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DataSet.py
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DataSet.py
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import numpy as np
import tensorflow as tf
class DataSet:
def __init__(self, x_range, y_range, t_range, Nx, Ny, Nt, N_bc):
self.x_range = x_range
self.y_range = y_range
self.t_range = t_range
self.Nx = Nx
self.Ny = Ny
self.Nt = Nt
self.N_bc = N_bc
self.e = np.array([[0., 0.], [1., 0.], [0., 1.], [-1., 0.], [0., -1.], [1., 1.], [-1., 1.], [-1., -1.], [1., -1.]])
self.w = np.full((9, 1), 0.0)
self.w[0] = 4 / 9
self.w[1:5] = 1 / 9
self.w[5:] = 1 / 36
self.RT = 100
self.xi = self.e * np.sqrt(3 * self.RT)
self.nu = 0.01
self.tau = self.nu / self.RT
self.sess = tf.Session()
self.x_l = self.x_range.min()
self.x_u = self.x_range.max()
self.y_l = self.y_range.min()
self.y_u = self.y_range.max()
def feq_gradient(self, rou, u, v, x, y, t):
rou_x = tf.gradients(rou, x)[0]
u_x = tf.gradients(u, x)[0]
v_x = tf.gradients(v, x)[0]
rou_y = tf.gradients(rou, y)[0]
u_y = tf.gradients(u, y)[0]
v_y = tf.gradients(v, y)[0]
rou_t = tf.gradients(rou, t)[0]
u_t = tf.gradients(u, t)[0]
v_t = tf.gradients(v, t)[0]
f_sum = self.feq_xy(rou, u, v, rou_x, rou_y, rou_t, u_x, v_x, u_y, v_y, u_t, v_t)
return f_sum
# concat of dfeq / dX
def feq_xy(self, rou, u, v, rou_x, rou_y, rou_t, u_x, v_x, u_y, v_y, u_t, v_t):
f_sum = self.dfeq_xy(rou, u, v, rou_x, rou_y, rou_t, u_x, v_x, u_y, v_y, u_t, v_t, 0)
for i in range(1, 9):
f_ = self.dfeq_xy(rou, u, v, rou_x, rou_y, rou_t, u_x, v_x, u_y, v_y, u_t, v_t, i)
f_sum = tf.concat([f_sum, f_], 1)
return f_sum
# difference of f_eq for x, y
def dfeq_xy(self, rou, u, v, rou_x, rou_y, rou_t, u_x, v_x, u_y, v_y, u_t, v_t, i):
feq_x = self.w[i, :] * rou_x * (1 + (self.xi[i, 0] * u + self.xi[i, 1] * v) / self.RT + (self.xi[i, 0] * u + self.xi[i, 1] * v) ** 2 / 2 / self.RT ** 2 - (u ** 2 + v ** 2) / 2 / self.RT) + \
self.w[i, :] * rou * ((self.xi[i, 0] * u_x + self.xi[i, 1] * v_x) / self.RT + (self.xi[i, 0] * u + self.xi[i, 1] * v) * (self.xi[i, 0] * u_x + self.xi[i, 1] * v_x) / self.RT ** 2 - (u * u_x + v * v_x) / self.RT)
# here need to change the equations
feq_y = self.w[i, :] * rou_y * (1 + (self.xi[i, 0] * u + self.xi[i, 1] * v) / self.RT + (self.xi[i, 0] * u + self.xi[i, 1] * v) ** 2 / 2 / self.RT ** 2 - (u ** 2 + v ** 2) / 2 / self.RT) + \
self.w[i, :] * rou * ((self.xi[i, 0] * u_y + self.xi[i, 1] * v_y) / self.RT + (self.xi[i, 0] * u + self.xi[i, 1] * v) * (self.xi[i, 0] * u_y + self.xi[i, 1] * v_y) / self.RT ** 2 - (u * u_y + v * v_y) / self.RT)
feq_t = self.w[i, :] * rou_t * (1 + (self.xi[i, 0] * u + self.xi[i, 1] * v) / self.RT + (self.xi[i, 0] * u + self.xi[i, 1] * v) ** 2 / 2 / self.RT ** 2 - (u ** 2 + v ** 2) / 2 / self.RT) + \
self.w[i, :] * rou * ((self.xi[i, 0] * u_t + self.xi[i, 1] * v_t) / self.RT + (self.xi[i, 0] * u + self.xi[i, 1] * v) * (self.xi[i, 0] * u_t + self.xi[i, 1] * v_t) / self.RT ** 2 - (u * u_t + v * v_t) / self.RT)
dfeq_xy = self.xi[i, 0] * feq_x + self.xi[i, 1] * feq_y + feq_t
return dfeq_xy
# concat of f_eq_i
def f_eq(self, rou, u, v):
f_eq_sum = self.f_eqk(rou, u, v, 0)
for i in range(1, 9):
f_eq = self.f_eqk(rou, u, v, i)
f_eq_sum = tf.concat([f_eq_sum, f_eq], 1)
return f_eq_sum
# f_eq equation
def f_eqk(self, rou, u, v, k):
f_eqk = self.w[k, :] * rou * (1 + (self.xi[k, 0]*u + self.xi[k, 1]*v) / self.RT + (self.xi[k, 0]*u + self.xi[k, 1]*v) ** 2 / 2 / self.RT ** 2 - (u*u + v*v) / 2 / self.RT)
return f_eqk
# the mean pde
def bgk(self, f_neq, rou, u, v, x, y, t):
feq_pre = self.feq_gradient(rou, u, v, x, y, t)
R_sum = 0
for k in range(9):
fneq_x = tf.gradients(f_neq[:, k][:, None], x)[0]
fneq_y = tf.gradients(f_neq[:, k][:, None], y)[0]
fneq_t = tf.gradients(f_neq[:, k][:, None], t)[0]
R = (fneq_t + self.xi[k, 0] * fneq_x + self.xi[k, 1] * fneq_y + feq_pre[:, k][:, None] + 1 / self.tau * (f_neq[:, k][:, None])) ** 2
R_sum = R_sum + R
return R_sum
# the equation residual
def Eq_res(self, f_neq, rou, u, v, x, y, t):
feq_pre = self.feq_gradient(rou, u, v, x, y, t)
Eq_sum = x * 0
for k in range(9):
fneq_x = tf.gradients(f_neq[:, k][:, None], x)[0]
fneq_y = tf.gradients(f_neq[:, k][:, None], y)[0]
fneq_t = tf.gradients(f_neq[:, k][:, None], t)[0]
Eq = tf.abs(fneq_t + self.xi[k, 0] * fneq_x + self.xi[k, 1] * fneq_y + feq_pre[:, k][:, None] + 1 / self.tau * (f_neq[:, k][:, None]))
Eq_sum = tf.concat([Eq_sum, Eq], 1)
return Eq_sum[:, 1:]
# boundary condition
def inward_judge(self, x, y):
x = tf.where(tf.equal(x, 2.0), x * 0 - 3.0, x)
x = tf.where(tf.equal(x, -0.5), x * 0 + 3.0, x)
x = tf.where(tf.equal(tf.abs(x), 3.0), x / 3.0, x * 0.0)
y = tf.where(tf.equal(y, 1.5), y * 0 - 3.0, y)
y = tf.where(tf.equal(y, -0.5), y * 0 + 3.0, y)
y = tf.where(tf.equal(tf.abs(y), 3.0), y / 3.0, y * 0.0)
return x, y
def bgk_cond(self, f_neq, rou, u, v, x, y, t):
feq_pre = self.feq_gradient(rou, u, v, x, y, t)
R_sum = 0
for k in range(9):
fneq_x = tf.gradients(f_neq, x)[0]
fneq_y = tf.gradients(f_neq, y)[0]
fneq_t = tf.gradients(f_neq, t)[0]
R = (fneq_t + self.xi[k, 0] * fneq_x + self.xi[k, 1] * fneq_y + feq_pre[:, k][:, None] + 1 / self.tau * (f_neq[:, k][:, None])) ** 2
R_sum = R_sum + R
return R_sum
def fBC(self, f_neq, rou, u, v, x_bc, y_bc, t_bc):
feq_ex = self.Ex_fneq_(rou, u, v, x_bc, y_bc, t_bc)
fbc_sum = 0
for i in range(9):
f = (f_neq[:, i][:, None] + self.tau * feq_ex[:, i][:, None]) ** 2
fbc_sum = fbc_sum + f
return fbc_sum
def u_train(self, x, y, t):
u = - np.cos(x) * np.sin(y) * np.exp(-2 * t * self.nu)
return u
def v_train(self, x, y, t):
v = np.sin(x) * np.cos(y) * np.exp(-2 * t * self.nu)
return v
def p_func(self, x, y, t):
p = -0.25 * (np.cos(2 * x) + np.cos(2 * y)) * np.exp(-4 * t * self.nu) + self.RT
return p
def rou_func(self, x, y, t):
rou = self.p_func(x, y, t) / self.RT
return rou
def Ex_fneq_(self, rou, u, v, x, y, t):
rou_x = (0.5 * np.sin(2 * x) * np.exp(-4 * t * self.nu)) / self.RT
rou_y = (0.5 * np.sin(2 * y) * np.exp(-4 * t * self.nu)) / self.RT
rou_t = ((np.cos(2 * x) + np.cos(2 * y)) * np.exp(-4 * t * self.nu)) / self.RT
u_x = np.sin(x) * np.sin(y) * np.exp(-2 * t * self.nu)
u_y = -np.cos(x) * np.cos(y) * np.exp(-2 * t * self.nu)
u_t = 2 * self.nu * np.cos(x) * np.sin(y) * np.exp(-2 * t * self.nu)
v_x = np.cos(x) * np.cos(y) * np.exp(-2 * t * self.nu)
v_y = -np.sin(x) * np.sin(y) * np.exp(-2 * t * self.nu)
v_t = -2 * self.nu * np.sin(x) * np.cos(y) * np.exp(-2 * t * self.nu)
f_sum = self.feq_xy(rou, u, v, rou_x, rou_y, rou_t, u_x, v_x, u_y, v_y, u_t, v_t)
f_sum = tf.cast(f_sum, dtype=tf.float32)
return f_sum
def Ex_func(self, x_star, y_star, t_star):
u = self.u_train(x_star, y_star, t_star)
v = self.v_train(x_star, y_star, t_star)
rou = self.rou_func(x_star, y_star, t_star)
f_eq = self.f_eq(rou, u, v)
# excat gradient need to change
f_neq = -self.tau * (self.Ex_fneq_(rou, u, v, x_star, y_star, t_star))
f_neq = tf.cast(f_neq, dtype=tf.float64)
f_i = f_neq + f_eq
# tensor change to array
f_eq = f_eq.eval(session=self.sess)
f_neq = f_neq.eval(session=self.sess)
f_i = f_i.eval(session=self.sess)
return u, v, f_eq, f_neq, f_i
def Data_Generation(self):
x_l = self.x_range.min()
x_u = self.x_range.max()
y_l = self.y_range.min()
y_u = self.y_range.max()
t_l = self.t_range.min()
t_u = self.t_range.max()
# domain data
x_data = np.random.random((16000, 1)) * (x_u - x_l) + x_l
y_data = np.random.random((16000, 1)) * (y_u - y_l) + y_l
t_data = np.random.random((16000, 1)) * (t_u - t_l) + t_l
# initial condition data
x_ini = np.linspace(self.x_range[0], self.x_range[1], self.Nx)
y_ini = np.linspace(self.y_range[0], self.y_range[1], self.Ny)
x_ini, y_ini = np.meshgrid(x_ini, y_ini)
x_ini = np.ravel(x_ini).T[:, None]
y_ini = np.ravel(y_ini).T[:, None]
t_ini = np.zeros_like(x_ini)
# boundary condition data
"""x_1 = (x_u - x_l) * np.random.random((300, 1)) + x_l
x_2 = (x_u - x_l) * np.random.random((300, 1)) + x_l
x_3 = np.full((300, 1), -0.5)
x_4 = np.full((300, 1), 2)
y_1 = np.full((300, 1), -0.5)
y_2 = np.full((300, 1), 1.5)
y_3 = (y_u - y_l) * np.random.random((300, 1)) + y_l
y_4 = (y_u - y_l) * np.random.random((300, 1)) + y_l
x_b = np.vstack((x_1, x_2, x_3, x_4))
y_b = np.vstack((y_1, y_2, y_3, y_4))"""
# y = pi
x_1 = np.linspace(self.x_range[0], self.x_range[1], self.N_bc)
t_1 = np.linspace(self.t_range[0], self.t_range[1], self.N_bc)
x_1, t_1 = np.meshgrid(x_1, t_1)
x_1 = np.ravel(x_1).T[:, None]
t_1 = np.ravel(t_1).T[:, None]
y_1 = np.ones_like(x_1) * np.pi
# y = - pi
x_2 = np.linspace(self.x_range[0], self.x_range[1], self.N_bc)
t_2 = np.linspace(self.t_range[0], self.t_range[1], self.N_bc)
x_2, t_2 = np.meshgrid(x_2, t_2)
x_2 = np.ravel(x_2).T[:, None]
t_2 = np.ravel(t_2).T[:, None]
y_2 = np.ones_like(x_2) * (-np.pi)
# x = - pi
y_3 = np.linspace(self.y_range[0], self.y_range[1], self.N_bc)
t_3 = np.linspace(self.t_range[0], self.t_range[1], self.N_bc)
y_3, t_3 = np.meshgrid(y_3, t_3)
y_3 = np.ravel(y_3).T[:, None]
t_3 = np.ravel(t_3).T[:, None]
x_3 = np.ones_like(y_3) * (-np.pi)
# x = pi
y_4 = np.linspace(self.y_range[0], self.y_range[1], self.N_bc)
t_4 = np.linspace(self.t_range[0], self.t_range[1], self.N_bc)
y_4, t_4 = np.meshgrid(y_4, t_4)
y_4 = np.ravel(y_4).T[:, None]
t_4 = np.ravel(t_4).T[:, None]
x_4 = np.ones_like(y_4) * np.pi
x_b = np.vstack((x_1, x_2, x_3, x_4))
y_b = np.vstack((y_1, y_2, y_3, y_4))
t_b = np.vstack((t_1, t_2, t_3, t_4))
u_b = self.u_train(x_b, y_b, t_b)
v_b = self.v_train(x_b, y_b, t_b)
rou_b = self.rou_func(x_b, y_b, t_b)
u_ini = self.u_train(x_ini, y_ini, t_ini)
v_ini = self.v_train(x_ini, y_ini, t_ini)
rou_ini = self.rou_func(x_ini, y_ini, t_ini)
return x_data, y_data, t_data, x_ini, y_ini, t_ini, x_b, y_b, t_b, u_b, v_b, rou_b, u_ini, v_ini, rou_ini