graph neural operator

[YichengDWu]

The implemented graph neural operator

is not the same one in the original paper

Is this intentional?

[yuehhua]

You can check the equation again. In paper, it defines

$$ e(x,y) = [v_t(x), v_t(y)] $$

[YichengDWu]

I only see

in the paper Neural Operator: Graph Kernel Network for Partial Differential Equations. Which one are you refering to?

[yuehhua]

I was supposed to think of $a(x)$ as node feature, and it lacks the coordinates here.

[YichengDWu]

$a(x)$ is not the trainable node embeddings but the nontrainable input function. If you are learning the operator from the initial condition to the solution at $t$, then $a(x)=u(0,x)$

[yuehhua]

Good! It can be fixed.

[YichengDWu]

Also note the output of the net is reshaped to be a matrix. It is in fact the NNConv as mentioned in the paper

[yuehhua]

Oh! I also missed this point.

[yuehhua]

@MilkshakeForReal You can check it if it is right.

[YichengDWu]

It looks good.