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FNO4D.py
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import torch
import numpy as np
import torch.nn as nn
import torch.nn.functional as F
import operator
from functools import reduce
from functools import partial
from timeit import default_timer
torch.manual_seed(0)
np.random.seed(0)
class SpectralConv4d(nn.Module):
def __init__(self, in_channels, out_channels, modes1, modes2, modes3, modes4):
super(SpectralConv4d, self).__init__()
"""
4D 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.modes3 = modes3
self.modes4 = modes4
self.scale = (1 / (in_channels * out_channels))
self.weights1 = nn.Parameter(self.scale * torch.rand(in_channels, out_channels, self.modes1, self.modes2, self.modes3, self.modes4, dtype=torch.cfloat))
self.weights2 = nn.Parameter(self.scale * torch.rand(in_channels, out_channels, self.modes1, self.modes2, self.modes3, self.modes4, dtype=torch.cfloat))
self.weights3 = nn.Parameter(self.scale * torch.rand(in_channels, out_channels, self.modes1, self.modes2, self.modes3, self.modes4, dtype=torch.cfloat))
self.weights4 = nn.Parameter(self.scale * torch.rand(in_channels, out_channels, self.modes1, self.modes2, self.modes3, self.modes4, dtype=torch.cfloat))
self.weights5 = nn.Parameter(self.scale * torch.rand(in_channels, out_channels, self.modes1, self.modes2, self.modes3, self.modes4, dtype=torch.cfloat))
self.weights6 = nn.Parameter(self.scale * torch.rand(in_channels, out_channels, self.modes1, self.modes2, self.modes3, self.modes4, dtype=torch.cfloat))
self.weights7 = nn.Parameter(self.scale * torch.rand(in_channels, out_channels, self.modes1, self.modes2, self.modes3, self.modes4, dtype=torch.cfloat))
self.weights8 = nn.Parameter(self.scale * torch.rand(in_channels, out_channels, self.modes1, self.modes2, self.modes3, self.modes4, dtype=torch.cfloat))
# Complex multiplication
def compl_mul4d(self, input, weights):
# (batch, in_channel, x,y,t ), (in_channel, out_channel, x,y,t) -> (batch, out_channel, x,y,t)
return torch.einsum("bixyzt,ioxyzt->boxyzt", input, weights)
def forward(self, x):
batchsize = x.shape[0]
#Compute Fourier coeffcients up to factor of e^(- something constant)
x_ft = torch.fft.rfftn(x, dim=[-4,-3,-2,-1])
# Multiply relevant Fourier modes
out_ft = torch.zeros(batchsize, self.out_channels, x.size(-4), x.size(-3), x.size(-2), x.size(-1)//2 + 1, dtype=torch.cfloat, device=x.device)
out_ft[:, :, :self.modes1, :self.modes2, :self.modes3, :self.modes4] = self.compl_mul4d(x_ft[:, :, :self.modes1, :self.modes2, :self.modes3, :self.modes4], self.weights1)
out_ft[:, :, -self.modes1:, :self.modes2, :self.modes3, :self.modes4] = self.compl_mul4d(x_ft[:, :, -self.modes1:, :self.modes2, :self.modes3, :self.modes4], self.weights2)
out_ft[:, :, :self.modes1, -self.modes2:, :self.modes3, :self.modes4] = self.compl_mul4d(x_ft[:, :, :self.modes1, -self.modes2:, :self.modes3, :self.modes4], self.weights3)
out_ft[:, :, :self.modes1, :self.modes2, -self.modes3:, :self.modes4] = self.compl_mul4d(x_ft[:, :, :self.modes1, :self.modes2, -self.modes3:, :self.modes4], self.weights4)
out_ft[:, :, -self.modes1:, -self.modes2:, :self.modes3, :self.modes4] = self.compl_mul4d(x_ft[:, :, -self.modes1:, -self.modes2:, :self.modes3, :self.modes4], self.weights5)
out_ft[:, :, -self.modes1:, :self.modes2, -self.modes3:, :self.modes4] = self.compl_mul4d(x_ft[:, :, -self.modes1:, :self.modes2, -self.modes3:, :self.modes4], self.weights6)
out_ft[:, :, :self.modes1, -self.modes2:, -self.modes3:, :self.modes4] = self.compl_mul4d(x_ft[:, :, :self.modes1, -self.modes2:, -self.modes3:, :self.modes4], self.weights7)
out_ft[:, :, -self.modes1:, -self.modes2:, -self.modes3:, :self.modes4] = self.compl_mul4d(x_ft[:, :, -self.modes1:, -self.modes2:, -self.modes3:, :self.modes4], self.weights8)
#Return to physical space
x = torch.fft.irfftn(out_ft, s=(x.size(-4), x.size(-3), x.size(-2), x.size(-1)))
return x
class Block4d(nn.Module):
def __init__(self, width, width2, modes1, modes2, modes3, modes4, out_dim):
super(Block4d, self).__init__()
self.modes1 = modes1
self.modes2 = modes2
self.modes3 = modes3
self.modes4 = modes4
self.width = width
self.width2 = width2
self.out_dim = out_dim
self.padding = 8
# channel
self.conv0 = SpectralConv4d(self.width, self.width, self.modes1, self.modes2, self.modes3, self.modes4)
self.conv1 = SpectralConv4d(self.width, self.width, self.modes1, self.modes2, self.modes3, self.modes4)
self.conv2 = SpectralConv4d(self.width, self.width, self.modes1, self.modes2, self.modes3, self.modes4)
self.conv3 = SpectralConv4d(self.width, self.width, self.modes1, self.modes2, self.modes3, self.modes4)
self.w0 = nn.Conv1d(self.width, self.width, 1)
self.w1 = nn.Conv1d(self.width, self.width, 1)
self.w2 = nn.Conv1d(self.width, self.width, 1)
self.w3 = nn.Conv1d(self.width, self.width, 1)
self.fc1 = nn.Linear(self.width, self.width2)
self.fc2 = nn.Linear(self.width2, self.out_dim)
def forward(self, x):
batchsize = x.shape[0]
size_x, size_y, size_z, size_t = x.shape[2], x.shape[3], x.shape[4], x.shape[5]
# print(size_x, size_y, size_z, size_t)
# channel
# print(x.shape)
x1 = self.conv0(x)
# print(x1.shape)
x2 = self.w0(x.view(batchsize, self.width, -1)).view(batchsize, self.width, size_x, size_y, size_z, size_t)
x = x1 + x2
x = F.gelu(x)
x1 = self.conv1(x)
x2 = self.w1(x.view(batchsize, self.width, -1)).view(batchsize, self.width, size_x, size_y, size_z, size_t)
x = x1 + x2
x = F.gelu(x)
x1 = self.conv2(x)
x2 = self.w2(x.view(batchsize, self.width, -1)).view(batchsize, self.width, size_x, size_y, size_z, size_t)
x = x1 + x2
x = F.gelu(x)
x1 = self.conv3(x)
x2 = self.w3(x.view(batchsize, self.width, -1)).view(batchsize, self.width, size_x, size_y, size_z, size_t)
x = x1 + x2
x = x[:, :, self.padding:-self.padding, self.padding*2:-self.padding*2,
self.padding*2:-self.padding*2, self.padding:-self.padding]
x = x.permute(0, 2, 3, 4, 5, 1) # pad the domain if input is non-periodic
x1 = self.fc1(x)
x = F.gelu(x1)
x = self.fc2(x)
return x
class FNO4d(nn.Module):
def __init__(self, modes1, modes2, modes3, modes4, width, in_dim):
super(FNO4d, self).__init__()
self.modes1 = modes1
self.modes2 = modes2
self.modes3 = modes3
self.modes4 = modes4
self.width = width
self.width2 = width*4
self.in_dim = in_dim
self.out_dim = 1
self.padding = 8 # pad the domain if input is non-periodic
self.fc0 = nn.Linear(self.in_dim, self.width)
self.conv = Block4d(self.width, self.width2,
self.modes1, self.modes2, self.modes3, self.modes4, self.out_dim)
def forward(self, x, gradient=False):
x = self.fc0(x)
x = x.permute(0, 5, 1, 2, 3, 4)
x = F.pad(x, [self.padding, self.padding, self.padding*2, self.padding*2, self.padding*2,
self.padding*2, self.padding, self.padding])
x = self.conv(x)
return x