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train_poisson_fno.py
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import os
import time
from os.path import expanduser
from phi.torch.flow import *
import numpy as np
import torch
import torch.nn as nn
import torch.nn.functional as F
assert TORCH.set_default_device('GPU')
class SpectralConv2d(nn.Module):
def __init__(self, in_channels, out_channels, modes1, modes2):
super(SpectralConv2d, self).__init__()
"""
2D Fourier layer. It does FFT, linear transform, and Inverse FFT.
"""
self.in_channels = in_channels
self.out_channels = out_channels
self.modes1 = modes1 # Number of Fourier modes to multiply, at most floor(N/2) + 1
self.modes2 = modes2
self.scale = (1 / (in_channels * out_channels))
self.weights1 = nn.Parameter(
self.scale * torch.rand(in_channels, out_channels, self.modes1, self.modes2, dtype=torch.cfloat))
self.weights2 = nn.Parameter(
self.scale * torch.rand(in_channels, out_channels, self.modes1, self.modes2, dtype=torch.cfloat))
# Complex multiplication
def compl_mul2d(self, input, weights):
# (batch, in_channel, x,y ), (in_channel, out_channel, x,y) -> (batch, out_channel, x,y)
return torch.einsum("bixy,ioxy->boxy", input, weights)
def forward(self, x):
batchsize = x.shape[0]
# Compute Fourier coeffcients up to factor of e^(- something constant)
x_ft = torch.fft.rfft2(x)
# Multiply relevant Fourier modes
out_ft = torch.zeros(batchsize, self.out_channels, x.size(-2), x.size(-1) // 2 + 1, dtype=torch.cfloat,
device=x.device)
out_ft[:, :, :self.modes1, :self.modes2] = \
self.compl_mul2d(x_ft[:, :, :self.modes1, :self.modes2], self.weights1)
out_ft[:, :, -self.modes1:, :self.modes2] = \
self.compl_mul2d(x_ft[:, :, -self.modes1:, :self.modes2], self.weights2)
# Return to physical space
x = torch.fft.irfft2(out_ft, s=(x.size(-2), x.size(-1)))
return x
class FNO2d(nn.Module):
def __init__(self, in_features, out_features, modes1, modes2, width):
super(FNO2d, self).__init__()
"""
The overall network. It contains 4 layers of the Fourier layer.
1. Lift the input to the desire channel dimension by self.fc0 .
2. 4 layers of the integral operators u' = (W + K)(u).
W defined by self.w; K defined by self.conv .
3. Project from the channel space to the output space by self.fc1 and self.fc2 .
input: the solution of the coefficient function and locations (a(x, y), x, y)
input shape: (batchsize, x=s, y=s, c=3)
output: the solution
output shape: (batchsize, x=s, y=s, c=1)
"""
self.modes1 = modes1
self.modes2 = modes2
self.width = width
self.padding = 9 # pad the domain if input is non-periodic
self.fc0 = nn.Linear(3, self.width) # input channel is 3: (a(x, y), x, y)
self.conv0 = SpectralConv2d(self.width, self.width, self.modes1, self.modes2)
self.conv1 = SpectralConv2d(self.width, self.width, self.modes1, self.modes2)
self.conv2 = SpectralConv2d(self.width, self.width, self.modes1, self.modes2)
self.conv3 = SpectralConv2d(self.width, self.width, self.modes1, self.modes2)
self.w0 = nn.Conv2d(self.width, self.width, 1)
self.w1 = nn.Conv2d(self.width, self.width, 1)
self.w2 = nn.Conv2d(self.width, self.width, 1)
self.w3 = nn.Conv2d(self.width, self.width, 1)
self.fc1 = nn.Linear(self.width, 128)
self.fc2 = nn.Linear(128, out_features)
def forward(self, x):
x = torch.permute(x, (0, 2, 3, 1))
grid = self.get_grid(x.shape, x.device)
x = torch.cat((x, grid), dim=-1)
x = self.fc0(x)
x = x.permute(0, 3, 1, 2)
x = F.pad(x, [0, self.padding, 0, self.padding])
x1 = self.conv0(x)
x2 = self.w0(x)
x = x1 + x2
x = F.gelu(x)
x1 = self.conv1(x)
x2 = self.w1(x)
x = x1 + x2
x = F.gelu(x)
x1 = self.conv2(x)
x2 = self.w2(x)
x = x1 + x2
x = F.gelu(x)
x1 = self.conv3(x)
x2 = self.w3(x)
x = x1 + x2
x = x[..., :-self.padding, :-self.padding]
x = x.permute(0, 2, 3, 1)
x = self.fc1(x)
x = F.gelu(x)
x = self.fc2(x)
x = torch.permute(x, (0, 3, 1, 2))
return x
def get_grid(self, shape, device):
batchsize, size_x, size_y = shape[0], shape[1], shape[2]
gridx = torch.tensor(np.linspace(0, 1, size_x), dtype=torch.float)
gridx = gridx.reshape(1, size_x, 1, 1).repeat([batchsize, 1, size_y, 1])
gridy = torch.tensor(np.linspace(0, 1, size_y), dtype=torch.float)
gridy = gridy.reshape(1, 1, size_y, 1).repeat([batchsize, size_x, 1, 1])
return torch.cat((gridx, gridy), dim=-1).to(device)
for seed in range(1):
math.seed(seed)
net = FNO2d(1, 1, modes1=12, modes2=12, width=32).to(TORCH.get_default_device().ref) # Default values from GitHub are (12, 12, 32) https://github.com/zongyi-li/fourier_neural_operator/blob/master/fourier_2d.py
os.path.exists(expanduser(f"~/phi/poisson_net2_FNO/{seed}")) or os.mkdir(expanduser(f"~/phi/poisson_net2_FNO/{seed}"))
torch.save(net.state_dict(), expanduser(f"~/phi/poisson_net2_FNO/{seed}/init.pth"))
for method in ['FNO']:
for learning_rate in [3e-3]:
scene = Scene.create(f"~/phi/poisson_net2_FNO/{seed}", name=f"{method}_lr{learning_rate}")
print(scene)
viewer = view(scene=scene, select='batch', gui='console')
optimizer = optim.Adam(net.parameters(), lr=learning_rate)
net.load_state_dict(torch.load(expanduser(f"~/phi/poisson_net2_FNO/{seed}/init.pth")))
math.seed(0)
viewer.info(f"Training method: {method}")
start_time = time.perf_counter()
for training_step in viewer.range():
if method == 'kFac':
net.zero_grad()
else:
optimizer.zero_grad()
x_gt = CenteredGrid(Noise(batch(batch=128)), x=64, y=64)
y_target = field.solve_linear(field.laplace, x_gt, Solve('CG', 1e-5, 0, x0=x_gt * 0))
prediction = field.native_call(net, y_target).vector[0]
x = field.stop_gradient(prediction)
if not field.isfinite(prediction):
raise RuntimeError(net.state_dict())
y = field.solve_linear(field.laplace, prediction, Solve('CG', 1e-5, 0, x0=x_gt * 0))
loss = y_l2 = field.l2_loss(y - y_target)
loss.sum.backward()
optimizer.step()
viewer.log_scalars(x_l1=field.l1_loss(x_gt - x), y_l2=y_l2)
if time.perf_counter() - start_time > 60 * 60 * 8: # 4100: # time limit
break
torch.save(net.state_dict(), viewer.scene.subpath(f'net_{method}.pth'))
print("All done.")