PDEs. arXiv, 2023. paper

    Haitao Lin, Lirong Wu, Yongjie Xu, Yufei Huang, Siyuan Li, Guojiang Zhao, Stan Z, and Li Cari.

  17. Learning-based solutions to nonlinear hyperbolic PDEs: Empirical insights on generalization errors. arXiv, 2023. paper

    Bilal Thonnam Thodi, Sai Venkata Ramana Ambadipudi, and Saif Eddin Jabari.

  18. Domain agnostic Fourier neural operators. arXiv, 2023. paper

    Ning Liu, Siavash Jafarzadeh, and Yue Yu.

  19. Spherical Fourier neural operators: Learning stable dynamics on the sphere. ICML, 2023. paper

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  20. Group equivariant Fourier neural operators for partial differential equations. ICML, 2023. paper

    Jacob Helwig, Xuan Zhang, Cong Fu, Jerry Kurtin, Stephan Wojtowytsch, and Shuiwang Ji.

  21. Speeding up Fourier neural operators via mixed precision. arXiv, 2023. paper

    Colin White, Renbo Tu, Jean Kossaifi, Gennady Pekhimenko, Kamyar Azizzadenesheli, and Anima Anandkumar.

  22. Geometry-informed neural operator for large-scale 3D PDEs. arXiv, 2023. paper

    Zongyi Li, Nikola Borislavov Kovachki, Chris Choy, Boyi Li, Jean Kossaifi, Shourya Prakash Otta, Mohammad Amin Nabian, Maximilian Stadler, Christian Hundt, Kamyar Azizzadenesheli, and Anima Anandkumar.

  23. Deep equilibrium based neural operators for steady-state PDEs. NIPS, 2023. paper

    Tanya Marwah, Ashwini Pokle, J Zico Kolter, Zachary Chase Lipton, Jianfeng Lu, and Andrej Risteski.

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  25. Approximating numerical flux by Fourier neural operators for the hyperbolic conservation laws. arXiv, 2024. paper

    Taeyoung Kim and Myungjoo Sang.

  26. Invertible Fourier neural operators for tackling both forward and inverse problems. arXiv, 2024. paper

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  28. Learning the boundary-to-domain mapping using lifting product Fourier neural operators for partial differential equations. ICML, 2024. paper

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  29. Accelerating phase field simulations through a hybrid adaptive fourier neural operator with U-net backbone. arXiv, 2024. paper

    Christophe Bonneville, Nathan Bieberdorf, Arun Hegde, Mark Asta, Habib N. Najm, Laurent Capolungo, and Cosmin Safta.

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  1. Message passing neural PDE solvers. ICLR, 2022. paper

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    Yunyang Li, Yusong Wang, Lin Huang, Han Yang, Xinran Wei, Jia Zhang, Tong Wang, Zun Wang, Bin Shao, and Tieyan Liu.

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    Federico Pichi, Beatriz Moya, and Jan S. Hesthaven.

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    Amit Roy, Juan Shu, Jia Li, Carl Yang, Olivier Elshocht, Jeroen Smeets, and Pan Li.

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    Sung Woong Cho, Jae Yong Lee, and Hyung Ju Hwang.

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  46. Spectral-refiner: Fine-tuning of accurate spatiotemporal neural operator for turbulent flows. arXiv, 2024. paper

    Shuhao Cao, Francesco Brarda, Ruipeng Li, and Yuanzhe Xi.

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    Yoeri Poels, Koen Minartz, Harshit Bansal, and Vlado Menkovski.

  1. Learning Green's functions associated with time-dependent partial differential equations. JMLR, 2022. paper

    Nicolas Boullé, Seick Kim, Tianyi Shi, and Alex Townsend.

  2. BI-GreenNet: Learning Green's functions by boundary integral network. arXiv, 2022. paper

    Guochang Lin, Fukai Chen, Pipi Hu, Xiang Chen, Junqing Chen, Jun Wang, and Zuoqiang Shi.

  3. DeepGreen: Deep learning of Green’s functions for nonlinear boundary value problems. Scientific Reports, 2021. paper

    Craig R. Gin, Daniel E. Shea, Steven L. Brunton, and J. Nathan Kutz.

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  6. Principled interpolation of Green's functions learned from data. arXiv, 2022. paper

    Harshwardhan Praveen, Nicolas Boulle, and Christopher Earls.

  7. Deep generalized Green's functions. arXiv, 2023. paper

    Rixi Peng, Juncheng Dong, Jordan Malof, Willie J. Padilla, Vahid Tarokh.

  8. Operator approximation of the wave equation based on deep learning of Green’s function. arXiv, 2023. paper

    Ziad Aldirany, R´egis Cottereau, Marc Laforest, and Serge Prudhomme.

  9. Deep surrogate model for learning Green's function associated with linear reaction-diffusion operator. arXiv, 2023. paper

    Junqing Ji, Lili Ju, and Xiaoping Zhang.

  10. Numerical solutions of boundary problems in partial differential equations: A deep learning framework with Green's function. JCP, 2024. paper

    Yuanjun Dai, Zhi Li, Yiran An, and Wanru Deng.

  1. Composing partial differential equations with physics-aware neural networks. ICML, 2022. paper

    Matthias Karlbauer, Timothy Praditia, Sebastian Otte, Sergey Oladyshkin, and Wolfgang Nowak.

  2. Learning the dynamics of physical systems from sparse observations with finite element networks. ICLR, 2022. paper

    Marten Lienen and Stephan Günnemann.

  3. A unified hard-constraint framework for solving geometrically complex PDEs. NIPS, 2022. paper

    Songming Liu, Zhongkai Hao, Chengyang Ying, Hang Su, Jun Zhu, and Ze Cheng.

  4. LSH-SMILE: Locality sensitive Hashing accelerated simulation and learning. NIPS, 2021. paper

    Chonghao Sima and Yexiang Xue.

  5. Amortized finite element analysis for fast PDE-constrained optimization. ICML, 2020. paper

    Tianju Xue, Alex Beatson, Sigrid Adriaenssens, and Ryan Adams.

  6. Learning neural PDE solvers with convergence guarantees. ICLR, 2019. paper

    Jun-Ting Hsieh, Shengjia Zhao, Stephan Eismann, Lucia Mirabella, and Stefano Ermon.

  7. Hybrid finite difference with the physics-informed neural network for solving PDE in complex geometries. arXiv, 2022. paper

    Zixue Xiang, Wei Peng, Weien Zhou, and Wen Yao.

  8. Multilayer perceptron-based surrogate models for finite element analysis. arXiv, 2022. paper

    Lawson Oliveira Lima, Julien Rosenberger, Esteban Antier, and Frederic Magoules.

  9. Integration of physics-informed operator learning and finite element method for parametric learning of partial differential equations. arXiv, 2024. paper

    Shahed Rezaei, Ahmad Moeineddin, Michael Kaliske, and Markus Apel.

  10. Error assessment of an adaptive finite elements—neural networks method for an elliptic parametric PDE. CMAME, 2024. paper

    Alexandre Caboussat, Maude Girardin, and Marco Picasso.

  11. Predicting unsteady incompressible fluid dynamics with finite volume informed neural network. Physics of Fluids, 2024. paper

    Tianyu Li, Shufan Zou, Xinghua Chang, Laiping Zhang, and Xiaogang Deng.

  12. Unified finite-volume physics informed neural networks to solve the heterogeneous partial differential equations. KBS, 2024. paper

    Di Mei, Kangcheng Zhou, and Chun-Ho Liu.

  1. PDE-Net: Learning PDEs from data. ICML, 2018. paper

    Zichao Long, Yiping Lu, Xianzhong Ma, and Bin Dong.

  2. PDE-Net 2.0: Learning PDEs from data with a numeric-symbolic hybrid deep network. JCP, 2019. paper

    Zichao Long, Yiping Lu, and Bin Dong.

  3. Physics-informed CNNs for super-resolution of sparse observations on dynamical systems. NIPS, 2022. paper

    Daniel Kelshaw, Georgios Rigas, and Luca Magri.

  4. Deep-pretrained-FWI: Combining supervised learning with physics-informed neural network. NIPS, 2022. paper

    Ana Paula O. Muller, Clecio R. Bom, Jessé C. Costa, Matheus Klatt, Elisângela L. Faria, Marcelo P. de Albuquerque, and Márcio P. de Albuquerque.

  5. Learning time-dependent PDEs with a linear and nonlinear separate convolutional neural network. JCP, 2022. paper

    Jiagang Qu, Weihua Cai, and YijunZhao.

  6. PhyCRNet: Physics-informed convolutional-recurrent network for solving spatiotemporal PDEs. JCP, 2022. paper

    Pu Ren, Chengping Rao, Yang Liu, Jianxun Wang, and Hao Sun.

  7. Spline-PINN: Approaching PDEs without data using fast, physics-informed Hermite-Spline CNNs. AAAI, 2019. paper

    Nils Wandel, Michael Weinmann, Michael Neidlin, and Reinhard Klein.

  8. Deep convolutional Ritz method: Parametric PDE surrogates without labeled data. arXiv, 2022. paper

    Jan Niklas Fuhg, Arnav Karmarkar, Teeratorn Kadeethum, Hongkyu Yoon, and Nikolaos Bouklas.

  9. Deep convolutional architectures for extrapolative forecasts in time-dependent flow problems. arXiv, 2022. paper

    Pratyush Bhatt, Yash Kumar, and Azzeddine Soulaimani.

  10. Phase2Vec: Dynamical systems embedding with a physics-informed convolutional network. arXiv, 2022. paper

    Matthew Ricci, Noa Moriel, Zoe Piran, and Mor Nitzan.

  11. Numerical approximation based on deep convolutional neural network for high-dimensional fully nonlinear merged PDEs and 2BSDEs. arXiv, 2022. paper

    Xu Xiao and Wenlin Qiu.

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    Matthias Fey, Jan Eric Lenssen, Frank Weichert, and Heinrich Muller.

  13. Physics-informed deep super-resolution for spatiotemporal data. arXiv, 2022. paper

    Pu Ren, Chengping Rao, Yang Liu, Zihan Ma, Qi Wang, Jianxun Wang, and Hao Sun.

  14. MeshFreeFLowNet: A physics-constrained deep continuous space-time super-resolution framework. SC20, 2020. paper

    Chiyu Max Jiang, Soheil Esmaeilzadeh, Kamyar Azizzadenesheli, Karthik Kashinath, Mustafa Mustafa, Hamdi A. Tchelepi, Philip Marcus Prabhat, and Anima Anandkumar.

  15. Convolutional neural operators. arXiv, 2023. paper

    Bogdan Raonić, Roberto Molinaro, Tobias Rohner, Siddhartha Mishra, and Emmanuel de Bezenac.

  16. An unsupervised latent/output physics-informed convolutional-LSTM network for solving partial differential equations using peridynamic differential operator. CMAME, 2023. paper

    Arda Mavi, Ali Can Bekar, Ehsan Haghigh, and Erdogan Madenci.

  17. Clifford neural layers for PDE modeling. ICLR, 2023. paper

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  18. Neural partial differential equations with functional convolution. arXiv, 2023. paper

    Ziqian Wu, Xingzhe He, Yijun Li, Cheng Yang, Rui Liu, Shiying Xiong, and Bo Zhu.

  19. Multilevel CNNs for parametric PDEs. arXiv, 2023. paper

    Cosmas Heiß, Ingo Gühring, and Martin Eigel.

  20. Encoding physics to learn reaction–diffusion processes. NMI, 2023. paper

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  21. PhySR: Physics-informed deep super-resolution for spatiotemporal data. JCP, 2023. paper

    Pu Ren, Chengping Rao, Yang Liu, Zihan Ma, Qi Wang, Jianxun Wang, and Hao Sun.

  22. Local convolution enhanced global Fourier neural operator for multiscale dynamic spaces prediction. arXiv, 2023. paper

    Xuanle Zhao, Yue Sun, Tielin Zhang, and Bo Xu.

  23. A practical existence theorem for reduced order models based on convolutional autoencoders. arXiv, 2024. paper

    Nicola Rares Franco and Simone Brugiapaglia.

  24. Closure discovery for coarse-grained partial differential equations using multi-agent reinforcement learning. arXiv, 2024. paper

    Jan-Philipp von Bassewitz, Sebastian Kaltenbach, and Petros Koumoutsakos.

  25. PARCv2: Physics-aware recurrent convolutional neural networks for spatiotemporal dynamics modeling. arXiv, 2024. paper

    Phong C.H. Nguyen, Xinlun Cheng, Shahab Arfaza, Pradeep Seshadri, Yen T. Nguyen, Munho Kim, Sanghun Choi, H.S. Udaykumar, and Stephen Baek.

  26. Neural operators with localized integral and differential kernels. arXiv, 2024. paper

    Miguel Liu-Schiaffini, Julius Berner, Boris Bonev, Thorsten Kurth, Kamyar Azizzadenesheli, and Anima Anandkumar.

  27. PDE-CNNs: Axiomatic derivations and applications. arXiv, 2024. paper

    Gijs Bellaard, Sei Sakata, Bart M. N. Smets, and Remco Duits.

  28. Symmetric basis convolutions for learning Lagrangian fluid mechanics. ICLR, 2024. paper

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  29. Fully differentiable Lagrangian convolutional neural network for continuity-consistent physics-informed precipitation nowcasting. arXiv, 2024. paper

    Peter Pavlík, Martin Výboh, Anna Bou Ezzeddine, and Viera Rozinajová.

  30. Theory guided Lagrange programming neural network for subsurface flow problems. EAAI, 2024. paper

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  17. Render unto numerics: Orthogonal polynomial neural operator for PDEs with non-periodic boundary conditions. arXiv, 2022. paper

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  22. Taming score-based diffusion priors for infinite-dimensional nonlinear inverse problems. arXiv, 2024. paper

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  1. Neural rough differential equations for long time series. ICML, 2021. paper

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  2. LEADS: Learning dynamical systems that generalize across environments. NIPS, 2021. paper

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  18. Neural signature kernels as infinite-width-depth-limits of controlled ResNets. ICML, 2023. paper

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  22. Elucidating the solution space of extended reverse-time SDE for diffusion models. arXiv, 2023. paper

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  23. ODE-based recurrent model-free reinforcement learning for POMDPs. arXiv, 2023. paper

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  24. A spectral approach for learning spatiotemporal neural differential equations. arXiv, 2023. paper

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  25. Invariant physics-informed neural networks for ordinary differential equations. arXiv, 2023. paper

    Shivam Arora, Alex Bihlo, and Francis Valiquette.

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  30. From Fourier to neural ODEs: Flow matching for modeling complex systems. ICML, 2024. paper

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  1. Prompting in-context operator learning with sensor data, equations, and natural language. arXiv, 2023. paper

    Liu Yang, Tingwei Meng, Siting Liu, and Stanley J. Osher.

  2. CrunchGPT: A chatGPT assisted framework for scientific machine learning. Journal of Machine Learning for Modeling and Computing, 2023. paper

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  3. Data-efficient operator learning via unsupervised pretraining and in-context learning. arXiv, 2024. paper

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  4. UPS: Towards foundation models for PDE solving via cross-modal adaptation. arXiv, 2024. paper

    Junhong Shen, Tanya Marwah, and Ameet Talwalkar.

  5. Towards a foundation model for partial differential equation: Multi-operator learning and extrapolation. arXiv, 2024. paper

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  6. Poseidon: Efficient foundation models for PDEs. arXiv, 2024. paper

    Maximilian Herde, Bogdan Raonić, Tobias Rohner, Roger Käppeli, Roberto Molinaro, Emmanuel de Bézenac, and Siddhartha Mishra.

  7. PStrategies for pretraining neural operators. arXiv, 2024. paper

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  1. PDEBench: An extensive benchmark for scientific machine learning. NIPS, 2022. paper

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  10. BubbleML: A multi-physics dataset and benchmarks for machine learning. arXiv, 2023. paper

    Sheikh Md Shakeel Hassan, Arthur Feeney, Akash Dhruv, Jihoon Kim, Youngjoon Suh, Jaiyoung Ryu, Yoonjin Won, and Aparna Chandramowlishwaran.

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  12. Zero coordinate shift: Whetted automatic differentiation for physics-informed operator learning. arXiv, 2023. paper

    Kuangdai Leng, Mallikarjun Shankar, and Jeyan Thiyagalingam.

  13. CFDBench: A comprehensive benchmark for machine learning methods in fluid dynamics. arXiv, 2023. paper

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    Valentin Duruisseaux and Amit Chakraborty.

  15. ClimSim: A large multi-scale dataset for hybrid physics-ML climate emulation. NIPS, 2023. paper

    Busecke, Nora Loose, Charles I Stern, Tom Beucler, Bryce Harrop, Benjamin R Hillman, Andrea Jenney, Savannah Ferretti, Nana Liu, Anima Anandkumar, Noah D Brenowitz, Veronika Eyring, Nicholas Geneva, Pierre Gentine, Stephan Mandt, Jaideep Pathak, Akshay Subramaniam, Carl Vondrick, Rose Yu, Laure Zanna, Tian Zheng, Ryan Abernathey, Fiaz Ahmed, David C Bader, Pierre Baldi, Elizabeth Barnes, Christopher Bretherton, Peter Caldwell, Wayne Chuang, Yilun Han, Yu Huang, Fernando Iglesias-Suarez, Sanket Jantre, Karthik Kashinath, Marat Khairoutdinov, Thorsten Kurth, Nicholas Lutsko, Po-Lun Ma, Griffin Mooers, J. David Neelin, David Randall, Sara Shamekh, Mark A Taylor, Nathan Urban, Janni Yuval, Guang Zhang, and Michael Pritchard.

  16. Benchmarking the robustness of neural network-based partial differential equation solvers. ICCAD, 2023. paper

    Jiaqi Gu, Mohit Dighamber, Zhengqi Gao, and Duane S. Boning.

  17. Physics-informed neural networks for advanced modeling. Journal of Open Source Software, 2024. paper/Github

    Dario Coscia, Anna Ivagnes, Nicola Demo, and Gianluigi Rozza.

  18. A novel A.I enhanced reservoir characterization with a combined mixture of experts -- NVIDIA modulus based physics informed neural operator forward model. arXiv, 2024. paper

    Clement Etienam, Yang Juntao, Issam Said, Oleg Ovcharenko, Kaustubh Tangsali, Pavel Dimitrov, and Ken Hester.

  19. An advanced physics-informed neural operator for comprehensive design optimization of highly-nonlinear systems: An aerospace composites processing case study. ICML, 2024. paper

    Milad Ramezankhani, Anirudh Deodhar, Rishi Yash Parekh, and Dagnachew Birru.

  1. Characterizing possible failure modes in physics-informed neural networks. NIPS, 2021. paper

    Aditi Krishnapriyan, Amir Gholami, Shandian Zhe, Robert Kirby, and Michael W. Mahoney.

  2. Understanding and mitigating gradient flow pathologies in physics-informed neural networks. SIAM Journal on Scientific Computing, 2021. paper

    Sifan Wang, Yujun Teng, and Paris Perdikaris.

  3. When and why PINNs fail to train: A neural tangent kernel perspective. JCP, 2022. paper

    SifanWang, XinlingYu, and Paris Perdikaris.

  4. When do extended physics-informed neural networks (XPINNs) improve generalization? SIAM Journal on Scientific Computing, 2022. paper

    Zheyuan Hu, Ameya D. Jagtap, George Em Karniadakis, and Kenji Kawaguchi.

  5. MARS: A method for the adaptive removal of stiffness in PDEs. JCP, 2022. paper

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  6. Learning similarity metrics for numerical simulations. ICML, 2020. paper

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  7. A curriculum-training-based strategy for distributing collocation points during physics-informed neural network training. NIPS, 2021. paper

    Marcus Münzer and Chris Bard.

  8. Parametric complexity bounds for approximating PDEs with neural networks. NIPS, 2021. paper

    Tanya Marwah, Zachary Lipton, and Andrej Risteski.

  9. Respecting causality for training physics-informed neural networks. CMAME, 2024. paper

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  10. CP-PINNS: Changepoints detection in PDEs using physics informed neural networks with total-variation penalty. arXiv, 2022. paper

    Zhikang Dong and Pawel Polak.

  11. Stochastic projection based approach for gradient free physics informed learning. arXiv, 2022. paper

    Navaneeth N and Souvik Chakraborty.

  12. Understanding the difficulty of training physics-informed neural networks on dynamical systems. arXiv, 2022. paper

    Franz M. Rohrhofer, Stefan Posch, Clemens Gößnitzer, and Bernhard C. Geiger.

  13. Mitigating learning complexity in physics and equality constrained artificial neural networks. arXiv, 2022. paper

    Victor Churchill and Dongbin Xiu.

  14. Improved training of physics-informed neural networks with model ensembles. arXiv, 2022. paper

    Katsiaryna Haitsiukevich and Alexander Ilin.

  15. The cost-accuracy trade-off in operator learning with neural networks. arXiv, 2022. paper

    Maarten V. de Hoop, Daniel Zhengyu Huang, Elizabeth Qian, and Andrew M. Stuart.

  16. Separable PINN: Mitigating the curse of dimensionality in physics-informed neural networks. NIPS, 2022. paper

    Junwoo Cho, Seungtae Nam, Hyunmo Yang, Seok-Bae Yun, Youngjoon Hong, and Eunbyung Park.

  17. A curriculum-training-based strategy for distributing collocation points during physics-informed neural network training. NIPS, 2022. paper

    Marcus Münzer and Chris Bard.

  18. Robustness of physics-informed neural networks to noise in sensor data. arXiv, 2022. paper

    Jian Cheng Wong, Pao-Hsiung Chiu, Chin Chun Ooi, and My Ha Da.

  19. Investigations on convergence behaviour of physics informed neural networks across spectral ranges and derivative orders. arXiv, 2023. paper

    Mayank Deshpande, Siddharth Agarwal, Vukka Snigdha, and Arya Kumar Bhattacharya.

  20. Stochastic projection based approach for gradient free physics informed learning. CMAME, 2023. paper

    Navaneeth N. and Souvik Chakraborty.

  21. Temporal consistency loss for physics-informed neural networks. arXiv, 2023. paper

    Sukirt Thakur, Maziar Raissi, Harsa Mitra, and Arezoo Ardekani.

  22. Can physics-informed neural networks beat the finite element method? arXiv, 2023. paper

    Tamara G. Grossmann, Urszula Julia Komorowska, Jonas Latz, and Carola-Bibiane Schönlieb.

  23. LSA-PINN: Linear boundary connectivity loss for solving PDEs on complex geometry. arXiv, 2023. paper

    Jian Cheng Wong, Pao-Hsiung Chiu, Chinchun Ooi, and My Ha Dao, and Yew-Soon Ong.

  24. On the Hyperparameters influencing a PINN’s generalization beyond the training domain. arXiv, 2023. paper

    Andrea Bonfanti, Roberto Santana, Marco Ellero, and Babak Gholami.

  25. DPM: A novel training method for physics-informed neural networks in extrapolation. AAAI, 2021. paper

    Jungeun Kim, Kookjin Lee, Dongeun Lee, Sheo Yon Jhin, and Noseong Park.

  26. Guiding continuous operator learning through physics-based boundary constraints. ICLR, 2023. paper

    Nadim Saad, Gaurav Gupta, Shima Alizadeh, and Danielle C. Maddix.

  27. Probing optimisation in physics-informed neural networks. ICLR, 2023. paper

    Nayara Fonseca, Veronica Guidetti, and Will Trojak.

  28. Nearly optimal VC-dimension and Pseudo-dimension bounds for deep neural network derivatives. arXiv, 2023. paper

    Yahong Yang, Haizhao Yang, and Yang Xiang.

  29. PDE+: Enhancing generalization via PDE with adaptive distributional diffusion. arXiv, 2023. paper

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  24. HyperLoRA for PDEs. arXiv, 2023. paper

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  5. Self-scalable Tanh (Stan): Faster convergence and better generalization in physics-informed neural networks. arXiv, 2022. paper

    Raghav Gnanasambandam, Bo Shen, Jihoon Chung, Xubo Yue, and Zhenyu (James) Kong.

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    Chuwei Wang, Shanda Li, Di He, and Liwei Wang.

  7. Loss landscape engineering via data regulation on PINNs. arXiv, 2022. paper

    Vignesh Gopakumar, Stanislas Pamela, and Debasmita Samaddar.

  8. Implicit stochastic gradient descent for training physics-informed neural networks. AAAI, 2023. paper

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  10. Fourier-MIONet: Fourier-enhanced multiple-input neural operators for multiphase modeling of geological carbon sequestration. arXiv, 2023. paper

    Zhongyi Jiang, Min Zhu, Dongzhuo Li, Qiuzi Li, Yanhua O. Yuan, and Lu Lu.

  11. Learning from integral losses in physics informed neural networks. arXiv, 2023. paper

    Ehsan Saleh, Saba Ghaffari, Timothy Bretl, Luke Olson, and Matthew West.

  12. A symmetry group based supervised learning method for solving partial differential equations. CMAME, 2023. paper

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  13. Loss jump during loss switch in solving PDEs with neural networks. arXiv, 2024. paper

    Zhiwei Wang, Lulu Zhang, Zhongwang Zhang, and Zhi-Qin John Xu.

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  15. Kronecker-factored approximate curvature for physics-informed neural networks. arXiv, 2024. paper

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  16. Astral: Training physics-informed neural networks with error majorants. arXiv, 2024. paper

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  17. Physics-Informed Parallel Neural Networks with self-adaptive loss weighting for the identification of continuous structural systems. CMAME, 2024. paper

    Rui Zhang, Gordon P. Warn, and Aleksandra Radlińska.

  18. A practical PINN framework for multi-scale problems with multi-magnitude loss terms. CMAME, 2024. paper

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  19. Neural operators meet conjugate gradients: The FCG-NO method for efficient PDE solving. ICML, 2024. paper

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  20. Neuroscience inspired neural operator for partilial differential equations. JCP, 2024. paper

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  1. ADLGM: An efficient adaptive sampling deep learning Galerkin method. JCP, 2023. paper

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  2. DMIS: Dynamic mesh-based importance sampling for training physics-informed neural networks. AAAI, 2023. paper

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  3. A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks. CMAME, 2023. paper

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  4. Mitigating propagation failures in PINNs using evolutionary sampling. arXiv, 2022. paper

    Arka Daw, Jie Bu, Sifan Wang, Paris Perdikaris, and Anuj Karpatne.

  5. Residual-quantile adjustment for adaptive training of physics-informed neural network. arXiv, 2022. paper

    Jiayue Han, Zhiqiang Cai, Zhiyou Wu, and Xiang Zhou.

  6. Adversarial sampling for solving differential equations with neural networks. NIPS, 2021. paper

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  7. A novel adaptive causal sampling method for physics-informed neural networks. arXiv, 2022. paper

    Jia Guo, Haifeng Wang, and Chenping Hou.

  8. Physics-informed neural networks with residual/gradient-based adaptive sampling methods for solving PDEs with sharp solutions. arXiv, 2023. paper

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  9. Active learning based sampling for high-dimensional nonlinear partial differential equations. JCP, 2023. paper

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  10. Adversarial adaptive sampling: Unify PINN and optimal yransport for the approximation of PDEs. ICLR, 2024. paper

    Kejun Tang, Jiayu Zhai, Xiaoliang Wan, and Chao Yang.

  11. Coupling parameter and particle dynamics for adaptive sampling in neural Galerkin schemes. arXiv, 2023. paper

    Yuxiao Wen, Eric Vanden-Eijnden, and Benjamin Peherstorfer.

  12. Mitigating propagation failures in physics-informed neural networks using retain-resample-release (R3) sampling. ICML, 2023. paper

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  13. Good lattice training: Physics-informed neural networks accelerated by number theory. arXiv, 2023. paper

    Takashi Matsubara and Takaharu Yaguchi.

  14. Adaptive importance sampling for Deep Ritz. arXiv, 2023. paper

    Xiaoliang Wan, Tao Zhou, and Yuancheng Zhou.

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    Kejun Tang, Jiayu Zhai, Xiaoliang Wan, and Chao Yang.

  16. DAS-PINNs: A deep adaptive sampling method for solving high-dimensional partial differential equations. JCP, 2023. paper

    Kejun Tang, Xiaoliang Wan, and Chao Yang.

  17. Deep adaptive sampling for surrogate modeling without labeled data. arXiv, 2024. paper

    Xili Wang, Kejun Tang, Jiayu Zhai, Xiaoliang Wan, and Chao Yang.

  18. Physics-informed neural networks for sampling. ICLR, 2024. paper

    Jingtong Sun, Julius Berner, Kamyar Azizzadenesheli, and Anima Anandkumar.

  19. PINNACLE: PINN adaptive collocation and experimental points selection. ICLR, 2024. paper

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  20. Annealed adaptive importance sampling method in PINNs for solving high dimensional partial differential equations. arXiv, 2024. paper

    Zhengqi Zhang, Jing Li, and Bin Liu.

  21. Solving partial differential equations with sampled neural networks. arXiv, 2024. paper

    Chinmay Datar, Taniya Kapoor, Abhishek Chandra, Qing Sun, Iryna Burak, Erik Lien Bolager, Anna Veselovska, Massimo Fornasier, and Felix Dietrich.

  22. A Gaussian mixture distribution-based adaptive sampling method for physics-informed neural networks. EAAI, 2024. paper

    Yuling Jiao, Di Li, Xiliang Lu, Jerry Zhijian Yang, and Cheng Yuan.

  23. Dynamical measure transport and neural PDE solvers for sampling. arXiv, 2024. paper

    Jingtong Sun, Julius Berner, Lorenz Richter, Marius Zeinhofer, Johannes Müller, Kamyar Azizzadenesheli, and Anima Anandkumar.

  1. MeshingNet: A new mesh generation method based on deep learning. ICCS, 2022. paper

    Zheyan Zhang, Yongxing Wang, Peter K. Jimack, and He Wang.

  2. M2N: Mesh movement networks for PDE solvers. arXiv, 2022. paper

    Wenbin Song, Mingrui Zhang, Joseph G. Wallwork, Junpeng Gao, Zheng Tian, Fanglei Sun, Matthew D. Piggott, Junqing Chen, Zuoqiang Shi, Xiang Chen, and Jun Wang.

  3. RANG: A residual-based adaptive node generation method for physics-informed neural networks. arXiv, 2022. paper

    Wei Peng, Weien Zhou, Xiaoya Zhang, Wen Yao, and Zheliang Liu.

  4. Learning a mesh motion technique with application to fluid-structure interaction and shape optimization. arXiv, 2022. paper

    Johannes Haubne and Miroslav Kuchta.

  5. Accelerated training of physics-informed neural networks (PINNs) using meshless discretizations. arXiv, 2022. paper

    Ramansh Sharma and Varun Shankar.

  6. An improved structured mesh generation method based on physics-informed neural networks. arXiv, 2022. paper

    Xinhai Chen, Jie Liu, Junjun Yan, Zhichao Wang, and Chunye Gong.

  7. Mesh-free Eulerian physics-informed neural networks. arXiv, 2022. paper

    Fabricio Arend Torres, Marcello Massimo Negri, Monika Nagy-Huber, Maxim Samarin, and Volker Roth.

  8. Fixed-budget online adaptive mesh learning for physics-informed neural networks. Towards parameterized problem inference. arXiv, 2022. paper

    Thi Nguyen Khoa Nguyen, Thibault Dairay, Raphaël Meunier, Christophe Millet, and Mathilde Mougeot.

  9. Learning controllable adaptive simulation for multi-resolution physics. ICLR, 2023. paper

    Tailin Wu, Takashi Maruyama, Qingqing Zhao, Gordon Wetzstein, and Jure Leskovec.

  10. A closest point method for surface PDEs with interior boundary conditions for geometry processing. arXiv, 2023. paper

    Nathan King, Haozhe Su, Mridul Aanjaneya, Steven Ruuth, and Christopher Batty.

  11. Efficient training of physics-informed neural networks with direct grid refinement algorithm. arXiv, 2023. paper

    Shikhar Nilabh and Fidel Grandia.

  12. Redefining Super-Resolution: Fine-mesh PDE predictions without classical simulations. arXiv, 2023. paper

    Rajat Kumar Sarkar, Ritam Majumdar, Vishal Jadhav, Sagar Srinivas Sakhinana, and Venkataramana Runkana.

  13. MMPDE-Net and moving sampling physics-informed neural networks based on moving mesh method. arXiv, 2023. paper

    Yu Yang, Qihong Yang, Yangtao Deng, and Qiaolin He.

  14. Reinforcement learning for adaptive mesh refinement. AISTATS, 2023. paper

    Jiachen Yang, Tarik Dzanic, Brenden Petersen, Jun Kudo, Ketan Mittal, Vladimir Tomov, Jean-Sylvain Camier, Tuo Zhao, Hongyuan Zha, Tzanio Kolev, Robert Anderson, and Daniel Faissol.

  15. Multiscale graph neural networks with adaptive mesh refinement for accelerating mesh-based simulations. arXiv, 2024. paper

    Roberto Perera and Vinamra Agrawal.

  16. Learning mesh motion techniques with application to fluid–structure interaction. CMAME, 2024. paper

    Johannes Haubner, Ottar Hellan, Marius Zeinhofer, and Miroslav Kuchta.

  17. Learning time-dependent PDE via graph neural networks and deep operator network for robust accuracy on irregular grids. arXiv, 2024. paper

    Sung Woong Cho, Jae Yong Lee, and Hyung Ju Hwang.

  18. Physics-informed mesh-independent deep compositional operator network. arXiv, 2024. paper

    Weiheng Zhong and Hadi Meidani.

  19. End-to-end mesh optimization of a hybrid deep learning black-box PDE solver. arXiv, 2024. paper

    Shaocong Ma, James Diffenderfer, Bhavya Kailkhura, and Yi Zhou.

  20. RoPINN: Region optimized physics-informed neural networks. arXiv, 2024. paper

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  1. Composing partial differential equations with physics-aware neural networks. ICLR, 2022. paper

    Matthias Karlbauer, Timothy Praditia, Sebastian Otte, Sergey Oladyshkin, Wolfgang Nowak, and Martin V. Butz.

  2. Learning composable energy surrogates for PDE order reduction. NIPS, 2020. paper

    Alex Beatson, Jordan T. Ash, Geoffrey Roeder, Tianju Xue, and Ryan P. Adams.

  3. Neural basis functions for accelerating solutions to high mach euler equations. ICML, 2022. paper

    David Witman, Alexander New, Hicham Alkandry, and Honest Mrema.

  4. PFNN-2: A domain decomposed penalty-free neural network method for solving partial differential equations. arXiv, 2022. paper

    Hailong Shen and Chao Yang.

  5. Finite basis physics-informed neural networks (FBPINNs): A scalable domain decomposition approach for solving differential equations. arXiv, 2021. paper

    Ben Moseley, Andrew Markham, and Tarje Nissen-Meyer.

  6. Finite basis physics-informed neural networks as a Schwarz domain decomposition method. arXiv, 2022. paper

    Victorita Dolean, Alexander Heinlein, Siddhartha Mishra, and Ben Moseley.

  7. NeuralStagger: Accelerating physics constrained neural PDE solver with spatial-temporal decomposition. ICML, 2023. paper

    Xinquan Huang, Wenlei Shi, Qi Meng, Yue Wang, Xiaotian Gao, Jia Zhang, and Tieyan Liu.

  8. Augmenting physical models with deep networksfor complex dynamics forecasting. Journal of Statistical Mechanics: Theory and Experiment, 2021. paper

    Yuan Yin, Vincent Le Guen, Jérémie Dona, Emmanuel de Bézenac, Ibrahim Ayed, Nicolas Thome, and Patrick Gallinari.

  9. LordNet: Learning to solve parametric partial differential equations without simulated data. arXiv, 2022. paper

    Wenlei Shi, Xinquan Huang, Xiaotian Gao, Xinran Wei, Jia Zhang, Jiang Bian, Mao Yang, and Tieyan Liu.

  10. An optimisation–based domain–decomposition reduced order model for the incompressible Navier-Stokes equations. arXiv, 2022. paper

    Ivan Prusak, Monica Nonino, Davide Torlo, Francesco Ballarin, and Gianluigi Rozza.

  11. NUNO: A general gramework for learning parametric PDEs with non-uniform data. ICML, 2023. paper

    Songming Liu, Zhongkai Hao, Chengyang Ying, Hang Su, Ze Cheng, and Jun Zhu.

  12. Enhancing training of physics-informed neural networks using domain-decomposition based preconditioning strategies. arXiv, 2023. paper

    Alena Kopaničáková, Hardik Kothari, George Em Karniadakis, and Rolf Krause.

  13. Multilevel domain decomposition-based architectures for physics-informed neural networks. arXiv, 2023. paper

    Victorita Dolean, Alexander Heinlein, Siddhartha Mishra, and Ben Moseley.

  14. Friedrichs' systems discretized with the Discontinuous Galerkin method: Domain decomposable model order reduction and Graph Neural Networks approximating vanishing viscosity solutions. arXiv, 2023. paper

    Francesco Romor, Davide Torlo, and Gianluigi Rozza.

  15. A deep domain decomposition method based on Fourier features. Journal of Computational and Applied Mathematics, 2023. paper

    Sen Li, Yingzhi Xia, Yu Liu, and Qifeng Liao.

  16. A unified scalable framework for causal sweeping strategies for physics-informed neural networks (PINNs) and their temporal decompositions. arXiv, 2023. paper

    Michael Penwarden, Ameya D. Jagtap, Shandian Zhe, George Em Karniadakis, and Robert M. Kirby.

  17. A generalized Schwarz-type non-overlapping domain decomposition method using physics-constrained neural networks. arXiv, 2023. paper

    Shamsulhaq Basir and Inanc Senocak.

  18. Breaking boundaries: Distributed domain decomposition with scalable physics-informed neural PDE solvers. arXiv, 2023. paper

    Arthur Feeney, Zitong Li, Ramin Bostanabad, and Aparna Chandramowlishwaran.

  19. Efficient learning of PDEs via Taylor expansion and sparse decomposition into value and Fourier domains. arXiv, 2023. paper

    Md Nasim and Yexiang Xue.

  20. Adaptive task decomposition physics-informed neural networks. CMAME, 2023. paper

    Jianchuan Yang, Xuanqi Liu, Yu Diao, Xi Chen, and Haikuo Hu.

  21. PF-DMD: Physics-fusion dynamic mode decomposition for accurate and robust forecasting of dynamical systems with imperfect data and physics. arXiv, 2023. paper

    Yuhui Yin, Chenhui Kou, Shengkun Jia, Lu Lu, Xigang Yuan, and Yiqing Luo.

  22. Subspace decomposition based DNN algorithm for elliptic type multi-scale PDEs. JCP, 2023. paper

    Xian Li, Zhiqin John Xu, and Lei Zhang.

  23. Adaptive deep Fourier residual method via overlapping domain decomposition. arXiv, 2024. paper

    Jamie M. Taylor, Manuela Bastidas, Victor M. Calo, and David Pardo.

  1. PDE-driven spatiotemporal disentanglement. ICLR, 2021. paper

    Jérémie Donà, Jean-Yves Franceschi, Sylvain Lamprier, and Patrick Gallinari.

  2. Disentangling physical dynamics from unknown factors for unsupervised video prediction. CVPR, 2020. paper

    Vincent Le Guen and Nicolas Thome.

  1. Solver-in-the-loop: Learning from differentiable physics to interact with iterative PDE-solvers. NIPS, 2020. paper

    Kiwon Um, Robert Brand, Yun (Raymond) Fei, Philipp Holl, and Nils Thuerey.

  2. Lie point symmetry data augmentation for neural PDE solvers. ICML, 2022. paper

    Johannes Brandstetter, Max Welling, and Daniel E. Worrall.

  3. Incorporating symmetry into deep dynamics models for improved generalization. ICLR, 2021. paper

    Rui Wang, Robin Walters, and Rose Yu.

  4. HyperSolvers: Toward fast continuous-depth models. NIPS, 2020. paper

    Michael Poli, Stefano Massaroli, Atsushi Yamashita, Hajime Asama, and Jinkyoo Park.

  5. PIXEL: Physics-informed cell representations for fast and accurate PDE solvers. NIPS, 2022. paper

    Namgyu Kang, Byeonghyeon Lee, Youngjoon Hong, Seok-Bae Yun, and Eunbyung Park.

  6. NeuralSim: Augmenting differentiable simulators with neural networks. ICRA, 2021. paper

    Eric Heiden, David Millard, Erwin Coumans, Yizhou Sheng, and Gaurav S. Sukhatme.

  7. DPM: A deep learning PDE augmentation method with application to large-eddy simulation. JCP, 2020. paper

    Justin Sirignano, Jonathan F.MacArt, and Jonathan B.Freund.

  8. General covariance data augmentation for neural PDE solvers. ICML, 2023. paper

    Vladimir Fanaskov, Tianchi Yu, Alexander Rudikov, and Ivan Oseledets.

  9. Learning preconditioners for conjugate gradient PDE solvers. ICML, 2023. paper

    Yichen Li, Peter Yichen Chen, Tao Du, and Wojciech Matusik.

  10. Autoregressive Renaissance in neural PDE solvers. ICLR, 2023. paper

    Yolanne Yi Ran Lee.

  11. Stability of implicit neural networks for long-term forecasting in dynamical systems. ICLR, 2023. paper

    Leon Migus, Julien Salomon, and Patrick Gallinari.

  12. Training deep surrogate models with large scale online learning. ICML, 2023. paper

    Lucas Meyer, Marc Schouler, Robert A. Caulk, Alejandro Ribes, and Bruno Raffin.

  13. Self-supervised learning with Lie symmetries for partial differential equations. arXiv, 2023. paper

    Grégoire Mialon, Quentin Garrido, Hannah Lawrence, Danyal Rehman, Yann LeCun, and Bobak T. Kiani.

  14. Interpretable neural PDE solvers using symbolic frameworks. arXiv, 2023. paper

    Yolanne Yi Ran Lee.

  15. Modeling accurate long rollouts with temporal neural PDE solvers. ICML, 2023. paper

    Phillip Lippe, Bastiaan S. Veeling, Paris Perdikaris, Richard E. Turner, and Johannes Brandstetter.

  16. Neural-integrated meshfree (NIM) method: A differentiable programming-based hybrid solver for computational mechanics. arXiv, 2023. paper

    Honghui Du and Qizhi He.

  17. A deep-genetic algorithm (deep-GA) approach for high-dimensional nonlinear parabolic partial differential equations. Computers & Mathematics with Applications, 2023. paper

    Endah R.M. Putri, Muhammad L. Shahab, Mohammad Iqbal, Imam Mukhlash, Amirul Hakam, Lutfi Mardianto, and Hadi Susanto.

  18. Physics-enhanced deep surrogates for partial differential equations. NMI, 2023. paper

    Raphaël Pestourie, Youssef Mroueh, Chris Rackauckas, Payel Das, and Steven G. Johnson.

  19. Better neural PDE solvers through data-free mesh movers. ICLR, 2024. paper

    Peiyan Hu, Yue Wang, and Zhiming Ma.

  20. Generating synthetic data for neural operators. arXiv, 2024. paper

    Erisa Hasani and Rachel A. Ward.

  21. A deep branching solver for fully nonlinear partial differential equations. JCP, 2024. paper

    Jiang Yu Nguwi, Guillaume Penent, and Nicolas Privault.

  22. Accelerating data generation for neural operators via Krylov subspace recycling. ICLR, 2024. paper

    Hong Wang, Zhongkai Hao, Jie Wang, Zijie Geng, Zhen Wang, Bin Li, and Feng Wu.

  23. Space and time continuous physics simulation from partial observations. ICLR, 2024. paper

    Janny Steeven, Nadri Madiha, Digne Julie, and Wolf Christian.

  24. Speeding up and reducing memory usage for scientific machine learning via mixed precision. arXiv, 2024. paper

    Joel Hayford, Jacob Goldman-Wetzler, Eric Wang, and Lu Lu.

  25. Neural operators meet conjugate gradients: The FCG-NO method for efficient PDE solving. arXiv, 2024. paper

    Alexander Rudikov, Vladimir Fanaskov, Ekaterina Muravleva, Yuri M. Laevsky, and Ivan Oseledets.

  26. Learning operators with stochastic gradient descent in general Hilbert spaces. arXiv, 2024. paper

    Lei Shi and Jiaqi Yang.

  27. Accelerating PDE data generation via differential operator action in solution space. ICML, 2024. paper

    Huanshuo Dong, Hong Wang, Haoyang Liu, Jian Luo, and Jie Wang.

  28. Correctness verification of neural networks approximating differential equations. arXiv, 2024. paper

    Petros Ellinas, Rahul Nellikath, Ignasi Ventura, Jochen Stiasny, and Spyros Chatzivasileiadis.

  29. DOF: Accelerating high-order differential operators with forward propagation. arXiv, 2024. paper

    Ruichen Li, Chuwei Wang, Haotian Ye, Di He, and Liwei Wang.

  30. Sobolev training for operator learning. arXiv, 2024. paper

    Namkyeong Cho, Junseung Ryu, and Hyung Ju Hwang.

  31. Scaling physics-informed hard constraints with mixture-of-experts. ICLR, 2024. paper

    Nithin Chalapathi, Yiheng Du, and Aditi Krishnapriyan.

  32. Learning semilinear neural operators: A unified recursive framework for prediction and data assimilation. ICLR, 2024. paper

    Ashutosh Singh, Ricardo Augusto Borsoi, Deniz Erdogmus, and Tales Imbiriba.

  33. Efficient and stable SAV-based methods for gradient flows arising from deep learning. JCP, 2024. paper

    Ziqi Ma, Zhiping Mao, and Jie Shen.

  34. Generative downscaling of PDE solvers with physics-guided diffusion models. arXiv, 2024. paper

    Yulong Lu and Wuzhe Xu.

  35. Nearest neighbors GParareal: Improving scalability of Gaussian processes for parallel-in-Time solvers. arXiv, 2024. paper

    Guglielmo Gattiglio, Lyudmila Grigoryeva, and Massimiliano Tamborrino.

  36. Large scale scattering using fast solvers based on neural operators. arXiv, 2024. paper

    Zongren Zou, Adar Kahana, Enrui Zhang, Eli Turkel, Rishikesh Ranade, Jay Pathak, and George Em Karniadakis.

  37. Position: Optimization in SciML should employ the function space geometry. ICML, 2024. paper

    Johannes Müller and Marius Zeinhofer.

  38. Scaling physics-informed hard constraints with mixture-of-experts. ICLR, 2024. paper

    Nithin Chalapathi, Yiheng Du, and Aditi S. Krishnapriyan.

  1. Auto-PINN: Understanding and optimizing physics-informed neural architecture. arXiv, 2022. paper

    Yicheng Wang, Xiaotian Han, Chiayuan Chang, Daochen Zha, Ulisses Braga-Neto, and Xia Hu.

  2. Building high accuracy emulators for scientific simulations with deep neural architecture search. Machine Learning: Science and Technology, 2022. paper

    M F Kasim, D Watson-Parris, L Deaconu, S Oliver, P Hatfield, D H Froula, G Gregori, M Jarvis, S Khatiwala, J Korenaga, J Topp-Mugglestone, E Viezzer, and S M Vinko.

  3. Learning operations for neural PDE solvers. ICLR, 2019. paper

    Nicholas Roberts, Mikhail Khodak, Tri Dao, Liam Li, Christopher Re, and Ameet Talwalkar.

  4. AutoPINN: When AutoML meets physics-informed neural networks. arXiv, 2022. paper

    Xinle Wu, Dalin Zhang, Miao Zhang, Chenjuan Guo, Shuai Zhao, Yi Zhang, Huai Wang, and Bin Yang.

  5. NAS-PINN: Neural architecture search-guided physics-informed neural network for solving PDEs. arXiv, 2023. paper

    Yifan Wang and Linlin Zhong.

  1. Neural implicit flow: A mesh-agnostic dimensionality reduction paradigm of spatio-temporal data. arXiv, 2022. paper

    Shaowu Pan, Steven L. Brunton, and J. Nathan Kutz.

  2. CROM: Continuous reduced-order modeling of PDEs using implicit neural representations. ICLR, 2023. paper

    Peter Yichen Chen, Jinxu Xiang, Dong Heon Cho, Yue Chang, G A Pershing, Henrique Teles Maia, Maurizio Chiaramonte, Kevin Carlberg, and Eitan Grinspun.

  3. MAgNet: Mesh agnostic neural PDE solver. NIPS, 2022. paper

    Oussama Boussif, Dan Assouline, Loubna Benabbou, and Yoshua Bengio.

  4. NTopo: Mesh-free topology optimization using implicit neural representations. NIPS, 2021. paper

    Jonas Zehnder, Yue Li, Stelian Coros, and Bernhard Thomaszewski.

  5. ContactNets: Learning discontinuous contact dynamics with smooth, implicit representations. ICLR, 2020. paper

    Samuel Pfrommer, Mathew Halm, and Michael Posa.

  6. Continuous PDE dynamics forecasting with implicit neural representations. ICLR, 2023. paper

    Yuan Yin, Matthieu Kirchmeyer, Jean-Yves Franceschi, Alain Rakotomamonjy, and Patrick Gallinari.

  7. Stability of implicit neural networks for long-term forecasting in dynamical systems. ICLR, 2023. paper

    Leon Migus, Julien Salomon, and Patrick Gallinari.

  8. Operator learning with neural fields: Tackling PDEs on general geometries. arXiv, 2023. paper

    Louis Serrano, Lise Le Boudec, Armand Kassaï Koupaï, Thomas X Wang, Yuan Yin, Jean-Noël Vittaut, and Patrick Gallinari.

  9. Accelerated solutions of convection-dominated partial differential equations using implicit feature tracking and empirical quadrature. arXiv, 2023. paper

    Marzieh Alireza Mirhoseini and Matthew J. Zahr.

  10. Implicit neural spatial representations for time-dependent PDEs. ICML, 2023. paper

    Honglin Chen, Rundi Wu, Eitan Grinspun, Changxi Zheng, and Peter Yichen Chen.

  11. Reduced-order modeling for parameterized PDEs via implicit neural representations. NIPS, 2023. paper

    Tianshu Wen, Kookjin Lee, and Youngsoo Choi.

  12. Geom-DeepONet: A point-cloud-based deep operator network for field predictions on 3D parameterized geometries. arXiv, 2024. paper

    Junyan He, Seid Koric, Diab Abueidda, Ali Najafi, and Iwona Jasiuk.

  13. Physics-aware neural implicit solvers for multiscale, parametric PDEs with applications in heterogeneous media. arXiv, 2024. paper

    Matthaios Chatzopoulos and Phaedon-Stelios Koutsourelakis.

  14. A resolution independent neural operator. arXiv, 2024. paper

    Bahador Bahmani, Somdatta Goswami, Ioannis G. Kevrekidis, and Michael D. Shields

  1. Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems. arXiv, 2021. paper

    Dongkun Zhang, Lu Lu, Ling Guo, and George Em Karniadakis.

  2. Adversarial uncertainty quantification in physics-informed neural networks. JCP, 2021. paper

    Yibo Yang and Paris Perdikaris.

  3. Conditional Karhunen-Loève expansion for uncertainty quantification and active learning in partial differential equation models. JCP, 2020. paper

    Ramakrishna Tipireddy, David A.Barajas-Solano, and Alexandre M.Tartakovsky.

  4. Physics-constrained deep learning for high-dimensional surrogate modeling and uncertainty quantification without labeled data. JCP, 2019. paper

    Yinhao Zhu, Nicholas Zabarasa, Phaedon-Stelios Koutsourelakisb, and Paris Perdikaris.

  5. Error-aware B-PINNs: Improving uncertainty quantification in Bayesian physics-informed neural networks. arXiv, 2022. paper

    Olga Graf, Pablo Flores, Pavlos Protopapas, and Karim Pichara.

  6. Physics-informed information field theory for modeling physical systems with uncertainty quantification. arXiv, 2023. paper

    Alex Alberts and Ilias Bilionis.

  7. Quantifying uncertainty for deep learning based forecasting and flow-reconstruction using neural architecture search ensembles. arXiv, 2023. paper

    Romit Maulik, Romain Egele, Krishnan Raghavan, and Prasanna Balaprakash.

  8. Physics-informed variational inference for uncertainty quantification of stochastic differential equations. JCP, 2023. paper

    Hyomin Shin and Minseok Choi.

  9. Uncertainty quantification in scientific machine learning: Methods, metrics, and comparisons. JCP, 2023. paper

    Apostolos F. Psaros, Xuhui Meng, Zongren Zou, Ling Guo, and George Em Karniadakis.

  10. Auto-weighted Bayesian physics-informed neural networks and robust estimations for multitask inverse problems in pore-scale imaging of dissolution. arXiv, 2023. paper

    Sarah Perez and Philippe Poncet.

  11. Neural SPDE solver for uncertainty quantification in high-dimensional space-time dynamics. arXiv, 2023. paper

    Maxime Beauchamp, Hugo Georgenthum, and Ronan Fablet.

  12. Ensemble models outperform single model uncertainties and predictions for operator-learning of hypersonic flows. NIPS, 2023. paper

    Victor J. Leon, Noah Ford, Honest Mrema, Jeffrey Gilbert, and Alexander New.

  13. Evaluating Uncertainty Quantification approaches for Neural PDEs in scientific applications. NIPS, 2023. paper

    Vardhan Dongre and Gurpreet Singh Hora.

  14. Uncertainty quantification for noisy inputs-outputs in physics-informed neural networks and neural operators. arXiv, 2023. paper

    Zongren Zou, Xuhui Meng, and George Em Karniadakis.

  15. Data-driven autoencoder numerical solver with uncertainty quantification for fast physical simulations. arXiv, 2023. paper

    Christophe Bonneville, Youngsoo Choi, Debojyoti Ghosh, and Jonathan L. Belof.

  16. Randomized physics-informed machine learning for uncertainty quantification in high-dimensional inverse problems. arXiv, 2023. paper

    Yifei Zong, David Barajas-Solano, and Alexandre M. Tartakovsky.

  17. Bayesian deep learning framework for uncertainty quantification in stochastic partial differential equations. SIAM Journal on Scientific Computing, 2024. paper

    Jeahan Jung, Hyomin Shin, and Minseok Choi.

  18. Uncertainty quantification for forward and inverse problems of PDEs via latent global evolution. AAAI, 2024. paper

    Tailin Wu, Willie Neiswanger, Hongtao Zheng, Stefano Ermon, and Jure Leskovec.

  19. Physics-constrained polynomial chaos expansion for scientific machine learning and uncertainty quantification. arXiv, 2024. paper

    Himanshu Sharma, Lukáš Novák, and Michael D. Shields.

  20. Physics-constrained polynomial chaos expansion for scientific machine learning and uncertainty quantification. arXiv, 2024. paper

    Himanshu Sharma, Lukáš Novák, and Michael D. Shields.

  21. Conformalized-DeepOnet: A distribution-free framework for uncertainty quantification in deep operator networks. arXiv, 2024. paper

    Christian Moya, Amirhossein Mollaali, Zecheng Zhang, Lu Lu, and Guang Lin.

  22. Leveraging viscous Hamilton-Jacobi PDEs for uncertainty quantification in scientific machine learning. arXiv, 2024. paper

    Zongren Zou, Tingwei Meng, Paula Chen, Jérôme Darbon, and George Em Karniadakis.

  1. A framework for data-driven solution and parameter estimation of PDEs using conditional generative adversarial networks. NCS, 2021. paper

    Teeratorn Kadeethum, Daniel O’Malley, Jan Niklas Fuhg, Youngsoo Choi, Jonghyun Lee, Hari S. Viswanathan, and Nikolaos Bouklas.

  2. Neural SDEs as infinite-dimensional GANs. ICML, 2021. paper

    Patrick Kidger, James Foster, Xuechen Li, and Terry J Lyons.

  3. PID-GAN: A GAN framework based on a physics-informed discriminator for uncertainty quantification with physics. KDD, 2021. paper

    Arka Daw, M. Maruf, and Anuj Karpatne.

  4. Generative adversarial neural operators. Transactions on Machine Learning Research, 2022. paper

    Md Ashiqur Rahman, Manuel A Florez, Anima Anandkumar, Zachary E Ross, and Kamyar Azizzadenesheli.

  5. Weak adversarial networks for high-dimensional partial differential equations. JCP, 2020. paper

    Yaohua Zang, Gang Bao, Xiaojing Ye, and Haomin Zhou.

  6. Wasserstein generative adversarial uncertainty quantification in physics-informed neural networks. JCP, 2022. paper

    Yihang Gao and Michael K. Ng.

  7. Competitive physics informed networks. ICLR, 2023. paper

    Qi Zeng, Yash Kothari, Spencer H Bryngelson, and Florian Tobias Schaefer.

  8. Learning generative neural networks with physics knowledge. Research in the Mathematical Sciences, 2022. paper

    Kailai Xu, Weiqiang Zhu, and Eric Darve.

  9. Diffusion generative models in infinite dimensions. arXiv, 2022. paper

    Gavin Kerrigan, Justin Ley, and Padhraic Smyth.

  10. Revisiting PINNs: Generative adversarial physics-informed neural networks and point-weighting method. arXiv, 2022. paper

    Wensheng Li, Chao Zhang, Chuncheng Wang, Hanting Guan, and Dacheng Tao.

  11. PIAT: Physics informed adversarial training for solving partial differential equations. arXiv, 2022. paper

    Simin Shekarpaz, Mohammad Azizmalayeri, and Mohammad Hossein Rohban.

  12. Physics-constrained generative adversarial networks for 3D turbulence. arXiv, 2022. paper

    Dima Tretiak, Arvind T. Mohan, and Daniel Livescu.

  13. Score-based diffusion models in function space. arXiv, 2023. paper

    Jae Hyun Lim, Nikola B. Kovachki, Ricardo Baptista, Christopher Beckham, Kamyar Azizzadenesheli, Jean Kossaifi, Vikram Voleti, Jiaming Song, Karsten Kreis, Jan Kautz, Christopher Pal, Arash Vahdat, and Anima Anandkumar.

  14. Infinite-dimensional diffusion models for function spaces. arXiv, 2023. paper

    Jakiw Pidstrigach, Youssef Marzouk, Sebastian Reich, and Sven Wang.

  15. A physics-informed diffusion model for high-fidelity flow field reconstruction. JCP, 2023. paper

    Dule Shu, Zijie Li, and Amir Barati Farimani.

  16. Generative modelling with inverse heat dissipation. ICLR, 2023. paper

    Severi Rissanen, Markus Heinonen, and Arno Solin.

  17. Differentiable Gaussianization layers for inverse problems regularized by deep generative models. ICLR, 2023. paper

    Dongzhuo Li.

  18. Transformer meets boundary value inverse problems. ICLR, 2023. paper

    Ruchi Guo, Shuhao Cao, and Long Chen.

  19. ViTO: Vision Transformer-operator. arXiv, 2023. paper

    Oded Ovadia, Adar Kahana, Panos Stinis, Eli Turkel, and George Em Karniadakis.

  20. Latent PINNs: Generative physics-informed neural networks via a latent representation learning. arXiv, 2023. paper

    Mohammad H. Taufik and Tariq Alkhalifah.

  21. Generative diffusion learning for parametric partial differential equations. arXiv, 2023. paper

    Ting Wang, Petr Plechac, and Jaroslaw Knap.

  22. Scalable Transformer for PDE surrogate modeling. arXiv, 2023. paper

    Zijie Li, Dule Shu, and Amir Barati Farimani.

  23. Latent traversals in generative models as potential flows. ICML, 2023. paper

    Yue Song, T. Anderson Keller, Nicu Sebe, and Max Welling.

  24. Learning space-time continuous neural PDEs from partially observed states. arXiv, 2023. paper

    Valerii Iakovlev, Markus Heinonen, and Harri Lähdesmäki.

  25. DiTTO: Diffusion-inspired temporal Transformer operator. arXiv, 2023. paper

    Oded Ovadia, Eli Turkel, Adar Kahana, and George Em Karniadakis.

  26. PINNsFormer: A Transformer-based framework For physics-informed neural networks. ICLR, 2024. paper

    Zhiyuan Zhao, Xueying Ding, and B. Aditya Prakash.

  27. CoCoGen: Physically-consistent and conditioned score-based generative models for forward and inverse problems. arXiv, 2023. paper

    Christian Jacobsen, Yilin Zhuang, and Karthik Duraisamy.

  28. Neuroexplicit diffusion models for inpainting of optical flow fields. arXiv, 2024. paper

    Tom Fischer, Pascal Peter, Joachim Weickert, and Eddy Ilg.

  1. Learning operators with coupled attention. JMLR, 2022. paper

    Matthew Thorpe, Tan Minh Nguyen, Hedi Xia, Thomas Strohmer, Andrea Bertozzi, Stanley Osher, and Bao Wang.

  2. Choose a Transformer: Fourier or Galerkin. NIPS, 2021. paper

    Shuhao Cao.

  3. Predicting physics in mesh-reduced space with temporal attention. ICLR, 2022. paper

    Xu Han, Han Gao, Tobias Pfaff, Jianxun Wang, and Liping Liu.

  4. SiT: Simulation transformer for particle-based physics simulation. ICLR, 2022. paper

    Yidi Shao, Chen Change Loy, and Bo Dai.

  5. Physics-informed long-sequence forecasting from multi-resolution spatiotemporal data. IJCAI, 2022. paper

    Chuizheng Meng, Hao Niu, Guillaume Habault, Roberto Legaspi, Shinya Wada, Chihiro Ono, and Yan Liu.

  6. TransFlowNet: A physics-constrained Transformer framework for spatio-temporal super-resolution of flow simulations. Journal of Computational Science, 2022. paper

    Xinjie Wang, Siyuan Zhu, Yundong Guo, Peng Han, Yucheng Wang, Zhiqiang Wei, and Xiaogang Jin.

  7. Self-adaptive physics-informed neural networks using a soft attention mechanism. AAAI-MLPS, 2021. paper

    Levi D. McClenny and Ulisses Braga-Neto.

  8. Transformer for partial differential equations' operator learning. arXiv, 2022. paper

    Zijie Li, Kazem Meidani, and Amir Barati Farimani.

  9. Physics-informed attention-based neural network for hyperbolic partial differential equations: Application to the Buckley–Leverett problem. Scientific Reports, 2022. paper

    Ruben Rodriguez-Torrado, Pablo Ruiz, Luis Cueto-Felgueroso, Michael Cerny Green, Tyler Friesen, Sebastien Matringe, and Julian Togelius.

  10. Self-adaptive physics-informed neural networks using a soft attention mechanism. AAAI-MLPS, 2021. paper

    Levi Mc Clenny and Ulisses Braga-Neto.

  11. Nonlinear reconstruction for operator learning of PDEs with discontinuities. ICLR, 2023. paper

    Samuel Lanthaler, Roberto Molinaro, Patrik Hadorn, and Siddhartha Mishra.

  12. GNOT: A general neural operator transformer for operator learning. ICML, 2023. paper

    Zhongkai Hao, Chengyang Ying, Zhengyi Wang, Hang Su, Yinpeng Dong, Songming Liu, Ze Cheng, Jun Zhu, and Jian Song.

  13. In-context operator learning for differential equation problems. arXiv, 2023. paper

    Liu Yang, Siting Liu, Tingwei Meng, and Stanley J. Osher.

  14. Learning neural PDE solvers with parameter-guided channel attention. ICML, 2023. paper

    Makoto Takamoto, Francesco Alesiani, and Mathias Niepert.

  15. Physics informed token Transformer. arXiv, 2023. paper

    Cooper Lorsung, Zijie Li, and Amir Barati Farimani.

  16. Improved operator learning by orthogonal attention. arXiv, 2023. paper

    Zipeng Xiao, Zhongkai Hao, Bokai Lin, Zhijie Deng, and Hang Su.

  17. Multi-scale time-stepping of partial differential equations with Transformers. arXiv, 2023. paper

    AmirPouya Hemmasian and Amir Barati Farimani.

  18. Deciphering and integrating invariants for neural operator learning with various physical mechanisms. arXiv, 2023. paper

    Rui Zhang, Qi Meng, and Zhiming Ma.

  19. Attention-enhanced neural differential equations for physics-informed deep learning of ion transport. NIPS, 2023. paper

    Danyal Rehman and John H. Lienhard.

  20. Inducing point operator Transformer: A flexible and scalable architecture for solving PDEs. arXiv, 2023. paper

    Seungjun Lee and Taeil Oh.

  21. Loss-attentional physics-informed neural networks. JCP, 2024. paper

    Yanjie Song, He Wang, He Yang, Maria Luisa Taccari, and Xiaohui Chen.

  22. PirateNets: Physics-informed deep learning with residual adaptive networks. arXiv, 2024. paper

    Sifan Wang, Bowen Li, Yuhan Chen, and Paris Perdikaris.

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  26. Bridging operator learning and conditioned neural fields: A unifying perspective. arXiv, 2024. paper

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  27. Unisolver: PDE-conditional transformers are universal PDE solvers. arXiv, 2024. paper

    Zhou Hang, Yuezhou Ma, Haixu Wu, Haowen Wang, and Mingsheng Long.

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    Benjamin Shih, Ahmad Peyvan, Zhongqiang Zhang, and George Em Karniadakis.

  29. Bridging operator learning and conditioned neural fields: A unifying perspective. arXiv, 2024. paper

    Sifan Wang, Jacob H Seidman, Shyam Sankaran, Hanwen Wang, George J. Pappas, and Paris Perdikaris.

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    Yue Yu, Ning Liu, Fei Lu, Tian Gao, Siavash Jafarzadeh, and Stewart Silling

  1. Convergence analysis of a quasi-Monte Carlo-based deep learning algorithm for solving partial differential equations. arXiv, 2022. paper

    Fengjiang Fu and Xiaoqun Wang.

  2. Solving PDEs by variational physics-informed neural networks: A posteriori error analysis. arXiv, 2022. paper

    Stefano Berrone, Claudio Canuto, and Moreno Pintore.

  3. A unified framework for the error analysis of physics-informed neural networks. arXiv, 2023. paper

    Marius Zeinhofer, Rami Masri, and Kent-André Mardal.

  4. Neural tangent kernel analysis of PINN for advection-diffusion equation. arXiv, 2022. paper

    M. H. Saadat, B. Gjorgiev, L. Das, and G. Sansavini.

  5. Error estimates for DeepONets: A deep learning framework in infinite dimensions. Transactions of Mathematics and Its Applications, 2022. paper

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  6. Hutchinson trace estimation for high-dimensional and high-order physics-informed neural networks. arXiv, 2023. paper

    Zheyuan Hu, Zekun Shi, George Em Karniadakis, and Kenji Kawaguchi.

  7. An analysis of universal differential equations for data-driven discovery of ordinary differential equations. arXiv, 2023. paper

    Mattia Silvestri, Federico Baldo, Eleonora Misino, and Michele Lombardi.

  8. Exponential convergence of deep operator networks for elliptic partial differential equations. SIAM Journal on Numerical Analysis, 2023. paper

    Carlo Marcati and Christoph Schwab.

  9. A discretization-invariant extension and analysis of some deep operator networks. arXiv, 2023. paper

    Zecheng Zhang, Wing Tat Leung, and Hayden Schaeffer.

  10. Machine learning for elliptic PDEs: Fast rate generalization bound, neural scaling law and minimax optimality. ICLR, 2022. paper

    Yiping Lu, Haoxuan Chen, Jianfeng Lu, Lexing Ying, and Jose Blanchet.

  11. Elliptic PDE learning is provably data-efficient. arXiv, 2023. paper

    Nicolas Boullé, Diana Halikias, and Alex Townsend.

  12. Error estimates of residual minimization using neural networks for linear PDEs. Journal of Machine Learning for Modeling and Computing, 2023. paper

    Yeonjong Shin, Zhongqiang Zhang, and George Em Karniadakis.

  13. Analysis of the generalization error of deep learning based on randomized quasi-Monte Carlo for solving linear Kolmogorov PDEs. arXiv, 2023. paper

    Jichang Xiao, Fengjiang Fu, and Xiaoqun Wang.

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    Birgit Hillebrecht and Benjamin Unger.

  15. Error estimation for physics-informed neural networks with implicit Runge-Kutta methods. arXiv, 2023. paper

    Jochen Stiasny and Spyros Chatzivasileiadis.

  16. Approximation of solution operators for high-dimensional PDEs. arXiv, 2024. paper

    Nathan Gaby and Xiaojing Ye.

  17. Accuracy analysis of physics-informed neural networks for approximating the critical SQG equation. arXiv, 2024. paper

    Elie Abdo, Ruimeng Hu, and Quyuan Lin.

  18. Deep Ritz method for elliptical multiple eigenvalue problems. Journal of Scientific Computing, 2024. paper

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  19. Inf-Sup neural networks for high-dimensional elliptic PDE problems. arXiv, 2024. paper

    Xiaokai Huo and Hailiang Liu.

  20. The challenges of the nonlinear regime for physics-informed neural networks. arXiv, 2024. paper

    Andrea Bonfanti, Giuseppe Bruno, and Cristina Cipriani.

  21. A hybrid iterative method based on MIONet for PDEs: Theory and numerical examples. arXiv, 2024. paper

    Jun Hu and Pengzhan Jin.

  22. A priori error estimation of physics-informed neural networks solving Allen--Cahn and Cahn--Hilliard equations. arXiv, 2024. paper

    Guangtao Zhang, Jiani Lin, Qijia Zhai, Huiyu Yang, Xujun Chen, Xiaoning Zheng, and Ieng Tak Leong.

  23. Convergence of the deep Galerkin method for mean field control problems. arXiv, 2024. paper

    William Hofgard, Jingruo Sun, and Asaf Cohen.

  24. Data complexity estimates for operator learning. arXiv, 2024. paper

    Nikola B. Kovachki, Samuel Lanthaler, and Hrushikesh Mhaskar.

  25. Bengining overfitting in fixed dimension via physics-informed learning with smooth iductive bias. arXiv, 2024. paper

    Honam Wong, Wendao Wu, Fanghui Liu, and Yiping Lu.

  26. Operator learning of Lipschitz operators: An information-theoretic perspective. arXiv, 2024. paper

    Samuel Lanthaler.

  27. Guaranteed approximation bounds for mixed-precision neural operators. ICLR, 2024. paper

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    Celal Soyarslan and Marc Pradas.

  29. A Deep BSDE approximation of nonlinear integro-PDEs with unbounded nonlocal operators. arXiv, 2024. paper

    Espen Robstad Jakobsen and Sehail Mazid.

  1. PAGP: A physics-assisted Gaussian process framework with active learning for forward and inverse problems of partial differential equations. arXiv, 2022. paper

    Jiahao Zhang, Shiqi Zhang, and Guang Lin.

  2. Solving and learning nonlinear PDEs with Gaussian processes. JCP, 2021. paper

    Yifan Chen, Bamdad Hosseini, Houman Owhadi, and Andrew M.Stuart.

  3. Neural-net-induced Gaussian process regression for function approximation and PDE solution. JCP, 2019. paper

    Guofei Pang, Liu Yang, and George Em Karniadakis.

  4. Learning neural optimal interpolation models and solvers. arXiv, 2022. paper

    Maxime Beauchamp, Joseph Thompson, Hugo Georgenthum, Quentin Febvre, and Ronan Fablet.

  5. Inference of nonlinear partial differential equations via constrained Gaussian processes. arXiv, 2022. paper

    Zhaohui Li, Shihao Yang, and Jeff Wu.

  6. Gaussian process priors for systems of linear partial differential equations with constant coefficients. arXiv, 2022. paper

    Marc Härkönen, Markus Lange-Hegermann, and Bogdan Raiţă.

  7. Sparse Cholesky factorization for solving nonlinear PDEs via Gaussian processes. arXiv, 2023. paper

    Yifan Chen, Houman Owhadi, and Florian Schäfer.

  8. A mini-batch method for solving nonlinear PDEs with Gaussian processes. arXiv, 2023. paper

    Xianjin Yang and Houman Owhadi.

  9. Random grid neural processes for parametric partial differential equations. ICML, 2023. paper

    Arnaud Vadeboncoeur, Ieva Kazlauskaite, Yanni Papandreou, Fehmi Cirak, Mark Girolami, and Omer Deniz Akyildiz.

  10. Gaussian process priors for systems of linear partial differential equations with constant coefficients. ICML, 2023. paper

    Marc Harkonen, Markus Lange-Hegermann, and Bogdan Raita.

  11. GPLaSDI: Gaussian process-based interpretable latent space dynamics identification through deep autoencoder. arXiv, 2023. paper

    Christophe Bonneville, Youngsoo Choi, Debojyoti Ghosh, and Jonathan L.Belof.

  12. Solving high frequency and multi-scale PDEs with Gaussian processes. ICLR, 2024. paper

    Shikai Fang, Madison Cooley, Da Long, Shibo Li, Robert Kirby, and Shandian Zhe.

  13. Physics-constrained convolutional neural networks for inverse problems in spatiotemporal partial differential equations. arXiv, 2024. paper

    Daniel Kelshaw and Luca Magri.

  1. PI-VAE: Physics-informed variational auto-encoder for stochastic differential equations. CMAME, 2022. paper

    Weiheng Zhong and Hadi Meidani.

  2. Robust SDE-based variational formulations for solving linear PDEs via deep learning. ICML, 2022. paper

    Lorenz Richter and Julius Berner.

  3. HP-VPINNs: Variational physics-informed neural networks with domain decomposition. CMAME, 2021. paper

    Ehsan Kharazmi, Zhongqiang Zhang, and George Em Karniadakis.

  4. Variational onsager neural networks (VONNs): A thermodynamics-based variational learning strategy for non-equilibrium PDEs. Journal of the Mechanics and Physics of Solids, 2022. paper

    Shenglin Huang, Zequn He, Bryan Chem, and Celia Reina.

  5. Variational Monte Carlo approach to partial differential equations with neural networks. arXiv, 2022. paper

    Moritz Reh and Martin Gärttner.

  6. Energetic variational neural network discretizations to gradient flows. arXiv, 2022. paper

    Ziqing Hu, Chun Liu, Yiwei Wang, and Zhiliang Xu.

  7. Variational Bayes deep operator network: A data-driven Bayesian solver for parametric differential equations. arXiv, 2022. paper

    Shailesh Garg and Souvik Chakraborty.

  8. Variational inference in neural functional prior using normalizing flows: Application to differential equation and operator learning problems. arXiv, 2023. paper

    Xuhui Meng.

  9. Neural network approximations of PDEs beyond linearity: A representational perspective. ICML, 2023. paper

    Tanya Marwah, Zachary Chase Lipton, Jianfeng Lu, and Andrej Risteski.

  1. Bayesian deep learning for partial differential equation parameter discovery with sparse and noisy data. JCP: X, 2022. paper

    Christophe Bonneville and Christopher Earls.

  2. B-PINNs: Bayesian physics-informed neural networks for forward and inverse PDE problems with noisy data. JCP, 2021. paper

    Liu Yang, Xuhui Meng, and George Em Karniadakis.

  3. Approximate Bayesian neural operators: Uncertainty quantification for parametric PDEs. arXiv, 2022. paper

    Emilia Magnani, Nicholas Krämer, Runa Eschenhagen, Lorenzo Rosasco, and Philipp Hennig.

  4. Bayesian autoencoders for data-driven discovery of coordinates, governing equations and fundamental constants. arXiv, 2022. paper

    L. Mars Gao and J. Nathan Kutz.

  5. Bayesian physics informed neural networks for data assimilation and spatio-temporal modelling of wildfires. arXiv, 2022. paper

    Joel Janek Dabrowski, Daniel Edward Pagendam, James Hilton, Conrad Sanderson, Daniel MacKinlay, Carolyn Huston, Andrew Bolt, and Petra Kuhnert.

  6. Bayesian deep operator learning for homogenized to fine-scale maps for multiscale PDE. arXiv, 2023. paper

    Zecheng Zhang, Christian Moya, Wing Tat Leung, Guang Lin, and Hayden Schaeffer.

  7. Bayesian deep learning framework for uncertainty quantification in stochastic partial differential equations. SIAM Journal on Scientific Computing, 2024. paper

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  1. Multiscale simulations of complex systems by learning their effective dynamics. NMI, 2022. paper

    Pantelis R. Vlachas, Georgios Arampatzis, Caroline Uhler, and Petros Koumoutsakos.

  2. A latent space solver for PDE generalization. ICLR, 2021. paper

    Rishikesh Ranade, Chris Hill, Haiyang He, Amir Maleki, and Jay Pathak.

  3. Approximate latent force model inference. AAAI, 2021. paper

    Jacob D. Moss, Felix L. Opolka, Bianca Dumitrascu, and Pietro Lió.

  4. Learning to accelerate partial differential equations via latent global evolution. NIPS, 2022. paper

    Tailin Wu, Takashi Maruyama, and Jure Leskovec.

  5. Exploring physical latent spaces for deep learning. arXiv, 2022. paper

    Chloe Paliard, Nils Thuerey, and Kiwon Um.

  6. Certified data-driven physics-informed greedy auto-encoder simulator. arXiv, 2022. paper

    Xiaolong He, Youngsoo Choi, William D. Fries, Jonathan L. Belof, and Jiun-Shyan Chen.

  7. Deep latent regularity network for modeling stochastic partial differential equations. AAAI, 2023. paper

    Shiqi Gong, Peiyan Hu, Qi Meng, Yue Wang, Rongchan Zhu, Bingguang Chen, Zhiming Ma, Hao Ni, and Tieyan Liu.

  8. Learning in latent spaces improves the predictive accuracy of deep neural operators. arXiv, 2023. paper

    Katiana Kontolati, Somdatta Goswami, George Em Karniadakis, and Michael D. Shields.

  9. Solving high-dimensional PDEs with latent spectral models. ICML, 2023. paper

    Haixu Wu, Tengge Hu, Huakun Luo, Jianmin Wang, and Mingsheng Long.

  10. Physics-informed generator-encoder adversarial networks with latent space matching for stochastic differential equations. arXiv, 2023. paper

    Ruisong Gao, Min Yang, and Jin Zhang.

  11. Smooth and sparse latent dynamics in operator learning with Jerk regularization arXiv, 2024. paper

    Xiaoyu Xie, Saviz Mowlavi, and Mouhacine Benosman.

  12. Latent neural PDE solver: A reduced-order modelling framework for partial differential equations arXiv, 2024. paper

    Zijie Li, Saurabh Patil, Francis Ogoke, Dule Shu, Wilson Zhen, Michael Schneier, John R. Buchanan Jr., and Amir Barati Farimani.

  1. Lagrangian PINNs: A causality–conforming solution to failure modes of physics-informed neural networks. arXiv, 2022. paper

    Rambod Mojgani, Maciej Balajewicz, and Pedram Hassanzadeh.

  2. AL-PINNs: Augmented Lagrangian relaxation method for physics-informed neural networks. arXiv, 2022. paper

    Hwijae Son, Sung Woong Cho, and Hyung Ju Hwang.

  3. Lagrangian flow networks for conservation laws. ICLR, 2024. paper

    Fabricio Arend Torres, Marcello Massimo Negri, Marco Inversi, and Jonathan Aellen.

  4. An adaptive augmented Lagrangian method for training physics and equality constrained artificial neural networks. arXiv, 2023. paper

    Shamsulhaq Basir and Inanc Senocak.

  5. Constrained optimization via exact augmented Lagrangian and randomized iterative sketching. ICML, 2023. paper

    Ilgee Hong, Sen Na, Michael W. Mahoney, and Mladen Kolar.

  6. An adaptive augmented Lagrangian method for training physics and equality constrained artificial neural networks. arXiv, 2023. paper

    Shamsulhaq Basir and Inanc Senocak.

  7. Partitioned neural network approximation for partial differential equations enhanced with Lagrange multipliers and localized loss functions. arXiv, 2023. paper

    Deok-Kyu Jang, Kyungsoo Kim, and Hyea Hyun Kim.

  1. Hierarchical deep learning of multiscale differential equation time-steppers. Philosophical Transactions of the Royal Society A, 2022. paper

    Yuying Liu, J. Nathan Kutz, and Steven L. Brunton.

  2. NH-PINN: Neural homogenization-based physics-informed neural network for multiscale problems. JCP, 2022. paper

    Wing Tat Leung, Guang Lin, and Zecheng Zhang.

  3. Deep multiscale model learning. JCP, 2020. paper

    Yating Wang, Siu Wun Cheung, Eric T.Chung, Yalchin Efendiev, and Min Wang.

  4. Multi-scale deep neural networks for solving high dimensional PDEs. arXiv, 2019. paper

    Samuel H. Rudy, Steven L. Brunton, Joshua L. Proctor, and J. Nathan Kutz.

  5. Towards multi-spatiotemporal-scale generalized PDE modeling. arXiv, 2022. paper

    Jayesh K. Gupta and Johannes Brandstetter.

  6. MultiAdam: Parameter-wise scale-invariant optimizer for multiscale training of physics-informed neural networks. ICML, 2023. paper

    Jiachen Yao, Chang Su, Zhongkai Hao, Songming Liu, Hang Su, and Jun Zhu.

  7. Learning homogenization for elliptic operators. arXiv, 2023. paper

    Kaushik Bhattacharya, Nikola Kovachki, Aakila Rajan, Andrew M. Stuart, and Margaret Trautner.

  8. Multi-grade deep learning for partial differential equations with applications to the Burgers equation. arXiv, 2023. paper

    Yuesheng Xu and Taishan Zeng.

  9. Multiscale neural operators for solving time-independent PDEs. NIPS, 2023. paper

    Winfried Ripken, Lisa Coiffard, Felix Pieper, and Sebastian Dziadzio.

  10. Multilevel scalable solvers for stochastic linear and nonlinear problems. arXiv, 2023. paper

    Sudhi Sharma, Pierre Jolivet, Victorita Dolean, and Abhijit Sarkar.

  11. Local convolution enhanced global Fourier neural operator for multiscale dynamic spaces prediction. arXiv, 2023. paper

    Xuanle Zhao, Yue Sun, Tielin Zhang, and Bo Xu.

  12. Mitigating spectral bias for the multiscale operator learning. JCP, 2024. paper

    Xinliang Liu, Bo Xu, Shuhao Cao, and Lei Zhang.

  13. SineNet: Learning temporal dynamics in time-dependent partial differential equations. ICLR, 2024. paper

    Xuan Zhang, Jacob Helwig, Yuchao Lin, Yaochen Xie, Cong Fu, Stephan Wojtowytsch, and Shuiwang Ji.

  14. Multiscale attention wavelet neural operator for capturing steep trajectories in biochemical systems. AAAI, 2024. paper

    Jiayang Su, Junbo Ma, Songyang Tong, Enze Xu, and Minghan Chen.

  15. A practical PINN framework for multi-scale problems with multi-magnitude loss terms. JCP, 2024. paper

    Yong Wang, Yanzhong Yao, Jiawei Guo, and Zhiming Gao.

  16. Enhancing multiscale simulations with constitutive relations-aware deep operator networks. arXiv, 2024. paper

    Hamidreza Eivazi, Mahyar Alikhani, Jendrik-Alexander Tröger, Stefan Wittek, Stefan Hartmann, and Andreas Rausch.

  17. UGrid: An efficient-and-rigorous neural multigrid solver for linear PDEs. ICML, 2024. paper

    Xi Han, Fei Hou, and Hong Qin.

  1. Multifidelity deep operator networks. arXiv, 2022. paper

    Amanda A. Howard, Mauro Perego, George Em Karniadakis, and Panos Stinis.

  2. Physics and equality constrained artificial neural networks: Application to forward and inverse problems with multi-fidelity data fusion. JCP, 2022. paper

    Lulu Zhang, Tao Luo, Yaoyu Zhang, Weinan E, Zhiqin John Xu, and Zheng Ma.

  3. A composite neural network that learns from multi-fidelity data: Application to function approximation and inverse PDE problems. JCP, 2020. paper

    Xuhui Meng and George Em Karniadakis.

  4. Multifidelity deep neural operators for efficient learning of partial differential equations with application to fast inverse design of nanoscale heat transport. Physical Review Research, 2022. paper

    Lu Lu, Raphaël Pestourie, Steven G. Johnson, and Giuseppe Romano.

  5. Multi-fidelity reduced-order surrogate modeling. arXiv, 2023. paper

    Paolo Conti, Mengwu Guo, Andrea Manzoni, Attilio Frangi, Steven L. Brunton, and J. Nathan Kutz.

  6. Multifidelity deep operator networks for data-driven and physics-informed problems. JCP, 2023. paper

    Amanda A. Howard, Mauro Perego, George Em Karniadakis, and Panos Stinis.

  7. A multi-fidelity machine learning based semi-Lagrangian finite volume scheme for linear transport equations and the nonlinear Vlasov-Poisson system. arXiv, 2023. paper

    Yongsheng Chen, Wei Guo, and Xinghui Zhong.

  8. Neural operator-based super-fidelity: A warm-start approach for accelerating steady-state simulations. arXiv, 2023. paper

    Xuhui Zhou, Jiequn Han, Muhammad I. Zafar, Christopher J. Roy, Heng Xiao.

  9. Multi-resolution partial differential equations preserved learning framework for spatiotemporal dynamics. AAAI, 2024. paper

    Xinyang Liu, Min Zhu, Lu Lu, Hao Sun, Jianxun Wang.

  10. Feature-adjacent multi-fidelity physics-informed machine learning for partial differential equations. JCP, 2024. paper

    Wenqian Chen and Panos Stinis.

  11. Data-driven constitutive meta-modeling of nonlinear rheology via multifidelity neural networks. JCP, 2024. paper

    Milad Saadat, William H. Hartt V, Norman J. Wagner, and Safa Jamali.

  1. Learning to optimize multigrid PDE solvers. ICML, 2019. paper

    Daniel Greenfeld, Meirav Galun, Ronen Basri, Irad Yavneh, and Ron Kimmel.

  2. Reducing operator complexity in algebraic multigrid with machine learning approaches. arXiv, 2023. paper

    Ru Huang, Kai Chang, Huan He, Ruipeng Li, and Yuanzhe Xi.

  3. Multi-grid tensorized Fourier neural operator for high-resolution PDEs. arXiv, 2023. paper

    Jean Kossaifi, Nikola Kovachki, Kamyar Azizzadenesheli, and Anima Anandkumar.

  4. MgNO: Efficient parameterization of linear operators via multigrid. ICLR, 2024 paper

    Juncai He, Xinliang Liu, and Jinchao Xu.

  5. MGCNN: A learnable multigrid solver for linear PDEs on structured grids. arXiv, 2023. paper

    Yan Xie, Minrui Lv, and Chensong Zhang.

  6. Neural physical simulation with multi-resolution hash grid encoding. AAAI, 2024. paper

    Haoxiang Wang, Tao Yu, Tianwei Yang, Hui Qiao, and Qionghai Dai.

  7. Multigrid-augmented deep learning preconditioners for the helmholtz equation using compact implicit layers. Journal on Scientific Computing, 2024. paper

    Bar Lerer, Ido Ben-Yair, and Eran Treister.

  8. Ugrid: An efficient-and-rigorous neural multigrid solver for linear PDEs. ICML, 2024. paper

    Xi Han, Fei Hou, and Hong Qin.

  1. Neural Galerkin scheme with active learning for high-dimensional evolution equations. arXiv, 2022. paper

    Joan Bruna, Benjamin Peherstorfer, and Eric Vanden-Eijnden.

  2. Discovering and forecasting extreme events via active learning in neural operators. arXiv, 2022. paper

    Ethan Pickering, Stephen Guth, George Em Karniadakis, and Themistoklis P. Sapsis.

  3. Active learning based sampling for high-dimensional nonlinear partial differential equations. JCP, 2023. paper

    Wenhan Gao and Chunmei Wang.

  4. An extreme learning machine-based method for computational PDEs in higher dimensions. arXiv, 2023. paper

    Yiran Wang and Suchuan Dong.

  5. Multi-resolution active learning of Fourier neural operators. arXiv, 2023. paper

    Shibo Li, Xin Yu, Wei Xing, Mike Kirby, Akil Narayan, and Shandian Zhe.

  6. A foundational neural operator that continuously learns without forgetting. arXiv, 2023. paper

    Tapas Tripura and Souvik Chakraborty.

  7. Neural Galerkin schemes with active learning for high-dimensional evolution equations. JCP, 2023. paper

    Joan Bruna, Benjamin Peherstorfer, and Eric Vanden-Eijnden.

  8. Active learning for neural PDE solvers. arXiv, 2024. paper

    Daniel Musekamp, Marimuthu Kalimuthu, David Holzmüller, Makoto Takamoto, and Mathias Niepert.

  1. Adversarial multi-task learning enhanced physics-informed neural networks for solving partial differential equations. IJCNN, 2022. paper

    Pongpisit Thanasutives, Masayuki Numao, and Ken-ichi Fukui.

  2. Synergistic learning with multi-task DeepONet for efficient pde problem solving. arXiv, 2024. paper

    Varun Kumar, Somdatta Goswami, Katiana Kontolati, Michael D. Shields, and George Em Karniadakis.

  1. Fast PDE-constrained optimization via self-supervised operator learning. arXiv, 2021. paper

    Sifan Wang, Mohamed Aziz Bhouri, and Paris Perdikaris.

  2. An extended physics informed neural network for preliminary analysis of parametric optimal control problems. arXiv, 2021. paper

    Nicola Demo, Maria Strazzullo, and Gianluigi Rozza.

  3. Optimal control of PDEs using physics-informed neural networks. JCP, 2023. paper

    Saviz Mowlavi and Saleh Nabi.

  4. Solving PDE-constrained control problems using operator learning. AAAI, 2022. paper

    Rakhoon Hwang, Jae Yong Lee, Jin Young Shin, and Hyung Ju Hwang.

  5. PDE-based optimal strategy for unconstrained online learning. ICML, 2022. paper

    Zhiyu Zhang, Ashok Cutkosky, and Ioannis Paschalidis.

  6. Control of partial differential equations via physics-informed neural networks. Journal of Optimization Theory and Applications, 2022. paper

    Carlos J. García-Cervera, Mathieu Kessler, and Francisco Periago.

  7. A machine learning framework for solving high-dimensional mean field game and mean field control problems. PNAS, 2020. paper

    Lars Ruthottoa, Stanley J. Osherc, Wuchen Lic, Levon Nurbekyanc, and Samy Wu Fung.

  8. Bi-level physics-informed neural networks for PDE constrained optimization using Broyden's hypergradients. ICLR, 2023. paper

    Zhongkai Hao, Chengyang Ying, Hang Su, Jun Zhu, Jian Song, and Ze Cheng.

  9. A combination technique for optimal control problems constrained by random PDEs. arXiv, 2022. paper

    Fabio Nobile and Tommaso Vanzan.

  10. A multilevel reinforcement learning framework for PDE-based control. arXiv, 2022. paper

    Atish Dixit and Ahmed H. Elsheikh.

  11. Optimal learning of high-dimensional classification problems using deep neural networks. arXiv, 2022. paper

    Philipp Petersen and Felix Voigtlaender.

  12. The ADMM-PINNs algorithmic framework for nonsmooth PDE-constrained optimization: A deep learning approach. arXiv, 2023. paper

    Yongcun Song, Xiaoming Yuan, and Hangrui Yue.

  13. Learning differentiable solvers for systems with hard constraints. ICLR, 2023. paper

    Geoffrey Négiar, Geoffrey_Négiar, Michael W. Mahoney, and Aditi Krishnapriyan.

  14. Volumetric optimal transportation by fast Fourier transform. ICLR, 2023. paper

    Na Lei, DONGSHENG An, Min Zhang, Xiaoyin Xu, and David Gu.

  15. PDE-based optimal strategy for unconstrained online learning. ICML, 2022. paper

    Zhiyu Zhang, Ashok Cutkosky, and Ioannis Paschalidis.

  16. PDE-constrained models with neural network terms: Optimization and global convergence. JCP, 2023. paper

    Justin Sirignano, Jonathan MacArt, and Konstantinos Spiliopoulos.

  17. Topology optimization using neural networks with conditioning field initialization for improved efficiency. arXiv, 2023. paper

    Hongrui Chen, Aditya Joglekar, and Levent Burak Kara.

  18. Deep reinforcement learning for optimal well control in subsurface systems with uncertain geology. JCP, 2023. paper

    Yusuf Nasir and Louis J. Durlofsky.

  19. Constrained optimization via exact augmented lagrangian and randomized iterative sketching. ICML, 2023. paper

    Ilgee Hong, Sen Na, Michael W. Mahoney, and Mladen Kolar.

  20. Efficient PDE-constrained optimization under high-dimensional uncertainty using derivative-informed neural operators. arXiv, 2023. paper

    Dingcheng Luo, Thomas O'Leary-Roseberry, Peng Chen, and Omar Ghattas.

  21. Dimension-independent certified neural network watermarks via mollifier smoothing. ICML, 2023. paper

    Jiaxiang Ren, Yang Zhou, Jiayin Jin, Lingjuan Lyu, and Da Yan.

  22. Accelerated primal-dual methods with enlarged step sizes and operator learning for nonsmooth optimal control problems. arXiv, 2023. paper

    Yongcun Song, Xiaoming Yuan, and Hangrui Yue.

  23. Accelerated primal-dual methods with enlarged step sizes and operator learning for nonsmooth optimal control problems. arXiv, 2023. paper

    Yongcun Song, Xiaoming Yuan, and Hangrui Yue.

  24. Operator learning for continuous spatial-temporal model with a hybrid optimization scheme. arXiv, 2023. paper

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  25. Deep neural operators as accurate surrogates for shape optimization. EAAI, 2023. paper

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  26. Accelerating Bayesian optimal experimental design with derivative-informed neural operators. arXiv, 2023. paper

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  27. A supervised learning scheme for computing Hamilton-Jacobi equation via density coupling. arXiv, 2024. paper

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  28. Optimization in SciML -- A function space perspective. arXiv, 2024. paper

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  29. Inverse design method for horn antennas based on knowledge-embedded physics-informed neural networks. IEEE Antennas and Wireless Propagation Letters, 2024. paper

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  30. G-RepsNet: A fast and general construction of equivariant networks for arbitrary matrix groups. arXiv, 2024. paper

    Sourya Basu, Suhas Lohit, and Matthew Brandr.

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  1. Physics-informed neural networks (PINNs) for fluid mechanics: A review. Acta Mechanica Sinica, 2021. paper

    Shengze Cai, Zhiping Mao, Zhicheng Wang, Minglang Yin, and George Em Karniadakis.

  2. Neural operator prediction of linear instability waves in high-speed boundary layers. JCP, 2022. paper

    Patricio Clark Di Leoni, Lu Lu, Charles Meneveau, George Karniadakis, and Tamer A. Zaki.

  3. A physics-informed convolutional neural network for the simulation and prediction of two-phase darcy flows in heterogeneous porous media. JCP, 2023. paper

    Zhao Zhang, Xia Yan, Piyang Liu, Kai Zhang, Renmin Han, and Sheng Wang.

  4. DiscretizationNet: A machine-learning based solver for Navier–Stokes equations using finite volume discretization. CMAME, 2021. paper

    Rishikesh Ranade, Chris Hillb, and Jay Pathak.

  5. Surrogate modeling for fluid flows based on physics-constrained deep learning without simulation data. CMAME, 2020. paper

    Luning Sun, Han Gao, Shaowu Pan, and Jianxun Wang.

  6. Towards physics-informed deep learning for turbulent flow prediction. KDD, 2020. paper

    Rui Wang, Karthik Kashinath, Mustafa Mustafa, Adrian Albert, and Rose Yu.

  7. Learning to estimate and refine fluid motion with physical dynamics. ICML, 2022. paper

    Mingrui Zhang, Jianhong Wang, James Tlhomole, and Matthew D. Piggott.

  8. Physics informed neural fields for smoke reconstruction with sparse data. ACM Transactions on Graphics, 2022. paper

    Mengyu Chu, Lingjie Liu, Quan Zheng, Erik Franz, Hans-Peter Seidel, Christian Theobalt, and Rhaleb Zayer.

  9. Physics-informed deep learning for traffic state estimation: A hybrid paradigm informed by second-order traffic models. AAAI, 2021. paper

    Rongye Shi, Zhaobin Mo, and Xuan Di.

  10. Residual-based adaptivity for two-phase flow simulation in porous media using physics-informed neural networks. CMAME, 2022. paper

    John M.Hanna, José V.Aguado, Sebastien Comas-Cardona, Ramz Askri, and Domenico Borzacchiello.

  11. Learned turbulence modelling with differentiable fluid solvers: Physics-based loss-functions and optimisation horizons. JFM, 2022. paper

    Björn List, Liwei Chen, and Nils Thuerey.

  12. Learning hydrodynamic equations for active matter from particle simulations and experiments. PNAS, 2023. paper

    Rohit Supekar, Boya Song, Alasdair Hastewell, Gary P. T. Choi, Alexander Mietke, and Jörn Dunkel.

  13. Physics informed neural networks: A case study for gas transport problems. JCP, 2023. paper

    Erik Laurin Strelow, Alf Gerisch, Jens Lang, and Marc E. Pfetsch.

  14. Turbulence model augmented physics informed neural networks for mean flow reconstruction. arXiv, 2023. paper

    Yusuf Patel, Vincent Mons, Olivier Marquet, and Georgios Rigas.

  15. RANS-PINN based simulation surrogates for predicting turbulent flows. arXiv, 2023. paper

    Shinjan Ghosh, Amit Chakraborty, Georgia Olympia Brikis, and Biswadip Dey.

  16. Meta-learning for airflow simulations with graph neural networks. arXiv, 2023. paper

    Wenzhuo Liu, Mouadh Yagoubi, and Marc Schoenauer.

  17. Learning operators for identifying weak solutions to the Navier-Stokes equations. arXiv, 2023. paper

    Dixi Wang and Cheng Yu.

  18. Physics-informed neural networks modeling for systems with moving immersed boundaries: Application to an unsteady flow past a plunging foil. arXiv, 2023. paper

    Rahul Sundar, Dipanjan Majumdar, Didier Lucor, and Sunetra Sarkar.

  19. A machine learning pressure emulator for hydrogen embrittlement. ICML, 2023. paper

    Minh Triet Chau, João Lucas de Sousa Almeida, Elie Alhajjar, and Alberto Costa Nogueira Junior.

  20. A probabilistic, data-driven closure model for RANS simulations with aleatoric, model uncertainty. arXiv, 2023. paper

    Atul Agrawal and Phaedon-Stelios Koutsourelakis.

  21. Physics-informed machine learning for calibrating macroscopic traffic flow models. arXiv, 2023. paper

    Yu Tang, Li Jin, and Kaan Ozbay.

  22. Radial basis function-differential quadrature-based physics-informed neural network for steady incompressible flows. Physics of Fluids, 2023. paper

    Yang Xiao, Liming Yang, Yinjie Du, Yuxin Song, and Chang Shu.

  23. Long-term predictions of turbulence by implicit U-Net enhanced Fourier neural operator. Physics of Fluids, 2023. paper

    Zhijie Li, Wenhui Peng, Zelong Yuan, and Jianchun Wang.

  24. Physics-informed neural networks for parametric compressible Euler equations. arXiv, 2023. paper

    Simon Wassing, Stefan Langer, and Philipp Bekemeyer.

  25. Simulation of rarefied gas flows using physics-informed neural network combined with discrete velocity method. Physics of Fluids, 2023. paper

    Linying Zhang, Wenjun Ma, Qin Lou, and Jun Zhang.

  26. Influence of adversarial training on super-resolution turbulence models. arXiv, 2023. paper

    Ludovico Nista, Christoph David Karl Schumann, Mathis Bode, Temistocle Grenga, Jonathan F. MacArt, Antonio Attili, and Heinz Pitsch.

  27. Turbulent flow simulation using autoregressive conditional diffusion models. arXiv, 2023. paper

    Georg Kohl, Liwei Chen, and Nils Thuerey.

  28. Physics-informed neural networks for studying heat transfer in porous media. International Journal of Heat and Mass Transfer, 2023. paper

    Jiaxuan Xu, Han Wei, and Hua Bao.

  29. Solution multiplicity and effects of data and eddy viscosity on Navier-Stokes solutions inferred by physics-informed neural networks. arXiv, 2023. paper

    Zhicheng Wang, Xuhui Meng, Xiaomo Jiang, Hui Xiang, and George Em Karniadakis.

  30. Towards real-time training of physics-informed neural networks: Applications in ultrafast ultrasound blood flow imaging. arXiv, 2023. paper

    Haotian Guan, Jinping Dong, and Weining Lee.

  31. Multi-physical predictions in electro-osmotic micromixer by auto-encoder physics-informed neural networks. Physics of Fluids, 2023. paper

    Naiwen Chang, Ying Huai, Tingting Liu, Xi Chen, and Yuqi Jin.

  32. Studying turbulent flows with physics-informed neural networks and sparse data. International Journal of Heat and Fluid Flow, 2023. paper

    S. Hanrahan, M. Kozul, and R.D. Sandberg.

  33. Enhancing physics informed neural networks for solving Navier–Stokes equations. International Journal for Numerical Methods in Fluids, 2023. paper

    Ayoub Farkane, Mounir Ghogho, Mustapha Oudani, and Mohamed Boutayeb.

  34. Physics-informed tensor basis neural network for turbulence closure modeling. arXiv, 2023. paper

    Leon Riccius, Atul Agrawal, and Phaedon-Stelios Koutsourelakis.

  35. Investigation of low and high-speed fluid dynamics problems using physics-informed neural network. International Journal of Computational Fluid Dynamics, 2023. paper

    Anubhav Joshi,Alexandros Papados, and Rakesh Kumar.

  36. Singular layer physics informed neural network method for plane parallel flows. arXiv, 2023. paper

    Tengyuan Chang, Gungmin Gie, Youngjoon Hong, and Chang-Yeol Jung.

  37. Data-efficient operator learning for solving high Mach number fluid flow problems. arXiv, 2023. paper

    Noah Ford, Victor J. Leon, Honest Merman, Jeffrey Gilbert, and Alexander New.

  38. Three-dimensional laminar flow using physics informed deep neural networks featured. Physics of Fluids, 2023. paper

    Saykat Kumar Biswas and N. K. Anand.

  39. Real-time prediction of gas flow dynamics in diesel engines using a deep neural operator framework. Applied Intelligence, 2023. paper

    Varun Kumar, Somdatta Goswami, Daniel Smith, and George Em Karniadakis.

  40. Semi-analytic physics informed neural network for convection-dominated boundary layer problems in 2D. arXiv, 2023. paper

    Gungmin Gie, Youngjoon Hong, Chang-Yeol Jung, and Dongseok Lee.

  41. The improved backward compatible physics-informed neural networks for reducing error accumulation and applications in data-driven higher-order rogue waves. arXiv, 2023. paper

    Shuning Lin and Yong Chen.

  42. Learning characteristic parameters and dynamics of centrifugal pumps under multi-phase flow using physics-informed neural networks. arXiv, 2023. paper

    Felipe de Castro Teixeira Carvalho, Kamaljyoti Nath, Alberto Luiz Serpa, and George Em Karniadakis.

  43. On the locality of local neural operator in learning fluid dynamics. arXiv, 2023. paper

    Ximeng Ye, Hongyu Li, Jingjie Huang, and Guoliang Qin.

  44. Multi-viscosity physics-informed neural networks for generating ultra high resolution flow field data. International Journal of Computational Fluid Dynamics, 2023. paper

    Sen Zhang, Xiaowei Guo, Chao Li, Ran Zhao, Canqun Yang, Wei Wang, and Yanxu Zhong.

  45. Towards high-accuracy deep learning inference of compressible flows over aerofoils. Computers & Fluids, 2023. paper

    Liwei Chen and Nils Thuerey.

  46. Data-driven and physics-informed deep learning operators for solution of heat conduction equation with parametric heat source. International Journal of Heat and Mass Transfer, 2023. paper

    Seid Koric and Diab W. Abueidda.

  47. Energy-preserving reduced operator inference for efficient design and control. arXiv, 2024. paper

    Tomoki Koike and Elizabeth Qian.

  48. Variable linear transformation improved physics-informed neural networks to solve thin-layer flow problems. JCP, 2024. paper

    Jiahao Wu, Yuxin Wu, Guihua Zhang, and Yang Zhang.

  49. Riemannonets: Interpretable neural operators for Riemann problems. arXiv, 2024. paper

    Ahmad Peyvan, Vivek Oommen, Ameya D. Jagtap, and George Em Karniadakis.

  50. Physics-informed neural networks for incompressible flows with moving boundaries. Physics of Fluids, 2024. paper

    Yongzheng Zhu, Weizhen Kong, Jian Deng, and Xin Bian.

  51. Solving the one dimensional vertical suspended sediment mixing equation with arbitrary eddy diffusivity profiles using temporal normalized physics-informed neural networks. Physics of Fluids, 2024. paper

    Shaotong Zhang, Jiaxin Deng, Xi'an Li, Zixi Zhao, Jinran Wu, Weide Li,Yougan Wang, and Dongsheng Jeng.

  52. Neural SPH: Improved neural modeling of Lagrangian fluid dynamics. arXiv, 2024. paper

    Artur P. Toshev, Jonas A. Erbesdobler, Nikolaus A. Adams, and Johannes Brandstetter.

  53. Continuous and discontinuous compressible flows in a converging–diverging channel solved by physics-informed neural networks without exogenous data. Scientific Reports, 2024. paper

    Hong Liang, Zilong Song, Chong Zhao, and Xin Bian.

  54. Gauss-Newton natural gradient descent for physics-informed computational fluid dynamics. arXiv, 2024. paper

    Anas Jnini, Flavio Vella, and Marius Zeinhofer.

  55. Residual-enhanced physics-guided machine learning with hard constraints for subsurface flow in reservoir engineering. TGRS, 2024. paper

    Haibo Cheng, Yunpeng He, Peng Zeng, and Valeriy Vyatkin.

  56. Discovering artificial viscosity models for discontinuous Galerkin approximation of conservation laws using physics-informed machine learning. arXiv, 2024. paper

    Matteo Caldana, Paola F. Antonietti, and Luca Dede'.

  57. EuLagNet: Eulerian fluid prediction with Lagrangian dynamics. arXiv, 2024. paper

    Qilong Ma, Haixu Wu, Lanxiang Xing, Jianmin Wang, and Mingsheng Long.

  58. Physics-informed neural networks with domain decomposition for the incompressible Navier–Stokes equations. Physics of Fluids, 2024. paper

    Linyan Gu, Shanlin Qin, Lei Xu, and Rongliang Chen.

  59. Two-stage initial-value iterative physics-informed neural networks for simulating solitary waves of nonlinear wave equations. JCP, 2024. paper

    Jin Song, Ming Zhong, George Em Karniadakis, and Zhenya Yan.

  60. Continuous and discontinuous compressible flows in a converging–diverging channel solved by physics-informed neural networks without exogenous data. Scientific Reports, 2024. paper

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  61. A fast general thermal simulation model based on multi-branch physics-informed deep operator neural network. Physics of Fluids, 2024. paper

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  62. Potential of physics-informed neural networks for solving fluid flow problems with parametric boundary conditions. Physics of Fluids, 2024. paper

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  63. Physics-informed neural networks for transonic flow around a cylinder with high Reynolds number. Physics of Fluids, 2024. paper

    Xiang Ren, Peng Hu, Hua Su, Feizhou Zhang, and Huahua Yu.

  64. Physics-informed neural networks enhanced particle tracking velocimetry: An example for turbulent Jet flow. TIM, 2024. paper

    Shengze Cai, Callum Gray, and George Em Karniadakis.

  65. SPI-MIONet for surrogate modeling in phase-field hydraulic fracturing. CMAME, 2024. paper

    Xiaoqiang Wang, Peichao Li, Kaile Jia, Shaoqi Zhang, Chun Li, Bangchen Wu, Yilun Dong, and Detang Lu.

  66. Strategies for multi-case physics-informed neural networks for tube flows: A study using 2D flow scenarios. Scientific Reports, 2024. paper

    Hong Shen Wong, Wei Xuan Chan, Bing Huan Li, and Choon Hwai Yap.

  67. Physics-informed neural networks for fully non-linear free surface wave propagation. Physics of Fluids, 2024. paper

    Haocheng Lu, Qian Wang, Wenhao Tang, and Hua Liu.

  68. HelmFluid: Learning Helmholtz dynamics for interpretable fluid prediction. ICML, 2024. paper

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  70. From zero to turbulence: Generative modeling for 3D flow simulation. ICLR, 2024. paper

    Marten Lienen, David Lüdke, Jan Hansen-Palmus, and Stephan Günnemann.

  71. Enhancing the accuracy of physics-informed neural networks for indoor airflow simulation with experimental data and Reynolds-averaged Navier–Stokes turbulence model. Physics of Fluids, 2024. paper

    Chi Zhang, Chih-Yung Wen, Yuan Jia, Yu-Hsuan Juan, Yee-Ting Lee, Zhengwei Chen, An-Shik Yang, and Zhengtong Li.

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    Haocheng Lu, Qian Wang, Wenhao Tang, and Hua Liu.

  73. Neural network with local converging input for unstructured-grid computational fluid dynamics. AIAA Journal, 2024. paper

    Weiming Ding, Haoxiang Huang, Tzu-Jung Lee, Yingjie Liu, and Vigor Yang.

  74. Flow field reconstruction from sparse sensor measurements with physics-informed neural networks. Physics of Fluids, 2024. paper

    Mohammad Yasin Hosseini and Yousef Shiri.

  75. Weak baselines and reporting biases lead to overoptimism in machine learning for fluid-related partial differential equations. arXiv, 2024. paper

    Nick McGreivy and Ammar Hakim.

  76. Physics-informed machine learning of the correlation functions in bulk fluids. Physics of Fluids, 2024. paper

    Wenqian Chen, Peiyuan Gao, and Panos Stinis.

  77. Groundwater inverse modeling: Physics-informed neural network with disentangled constraints and errors. Journal of Hydrology, 2024. paper

    Yuzhe Ji, Yuanyuan Zha, Tian-Chyi J. Yeh, Liangsheng Shi, and Yanling Wang.

  78. Inferring turbulent velocity and temperature fields and their statistics from Lagrangian velocity measurements using physics-informed Kolmogorov-Arnold networks. arXiv, 2024. paper

    Juan Diego Toscano, Theo Käufer, Zhibo Wang, Martin Maxey, Christian Cierpka, and George Em Karniadakis.

  79. Physics-informed neural networks for advection–diffusion–Langmuir adsorption processes . Physics of Fluids, 2024. paper

    Bo Huang, Haobo Hua, Huan Han, Sensen He, Yuanye Zhou, Shuhong Liu, and Zhigang Zuo.

  1. Machine learning accelerated PDE backstepping observers. arXiv, 2022. paper

    Yuanyuan Shi, Zongyi Li, Huan Yu, Drew Steeves, Anima Anandkumar, and Miroslav Krstic.

  2. Neural solvers for fast and accurate numerical optimal control. NIPS, 2021. paper

    Federico Berto, Stefano Massaroli, Michael Poli, and Jinkyoo Park.

  3. Bellman neural networks for the class of optimal control problems with integral quadratic cost. TAI, 2022. paper

    Enrico Schiassi, Andrea D'Ambrosio, and Roberto Furfaro.

  4. Offline supervised learning vs online direct policy optimization: A comparative study and a unifie training paradigm for neural network-based optimal feedback control. arXiv, 2022. paper

    Yue Zhao and Jiequn Han.

  5. Policy evaluation and temporal–difference learning in continuous time and space: A martingale approach. JMLR, 2022. paper

    Yanwei Jia and Xunyu Zhou.

  6. Physics-informed kernel embeddings: Integrating prior system knowledge with data-driven control. arXiv, 2023. paper

    Adam J. Thorpe, Cyrus Neary, Franck Djeumou, Meeko M. K. Oishi, and Ufuk Topcu.

  7. Distributed control of partial differential equations using convolutional reinforcement learning. arXiv, 2023. paper

    Sebastian Peitz, Jan Stenner, Vikas Chidananda, Oliver Wallscheid, Steven L. Brunton, and Kunihiko Taira.

  8. Neural control of parametric solutions for high-dimensional evolution PDEs. arXiv, 2023. paper

    Nathan Gaby, Xiaojing Ye, and Haomin Zhou.

  9. Bridging physics-informed neural networks with reinforcement learning: Hamilton-Jacobi-Bellman proximal policy optimization (HJBPPO). arXiv, 2023. paper

    Amartya Mukherjee and Jun Liu.

  10. AONN: An adjoint-oriented neural network method for all-at-once solutions of parametric optimal control problems. arXiv, 2023. paper

    Pengfei Yin, Guangqiang Xiao, Kejun Tang, and Chao Yang.

  11. Neural operators for bypassing gain and control computations in PDE backstepping. arXiv, 2023. paper

    Luke Bhan, Yuanyuan Shi, and Miroslav Krstic.

  12. Neural operators of backstepping controller and observer gain functions for reaction-diffusion PDEs. arXiv, 2023. paper

    Miroslav Krstic, Luke Bhan, and Yuanyuan Shi.

  13. Leveraging multi-time Hamilton-Jacobi PDEs for certain scientific machine learning problems. arXiv, 2023. paper

    Paula Chen, Tingwei Meng, Zongren Zou, Jérôme Darbon, and George Em Karniadakis.

  14. Learning to control PDEs with differentiable physics. ICLR, 2020. paper

    Philipp Holl, Nils Thuerey, and Vladlen Koltun.

  15. A generalizable physics-informed learning framework for risk probability estimation. L4DC, 2020. paper

    Zhuoyuan Wang and Yorie Nakahira.

  16. Operator learning for nonlinear adaptive control. L4DC, 2023. paper

    Luke Bhan, Yuanyuan Shi and Miroslav Krstic.

  17. Optimal temperature trajectory for tubular reactor using physics informed neural networks. JCP, 2023. paper

    Rahul Patel, Sharad Bhartiya, and Ravindra Gudi.

  18. Physics-informed recurrent neural network modeling for predictive control of nonlinear processes. Journal of Process Control, 2023. paper

    Yingzhe Zheng, Cheng Hu, Xiaonan Wang, and Zhe Wu.

  19. **Physics-guided neural networks for inversion-based feedforward control applied to hybrid stepper motors.**arXiv, 2023. paper

    Daiwei Fan, Max Bolderman, Sjirk Koekebakker, Hans Butler, and Mircea Lazar.

  20. Physics-informed recurrent neural network modeling for predictive control of nonlinear processes. JCP, 2023. paper

    Yingzhe Zheng, Cheng Hu, Xiaonan Wang, and Zhe Wu.

  21. Optimal Dirichlet boundary control by Fourier neural operators applied to nonlinear optics. arXiv, 2023. paper

    Nils Margenberg, Franz X. Kärtner, and Markus Bause.

  22. Neural operators for delay-compensating control of hyperbolic PIDEs. arXiv, 2023. paper

    Jie Qi, Jing Zhang, and Miroslav Krstic.

  23. Physics-informed online learning of gray-box models by moving horizon estimation. European Journal of Control, 2023. paper

    Kristoffer Fink Løwenstein, Daniele Bernardini, Lorenzo Fagiano, and Alberto Bemporad.

  24. Online identification and control of PDEs via reinforcement learning methods. arXiv, 2023. paper

    Alessandro Alla, Agnese Pacifico, Michele Palladino, and Andrea Pesare.

  25. The hard-constraint PINNs for interface optimal control problems. arXiv, 2023. paper

    Ming-Chih Lai, Yongcun Song, Xiaoming Yuan, Hangrui Yue, and Tianyou Zeng.

  26. Deep learning of delay-compensated backstepping for reaction-diffusion PDEs. arXiv, 2023. paper

    Shanshan Wang, Mamadou Diagne, and Miroslav Krstić.

  27. Computationally efficient data-driven discovery and linear representation of nonlinear systems for control. arXiv, 2023. paper

    Madhur Tiwari, George Nehma, and Bethany Lusch.

  28. Physics-informed state-space neural networks for transport phenomena. arXiv, 2023. paper

    Akshay J Dave and Richard B. Vilim.

  29. A comparison of mesh-free differentiable programming and data-driven strategies for optimal control under PDE constraints. arXiv, 2023. paper

    Roussel Desmond Nzoyem, David A.W. Barton, and Tom Deakin.

  30. A data-driven tracking control framework using physics-informed neural networks and deep reinforcement learning for dynamical systems. JCP, 2023. paper

    R.R. Faria, B.D.O. Capron, A.R. Secchi, and M.B. De Souza Jr.

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    Paula Chen, Tingwei Meng, Zongren Zou, Jérôme Darbon, and George Em Karniadakis.

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    Jun Liu, Yiming Meng, Maxwell Fitzsimmons, and Ruikun Zhou.

  33. Taming waves: A physically-interpretable machine learning framework for realizable control of wave dynamics. arXiv, 2023. paper

    Tristan Shah, Feruza Amirkulova, and Stas Tiomkin.

  34. Neural operators for boundary stabilization of stop-and-go traffic. arXiv, 2023. paper

    Yihuai Zhang, Ruiguo Zhong, and Huan Yu.

  35. Neural operator approximations of backstepping kernels for 2×2 hyperbolic PDEs. arXiv, 2023. paper

    Shanshan Wang, Mamadou Diagne, and Miroslav Krstić.

  36. Lyapunov-based physics-informed long short-term memory (LSTM) neural network-based adaptive control. IEEE Control Systems Letters, 2023. paper

    Rebecca G. Hart, Emily J. Griffis, Omkar Sudhir Patil, and Warren E. Dixon.

  37. Gain scheduling with a neural operator for a transport PDE with nonlinear recirculation. arXiv, 2024. paper

    Maxence Lamarque, Luke Bhan, Rafael Vazquez, and Miroslav Krstic.

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  39. Adaptive neural-operator backstepping control of a benchmark hyperbolic PDE. arXiv, 2024. paper

    Maxence Lamarque, Luke Bhan, Yuanyuan Shi, and Miroslav Krstic.

  40. Physical-informed neural network for MPC-based trajectory tracking of vehicles with noise considered. TIV, 2024. paper

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    Nicolò Botteghi and Urban Fasel.

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  48. Generalizable physics-informed learning for stochastic safety-critical systems. arXiv, 2024. paper

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  1. FourCastNet: A global data-driven high-resolution weather model using adaptive Fourier neural operators. arXiv, 2022. paper

    Jaideep Pathak, Shashank Subramanian, Peter Harrington, Sanjeev Raja, Ashesh Chattopadhyay, Morteza Mardani, Thorsten Kurth, David Hall, Zongyi Li, Kamyar Azizzadenesheli, Pedram Hassanzadeh, Karthik Kashinath, and Animashree Anandkumar.

  2. Fourier neural operators for arbitrary resolution climate data downscaling. JMLR, 2023. paper

    Qidong Yang, Alex Hernandez-Garcia, Paula Harder, Venkatesh Ramesh, Prasanna Sattegeri, Daniela Szwarcman, Campbell D. Watson, and David Rolnick.

  3. Modelling atmospheric dynamics with spherical Fourier neural operators. ICLR, 2023. paper

    Boris Bonev, Thorsten Kurth, Christian Hundt, Jaideep Pathak, Maximilian Baust, Karthik Kashinath, and Anima Anandkumar.

  4. Spatiotemporal modeling of European paleoclimate using doubly sparse Gaussian processes. NIPS, 2022. paper

    Seth D. Axen, Alexandra Gessner, Christian Sommer, Nils Weitzel, and Álvaro Tejero-Cantero.

  5. ClimSim: An open large-scale dataset for training high-resolution physics emulators in hybrid multi-scale climate simulators. arXiv, 2023. paper

    Sungduk Yu, Walter M. Hannah, Liran Peng, Mohamed Aziz Bhouri, Ritwik Gupta, Jerry Lin, Björn Lütjens, Justus C. Will, Tom Beucler, Bryce E. Harrop, Benjamin R. Hillman, Andrea M. Jenney, Savannah L. Ferretti, Nana Liu, Anima Anandkumar, Noah D. Brenowitz, Veronika Eyring, Pierre Gentine, Stephan Mandt, Jaideep Pathak, Carl Vondrick, Rose Yu, Laure Zanna, Ryan P. Abernathey, Fiaz Ahmed, David C. Bader, Pierre Baldi, Elizabeth A. Barnes, Gunnar Behrens, Christopher S. Bretherton, Julius J. M. Busecke, Peter M. Caldwell, Wayne Chuang, Yilun Han, Yu Huang, Fernando Iglesias-Suarez, Sanket Jantre, Karthik Kashinath, Marat Khairoutdinov, Thorsten Kurth, Nicholas J. Lutsko, Po-Lun Ma, Griffin Mooers, J. David Neelin, David A. Randall, Sara Shamekh, Akshay Subramaniam, Mark A. Taylor, Nathan M. Urban, Janni Yuval, Guang J. Zhang, Tian Zheng, and Michael S. Pritchard.

  6. Seismic traveltime simulation for variable velocity models using physics-informed Fourier neural operator. arXiv, 2023. paper

    Chao Song, Tianshuo Zhao, Umair bin Waheed, and Cai Liu.

  7. DeepPhysiNet: Bridging deep learning and atmospheric physics for accurate and continuous weather modeling. arXiv, 2024. paper

    Wenyuan Li, Zili Liu, Keyan Chen, Hao Chen, Shunlin Liang, Zhengxia Zou, and Zhenwei Shi.

  8. Residual-enhanced physics-guided machine learning with hard constraints for subsurface flow in reservoir engineering. TGRS, 2024. paper

    Haibo Cheng, Yunpeng He, Peng Zeng, and Valeriy Vyatkin.

  1. Wavelet neural operator for solving parametric partial differential equations in computational mechanics problems. CMAME, 2023. paper

    Tapas Tripura and Souvik Chakraborty.

  2. Graph neural networks for airfoil design. arXiv, 2023. paper

    Florent Bonnet.

  3. Exact Dirichlet boundary physics-informed neural network EPINN for solid mechanics. CMAME, 2023. paper

    Jiaji Wang, Y.L. Mo, Bassam Izzuddin, and Chul-Woo Kim.

  4. Solving multi-material problems in solid mechanics using physics-informed neural networks based on domain decomposition technology. CMAME, 2023. paper

    Yu Diao, Jianchuan Yang, Ying Zhang, Dawei Zhang, and Yiming Du.

  5. A novel key performance analysis method for permanent magnet coupler using physics-informed neural networks. Engineering with Computers, 2023. paper

    Huayan Pu, Bo Tan, Jin Yi, Shujin Yuan, Jinglei Zhao, Ruqing Bai, and Jun Luo.

  6. Mechanical characterization and inverse design of stochastic architected metamaterials using neural operators. arXiv, 2023. paper

    Hanxun Jin, Enrui Zhang, Boyu Zhang, Sridhar Krishnaswamy, George Em Karniadakis, and Horacio D. Espinosa.

  7. A deep learning energy-based method for classical elastoplasticity. International Journal of Plasticity, 2023. paper

    Junyan He, Diab Abueidda, Rashid Abu Al-Ru, Seid Koric, and Iwona Jasiuk.

  8. Physics-informed neural networks for magnetostatic problems on axisymmetric transformer geometries. IEEE Journal of Emerging and Selected Topics in Industrial Electronics, 2023. paper

    Philipp Brendel, Vlad Medvedev, and Andreas Rosskopf.

  9. Neural born series operator for biomedical ultrasound computed tomography. arXiv, 2023. paper

    Zhijun Zeng, Yihang Zheng, Youjia Zheng, Yubing Li, Zuoqiang Shi, and He Sun.

  10. Learning thermoacoustic interactions in combustors using a physics-informed neural network. arXiv, 2024. paper

    Sathesh Mariappan, Kamaljyoti Nath, and George Em Karniadakis.

  11. Flight dynamic uncertainty quantification modeling using physics-informed neural networks. AIAA, 2024. paper

    Nathaniel Michek, Piyush Mehta, and Wade Huebsch.

  12. Peridynamic neural operators: A data-driven nonlocal constitutive model for complex material responses. arXiv, 2024. paper

    Siavash Jafarzadeh, Stewart Silling, Ning Liu, Zhongqiang Zhang, and Yue Yu.

  13. Stochastic dynamics of aircraft ground taxiing via improved physics-informed neural networks. Nonlinear Dynamics, 2024. paper

    Ying Zhang, Zhengrong Jin, Long Wang, Kaixin Zheng, and Wantao Jia.

  14. Damage identification for plate structures using physics-informed neural networks. MSSP, 2024. paper

    Wei Zhou and Yongfeng Xu.

  15. Quantification of gradient energy coefficients using physics-informed neural networks. International Journal of Mechanical Sciences, 2024. paper

    Lan Shang, Yunhong Zhao, Sizheng Zheng, Jin Wang, Tongyi Zhang, and Jie Wang.

  16. MPIPN: A multi physics-informed PointNet for solving parametric acoustic-structure systems. arXiv, 2024. paper

    Chu Wang, Jinhong Wu, Yanzhi Wang, Zhijian Zha, and Qi Zhou.

  17. A hierarchically normalized physics-informed neural network for solving differential equations: Application for solid mechanics problems. EAAI, 2024. paper

    Thang Le-Duc, Seunghye Lee, H. Nguyen-Xuan, and Jaehong Lee.

  18. Physics-informed machine learning using low-fidelity flowfields for inverse airfoil shape design. AIAA, 2024. paper

    Benjamin Y. J. Wong, Murali Damodaran, and Boo Cheong Khoo.

  19. A hard constraint and domain decomposition based physics-informed neural network framework for nonhomogeneous transient thermal analysis. TCPMT, 2024. paper

    Zengkai Wu, Li Jun Jiang, Sheng Sun, and Ping Li.

  20. Boundary integrated neural networks for 2D elastostatic and piezoelectric problems. IJMS, 2024. paper

    Peijun Zhang, Longtao Xie, Yan Gu, Wenzhen Qu, Shengdong Zhao, and Chuanzeng Zhang.

  21. Transferable machine learning model for the aerodynamic prediction of swept wings. Physics of Fluids, 2024. paper

    Yunjia Yang, Runze Li, Yufei Zhang, Lu Lu, and Haixin Chen.

  22. Data-driven methods for the inverse problem of suspension system excited by jump and diffusion stochastic track excitation. International Journal of Non-Linear Mechanics, 2024. paper

    Wantao Jia, Menglin Hu, Wanrong Zan, and Fei Ni.

  23. On Physics-Informed Neural Networks training for coupled hydro-poromechanical problems. JCP, 2024. paper

    Caterina Millevoi, Nicolò Spiezia, and Massimiliano Ferronato.

  1. Hybrid learning of time-series inverse dynamics models for locally isotropic robot motion. RAL, 2022. paper

    Tolga-Can Çallar and Sven Böttger.

  2. NTFields: Neural time fields for physics-informed robot motion planning. ICLR, 2023. paper

    Ruiqi Ni and Ahmed H Qureshi.

  3. Online parameter estimation using physics-informed deep learning for vehicle stability algorithms. arXiv, 2023. paper

    Kemal Koysuren, Ahmet Faruk Keles, and Melih Cakmakci.

  4. A locality-based neural solver for optical motion capture. SIGGRAPH, 2023. paper

    Xiaoyu Pan, Bowen Zheng, Xinwei Jiang, Guanglong Xu, Xianli Gu, Jingxiang Li, Qilong Kou, He Wang, Tianjia Shao, Kun Zhou, and Xiaogang Jin.

  5. Approximating high-dimensional minimal surfaces with physics-informed neural networks. arXiv, 2023. paper

    Steven Zhou and Xiaojing Ye.

  6. A spatial-temporally adaptive PINN framework for 3D bi-ventricular electrophysiological simulations and parameter inference. MICCAI, 2023. paper

    Yubo Ye, Huafeng Liu, Xiajun Jiang, Maryam Toloubidokhti, and Linwei Wang.

  7. Using the Transformer model for physical simulation: An application on transient thermal analysis for 3D printing process simulation. NIPS, 2023. paper

    Qian Chen, Luyang Kong, Florian Dugast, and Albert To.

  8. Physics-informed neural network for solution of forward and inverse kinematic wave problems. Journal of Hydrology, 2024. paper

    Qingzhi Hou, Yixin Li, Vijay P. Singh, Zewei Sun, and Jianguo Wei.

  9. PhyGrasp: Generalizing robotic grasping with physics-informed large multimodal models. arXiv, 2024. paper

    Dingkun Guo, Yuqi Xiang, Shuqi Zhao, Xinghao Zhu, Masayoshi Tomizuka, Mingyu Ding, and Wei Zhan.

  10. Structure-preserving operator learning: Modeling the collision operator of kinetic equations. arXiv, 2024. paper

    Jae Yong Lee, Steffen Schotthöfer, Tianbai Xiao, Sebastian Krumscheid, and Martin Frank.

  1. Dynamic weights enabled physics-informed neural network for simulating the mobility of engineered nano-particles in a contaminated aquifer. NIPS, 2022. paper

    Shikhar Nilabh and Fidel Grandia.

  2. Learning two-phase microstructure evolution using neural operators and autoencoder architectures. NPJ Computational Materials, 2022. paper

    Vivek Oommen, Khemraj Shukla, Somdatta Goswami, Rémi Dingreville, and George Em Karniadakis.

  3. Predicting glass structure by physics-informed machine learning. NPJ Computational Materials, 2022. paper

    Mikkel L. Bødker, Mathieu Bauchy, Tao Du, John C. Mauro, and Morten M. Smedskjaer.

  4. Physics-informed deep learning for solving phonon Boltzmann transport equation with large temperature non-equilibrium. NPJ Computational Materials, 2022. paper

    Ruiyang Li, Jianxun Wang, Eungkyu Lee, and Tengfei Luo.

  5. Design of Turing systems with physics-informed neural networks. arXiv, 2022. paper

    Jordon Kho, Winston Koh, Jian Cheng Wong, Pao-Hsiung Chiu, and Chin Chun Ooi.

  6. Spatio-temporal super-resolution of dynamical systems using physics-informed deep-learning. AAAI, 2023. paper

    Rajat Arora and Ankit Shrivastava.

  7. Rapid seismic waveform modeling and inversion with neural operators. TGRS, 2023. paper

    Yan Yang, Angela F. Gao, Kamyar Azizzadenesheli, Robert W. Clayton, and Zachary E. Ross.

  8. Accelerating heat exchanger design by combining Physics-Informed deep learning and transfer learning. Chemical Engineering Science, 2023. paper

    Zhiyong Wu, Bingjian Zhang, Haoshui Yu, Jingzheng Ren, Ming Pan, Chang He, and Qinglin Chen.

  9. Energy stable neural network for gradient flow equations. arXiv, 2023. paper

    Ganghua Fan, Tianyu Jin, Yuan Lan, Yang Xiang, and Luchan Zhang.

  10. Physics-informed neural network with transfer learning (TL-PINN) based on domain similarity measure for prediction of nuclear reactor transients. Scientific Reports, 2023. paper

    Konstantinos Prantikos, Stylianos Chatzidakis, Lefteri H. Tsoukalas, and Alexander Heifetz.

  11. Plasma surrogate modelling using Fourier neural operators. arXiv, 2023. paper

    Vignesh Gopakumar, Stanislas Pamela, Lorenzo Zanisi, Zongyi Li, Ander Gray, Daniel Brennand, Nitesh Bhatia, Gregory Stathopoulos, Matt Kusner, Marc Peter Deisenroth, Anima Anandkumar, JOREK Team, and MAST Team.

  12. Training a deep operator network as a surrogate solver for two-dimensional parabolic-equation models. Journal of the Acoustical Society of America, 2023. paper

    Liang Xu, Haigang Zhang, and Minghui Zhang.

  13. Grad-Shafranov equilibria via data-free physics informed neural networks. arXiv, 2023. paper

    Byoungchan Jang, Alan A. Kaptanoglu, Rahul Gaur, Shaw Pan, Matt Landreman, and William Dorland.

  14. Physics-informed deep learning of rate-and-state fault friction. arXiv, 2023. paper

    Cody Rucker and Brittany A. Erickson.

  15. Physics-informed neural networks with embedded analytical models: Inverse design of multilayer dielectric-loaded rectangular waveguide devices. IEEE Transactions on Microwave Theory and Techniques, 2023. paper

    Yinqing Pan, Ren Wang, and Bingzhong Wang.

  16. En-DeepONet: An enrichment approach for enhancing the expressivity of neural operators with applications to seismology. CMAME, 2023. paper

    Ehsan Haghighat, Umair bin Waheed, and George Karniadakis.

  17. Solving seismic wave equations on variable velocity models with Fourier neural operator. TGRS, 2023. paper

    Bian Li, Hanchen Wang, Shihang Feng, Xiu Yang, and Youzuo Lin.

  18. Calculating quasi-normal modes of Schwarzschild black holes with physics informed neural networks. arXiv, 2024. paper

    Nirmal Patel, Aycin Aykutalp, and Pablo Laguna.

  19. Deep neural operator-driven real-time inference to enable digital twin solutions for nuclear energy systems. Scientific Reports, 2024. paper

    Kazuma Kobayashi and Syed Bahauddin Alam.

  20. A physics-informed deep learning description of Knudsen layer reactivity reduction. arXiv, 2024. paper

    Christopher J. McDevitt and Xianzhu Tang.

  21. Inverse design method for horn antennas based on knowledge-embedded physics-informed neural networks. IEEE Antennas and Wireless Propagation Letters, 2024. paper

    Jinpin Liu, Bingzhong Wang, Chuan-Sheng Chen, and Ren Wang.

  22. Combined analysis of thermofluids and electromagnetism using physics-informed neural networks. EAAI, 2024. paper

    Yeonhwi Jeong, Junhyoung Jo, Tonghun Lee, and Jihyung Yoo.

  23. Fully convolutional network enhanced DeepONet-based surrogate of predicting the travel-time fields. TGRS, 2024. paper

    Yifan Mei, Yijie Zhang, Xueyu Zhu, Rongxi Gou, and Jinghuai Gao.

  24. Seismic wavefields modeling with variable horizontally-layered velocity models via velocity-encoded PINN. TGRS, 2024. paper

    Jingbo Zou, Cai Liu, Pengfei Zhao, and Chao Song.

  25. SPI-MIONet for surrogate modeling in phase-field hydraulic fracturing. CMAME, 2024. paper

    Xiaoqiang Wang, Peichao Li, Kaile Jia, Shaoqi Zhang, Chun Li, Bangchen Wu, Yilun Dong, and Detang Lu.

  26. A physics-informed neural networks modeling with coupled fluid flow and heat transfer – Revisit of natural convection in cavity. International Communications in Heat and Mass Transfer, 2024. paper

    Zahra Hashemi, Maysam Gholampour, Mingchang Wu, Tingya Liu, Chuanyi Liang, and Chichuan Wang.

  1. Learning to diffuse: A new perspective to design PDEs for visual analysis. TPAMI, 2016. paper

    Risheng Liu, Guangyu Zhong, Junjie Cao, Zhouchen Lin, Shiguang Shan, and Zhongxuan Luo.

  2. Reformulating optical flow to solve image-based inverse problems and quantify uncertainty. TPAMI, 2022. paper

    Aleix Boquet-Pujadas and Jean-Christophe Olivo-Marin.

  3. WarpPINN: Cine-MR image registration with physics-informed neural networks. arXiv, 2022. paper

    Pablo Arratia Lopez, Hernan Mella, Sergio Uribe, Daniel E. Hurtado, and Francisco Sahli Costabal.

  4. NODE-ImgNet: A PDE-informed effective and robust model for image denoising. arXiv, 2023. paper

    Xinheng Xie, Yue Wu, Hao Nib, and Cuiyu He.

  5. Microscopy image reconstruction with physics-informed denoising diffusion probabilistic model. arXiv, 2023. paper

    Rui Li, Gabriel della Maggiora, Vardan Andriasyan, Anthony Petkidis, Artsemi Yushkevich, Mikhail Kudryashev, and Artur Yakimovich.

  6. TGM-Nets: A deep learning framework for enhanced forecasting of tumor growth by integrating imaging and modeling. EAAI, 2023. paper

    Qijing Chen, Qi Ye, Weiqi Zhang, He Li, and Xiaoning Zheng.

  7. The use of physics-informed neural network approach to image restoration via nonlinear PDE tools. Computers & Mathematics with Applications, 2023. paper

    Neda Namaki, M.R. Eslahchi, and Rezvan Salehi.

  8. Personalized predictions of glioblastoma infiltration: Mathematical models, physics-informed neural networks and multimodal scans. arXiv, 2023. paper

    Ray Zirui Zhang, Ivan Ezhov, Michal Balcerak, Andy Zhu, Benedikt Wiestler, Bjoern Menze, and John Lowengrub.

  9. Real-time FJ/MAC PDE solvers via tensorized, back-propagation-free optical PINN training. arXiv, 2024. paper

    Yequan Zhao, Xian Xian, Xinling Yu, Ziyue Liu, Zhixiong Chen, Geza Kurczveil, Raymond G. Beausoleil, and Zheng Zhang.

  10. Performance of Fourier-based activation function in physics-informed neural networks for patient-specific cardiovascular flows. Computer Methods and Programs in Biomedicine, 2024. paper

    Arman Aghaee and M. Owais Khan.

  11. Effective medium properties of stealthy hyperuniform photonic structures using multiscale physics-informed neural networks. arXiv, 2024. paper

    Roberto Riganti, Yilin Zhu, Wei Cai, Salvatore Torquato, and Luca Dal Negro.

  1. Combustion chemistry acceleration with DeepONets. Fuel, 2024. paper

    Anuj Kumar and Tarek Echekki.

  1. Microstructure-sensitive deformation modeling and materials design with physics-informed neural networks. AIAA Journal, 2024. paper

    Mahmudul Hasan, Zekeriya Ender Eger, Arulmurugan Senthilnathan, and Pınar Acar.

  2. A novel Fourier neural operator framework for classification of multi-sized images: Application to three dimensional digital porous media. Physics of Fluids, 2024. paper

    Ali Kashefi and Tapan Mukerji.

  3. A fast learning-based surrogate of electrical machines using a reduced basis. ICML, 2024. paper

    Alejandro Ribés, Nawfal Benchekroun, and Théo Delagnes.

  4. Discontinuous Galerkin method with a novel physics-informed flux for elastic wave simulations in heterogeneous media. TGRS, 2024. paper

    Xijun He, Xueyuan Huang, Dinghui Yang, Jiandong Huang, and Yanjie Zhou.

  1. Symmetry-informed geometric representation for molecules, proteins, and crystalline materials. arXiv, 2023. paper

    Shengchao Liu, Weitao Du, Yanjing Li, Zhuoxinran Li, Zhiling Zheng, Chenru Duan, Zhiming Ma, Omar Yaghi, Anima Anandkumar, Christian Borgs, Jennifer Chayes, Hongyu Guo, and Jian Tang.

  2. Solving nonconvex energy minimization problems in martensitic phase transitions with a mesh-free deep learning approach. CMAME, 2023. paper

    Xiaoli Chen, Phoebus Rosakis, Zhizhang Wu, and Zhiwen Zhang.

  3. A physics-guided bi-fidelity Fourier-featured operator learning framework for predicting time evolution of drag and lift coefficients. arXiv, 2023. paper

    Amirhossein Mollaali, Izzet Sahin, Iqrar Raza, Christian Moya, Guillermo Paniagua, and Guang Lin.

  4. Mixed form based physics-informed neural networks for performance evaluation of two-phase random materials. EAAI, 2023. paper

    Xiaodan Ren and Xianrui Lyu.

  5. Deep learning based solution of nonlinear partial differential equations arising in the process of arterial blood flow. Mathematics and Computers in Simulation, 2023. paper

    Bivas Bhaumik, Soumen De, and Satyasaran Changdar.

  6. Physics-informed neural networks for solving dynamic two-phase interface problems. SIAM Journal on Scientific Computing, 2023. paper

    Xingwen Zhu, Xiaozhe Hu, and Pengtao Sun.

  7. Rethinking materials simulations: Blending direct numerical simulations with neural operators. arXiv, 2023. paper

    Vivek Oommen, Khemraj Shukla, Saaketh Desai, Remi Dingreville, and George Em Karniadakis.

  8. A conservative hybrid physics-informed neural network method for Maxwell-Ampère-Nernst-Planck equations. arXiv, 2023. paper

    Cheng Chang, Zhouping Xin, and Tieyong Zeng.

  9. A data-driven physics-constrained deep learning computational framework for solving von Mises plasticity. EAAI, 2023. paper

    Arunabha M. Roy and Suman Guha.

  10. Learning stiff chemical kinetics using extended deep neural operators. CMAME, 2024. paper

    Somdatta Goswami, Ameya D. Jagtap, Hessam Babaee, Bryan T. Susi, and George Em Karniadakis.

  11. Deep-learning based parameter identification enables rationalization of battery material evolution in complex electrochemical systems. Journal of Computational Science, 2023. paper

    Ivonne Sgura, Luca Mainetti, Francesco Negro, Maria Grazia Quarta, and Benedetto Bozzini.

  12. AI-aided geometric design of anti-infection catheters. Science Advances, 2023. paper

    Tingtao Zhou, Xuan Wan, Daniel Zhengyu Huang, Zongyi Li, Zhiwei Peng, Anima Anandkumar, John F. Brady, Paul W. Sternberg, and Chiara Daraio.

  13. Physics-informed deep learning to solve three-dimensional Terzaghi’s consolidation equation: Forward and inverse problems. arXiv, 2024. paper

    Biao Yuan, Ana Heitor, He Wang, and Xiaohui Chen.

  14. Solving the discretised multiphase flow equations with interface capturing on structured grids using machine learning libraries. arXiv, 2024. paper

    Boyang Chen, Claire E. Heaney, Jefferson L. M. A. Gomes, Omar K. Matar, and Christopher C. Pain.

  15. Combustion chemistry acceleration with DeepONets. Fuel, 2024. paper

    Anuj Kumar and Tarek Echekki.

  16. Identifying heterogeneous micromechanical properties of biological tissues via physics-informed neural networks. arXiv, 2024. paper

    Wensi Wu, Mitchell Daneker, Kevin T. Turner, Matthew A. Jolley, and Lu Lu.

  17. Adaptive data-driven deep-learning surrogate model for frontal polymerization in dicyclopentadiene. The Journal of Physical Chemistry B, 2024. paper

    Qibang Liu, Diab Abueidda, Sagar Vyas, Yuan Gao, Seid Koric, and Philippe H. Geubelle.

  1. Physics-informed neural network for lithium-ion battery degradation stable modeling and prognosis. NC, 2024. paper

    Fujin Wang, Zhi Zhai, Zhibin Zhao, Yi Di, and Xuefeng Chen.

  1. Physics-informed neural networks for quantum eigenvalue problems. IJCNN, 2022. paper

    Henry Jin, Marios Mattheakis, and Pavlos Protopapas.

  2. Quantum-inspired tensor neural networks for partial differential equations. arXiv, 2022. paper

    Raj Patel, Chia-Wei Hsing, Serkan Sahin, Saeed S. Jahromi, Samuel Palmer, Shivam Sharma, Christophe Michel, Vincent Porte, Mustafa Abid, Stephane Aubert, Pierre Castellani, Chi-Guhn Lee, Samuel Mugel, and Roman Orus.

  3. Quantum Fourier networks for solving parametric PDEs. arXiv, 2023. paper

    Nishant Jain, Jonas Landman, Natansh Mathur, and Iordanis Kerenidis.

  4. Q-Flow: Generative modeling for differential equations of open quantum dynamics with normalizing flows. ICML, 2023. paper

    Owen M Dugan, Peter Y. Lu, Rumen Dangovski, Di Luo, and Marin Soljacic.

  5. Physics-informed quantum machine learning: Solving nonlinear differential equations in latent spaces without costly grid evaluations. arXiv, 2023. paper

    Annie E. Paine, Vincent E. Elfving, and Oleksandr Kyriienko.

  6. Physics-informed quantum machine learning for solving partial differential equations. arXiv, 2023. paper

    Abhishek Setty, Rasul Abdusalamov, and Mikhail Itskov.

  1. Approximating discontinuous Nash equilibria values of two-player general-sum differential games. arXiv, 2022. paper

    Lei Zhang, Mukesh Ghimire, Wenlong Zhang, Zhe Xu, and Yi Ren.

  2. Solving two-player general-sum games between swarms. arXiv, 2023. paper

    Mukesh Ghimire, Lei Zhang, Wenlong Zhang, Yi Ren, and Zhe Xu.

  3. Value approximation for two-player general-sum differential games with state constraints. arXiv, 2023. paper

    Lei Zhang, Mukesh Ghimire, Wenlong Zhang, Zhe Xu, and Yi Ren.

  4. Unsupervised solution operator learning for mean-field games via sampling-invariant parametrizations. arXiv, 2024. paper

    Han Huang and Rongjie Lai.

  5. Pontryagin neural operator for solving general-sum differential games with parametric state constraints. L4DC, 2024. paper

    Lei Zhang, Mukesh Ghimire, Zhe Xu, Wenlong Zhang, and Yi Ren.

  1. Physics-aware machine learning surrogates for real-time manufacturing digital twin. Manufacturing Letters, 2022. paper

    Aditya Balu, Soumik Sarkar, Baskar Ganapathysubramanian, and Adarsh Krishnamurthy.

  2. Multi-scale digital twin: Developing a fast and physics-informed surrogate model for groundwater contamination with uncertain climate models. arXiv, 2022. paper

    Lijing Wang, Takuya Kurihana, Aurelien Meray, Ilijana Mastilovic, Satyarth Praveen, Zexuan Xu, Milad Memarzadeh, Alexander Lavin, and Haruko Wainwright.

  3. SciAI4Industry--Solving PDEs for industry-scale problems with deep learning. arXiv, 2022. paper

    Philipp A. Witte, Russell J. Hewett, Kumar Saurabh, AmirHossein Sojoodi, and Ranveer Chandra.

  4. Operator learning framework for digital twin and complex engineering systems. arXiv, 2023. paper

    Kazuma Kobayashi, James Daniell, and Syed B. Alam.

  5. Towards solving industry-grade surrogate modeling problems using physics informed machine learning. arXiv, 2023. paper

    Saakaar Bhatnagar, Andrew Comerford, and Araz Banaeizadeh.

  6. Data-driven physics-informed neural networks: A digital twin perspective. arXiv, 2024. paper

    Sunwoong Yang, Hojin Kim, Yoonpyo Hong, Kwanjung Yee, Romit Maulik, and Namwoo Kang.

  7. Physically informed synchronic-adaptive learning for industrial systems modeling in heterogeneous media with unavailable time-varying interface. arXiv, 2024. paper

    Aina Wang, Pan Qin, and Ximing Sun.

  8. Improved generalization with deep neural operators for engineering systems: Path towards digital twin. EAAI, 2024. paper

    Kazuma Kobayashi, James Daniell, and Syed Bahauddin Alam.

  9. A deep transfer operator learning method for temperature field reconstruction in a lithium-ion battery pack. TII, 2024. paper

    Yuchen Wang, Can Xiong, Changjiang Ju, Genke Yang, Yuwang Chen, and Xiaotian Yu.

  10. ro-PINN: A reduced order physics-informed neural network for solving the macroscopic model of pedestrian flows. Transportation Research Part C: Emerging Technologies, 2024. paper

    Renbin Pan, Feng Xiao, and Minyu Shen.

  1. A deep learning based numerical PDE method for option pricing. Computational Economics, 2023. paper

    Xiang Wang, Jessica Li, and Jichun Li.

  1. Occupancy networks: Learning 3D reconstruction in function space. CVPR, 2019. paper

    Lars Mescheder, Michael Oechsle, Michael Niemeyer, Sebastian Nowozin, and Andreas Geiger.

  2. Transfer learning for flow reconstruction based on multifidelity data. AIAA Journal, 2022. paper

    Jiaqing Kou, Chenjia Ning, and Weiwei Zhang.

  3. Learning-based state reconstruction for a scalar hyperbolic PDE under noisy lagrangian sensing. L4DC, 2022. paper

    Matthieu Barreau, John Liu, and Karl Henrik Johansson.

  1. A novel physics-informed neural network for modeling electromagnetism of a permanent magnet synchronous motor. Advanced Engineering Informatics, 2023. paper

    Seho Son, Hyunseung Lee, Dayeon Jeong, Ki-Yong Oh, and Kyung Ho Sun.

  2. A novel key performance analysis method for permanent magnet coupler using physics informed neural networks. Engineering with Computer, 2023. paper

    Huayan Pu, Bo Tan, Jin Yi, Shujin Yuan, Jinglei Zhao, Ruqing Bai, and Jun Luo .

  3. Physics-informed neural networks for solving parametric magnetostatic problems. TEC, 2023. paper

    Andrés Beltrán-Pulido, Ilias Bilionis, and Dionysios Aliprantis.

  4. Physics-informed neural networks for solving 2-D magnetostatic fields. TMAG, 2023. paper

    Zhi Gong, Yang Chu, and Shiyou Yang.

  5. Physics-informed sparse neural network for permanent magnet eddy current device modeling and analysis. LMAG, 2023. paper

    Dazhi Wang, Sihan Wang, Deshan Kong, Jiaxing Wang, Wenhui Li, and Michael Pecht

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