fourier_1d.py

import numpy as np
import torch
import torch.nn as nn
import torch.nn.functional as F
from torch.nn.parameter import Parameter
import matplotlib.pyplot as plt

import operator
from functools import reduce
from functools import partial
from timeit import default_timer
from utilities3 import *

torch.manual_seed(0)
np.random.seed(0)

#Complex multiplication
def compl_mul1d(a, b):
    # (batch, in_channel, x ), (in_channel, out_channel, x) -> (batch, out_channel, x)
    op = partial(torch.einsum, "bix,iox->box")
    return torch.stack([
        op(a[..., 0], b[..., 0]) - op(a[..., 1], b[..., 1]),
        op(a[..., 1], b[..., 0]) + op(a[..., 0], b[..., 1])
    ], dim=-1)

################################################################
#  1d fourier layer
################################################################
class SpectralConv1d(nn.Module):
    def __init__(self, in_channels, out_channels, modes1):
        super(SpectralConv1d, self).__init__()
        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.scale = (1 / (in_channels*out_channels))
        self.weights1 = nn.Parameter(self.scale * torch.rand(in_channels, out_channels, self.modes1, 2))

    def forward(self, x):
        batchsize = x.shape[0]
        #Compute Fourier coeffcients up to factor of e^(- something constant)
        x_ft = torch.rfft(x, 1, normalized=True, onesided=True)

        # Multiply relevant Fourier modes
        out_ft = torch.zeros(batchsize, self.in_channels, x.size(-1)//2 + 1, 2, device=x.device)
        out_ft[:, :, :self.modes1] = compl_mul1d(x_ft[:, :, :self.modes1], self.weights1)

        #Return to physical space
        x = torch.irfft(out_ft, 1, normalized=True, onesided=True, signal_sizes=(x.size(-1), ))
        return x

class SimpleBlock1d(nn.Module):
    def __init__(self, modes, width):
        super(SimpleBlock1d, self).__init__()

        self.modes1 = modes
        self.width = width
        self.fc0 = nn.Linear(2, self.width)

        self.conv0 = SpectralConv1d(self.width, self.width, self.modes1)
        self.conv1 = SpectralConv1d(self.width, self.width, self.modes1)
        self.conv2 = SpectralConv1d(self.width, self.width, self.modes1)
        self.conv3 = SpectralConv1d(self.width, self.width, self.modes1)
        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.bn0 = torch.nn.BatchNorm1d(self.width)
        self.bn1 = torch.nn.BatchNorm1d(self.width)
        self.bn2 = torch.nn.BatchNorm1d(self.width)
        self.bn3 = torch.nn.BatchNorm1d(self.width)


        self.fc1 = nn.Linear(self.width, 128)
        self.fc2 = nn.Linear(128, 1)

    def forward(self, x):

        x = self.fc0(x)
        x = x.permute(0, 2, 1)

        x1 = self.conv0(x)
        x2 = self.w0(x)
        x = self.bn0(x1 + x2)
        x = F.relu(x)
        x1 = self.conv1(x)
        x2 = self.w1(x)
        x = self.bn1(x1 + x2)
        x = F.relu(x)
        x1 = self.conv2(x)
        x2 = self.w2(x)
        x = self.bn2(x1 + x2)
        x = F.relu(x)
        x1 = self.conv3(x)
        x2 = self.w3(x)
        x = self.bn3(x1 + x2)


        x = x.permute(0, 2, 1)
        x = self.fc1(x)
        x = F.relu(x)
        x = self.fc2(x)
        return x

class Net1d(nn.Module):
    def __init__(self, modes, width):
        super(Net1d, self).__init__()

        self.conv1 = SimpleBlock1d(modes, width)


    def forward(self, x):
        x = self.conv1(x)
        return x.squeeze()

    def count_params(self):
        c = 0
        for p in self.parameters():
            c += reduce(operator.mul, list(p.size()))

        return c


################################################################
#  configurations
################################################################
ntrain = 1000
ntest = 100

sub = 1 #subsampling rate
h = 2**10 // sub
s = h

batch_size = 20
learning_rate = 0.001

epochs = 500
step_size = 100
gamma = 0.5

modes = 16
width = 64


################################################################
# read data
################################################################
dataloader = MatReader('data/burgers_data_R10.mat')
x_data = dataloader.read_field('a')[:,::sub]
y_data = dataloader.read_field('u')[:,::sub]

x_train = x_data[:ntrain,:]
y_train = y_data[:ntrain,:]
x_test = x_data[-ntest:,:]
y_test = y_data[-ntest:,:]

# cat the locations information
grid = np.linspace(0, 2*np.pi, s).reshape(1, s, 1)
grid = torch.tensor(grid, dtype=torch.float)
x_train = torch.cat([x_train.reshape(ntrain,s,1), grid.repeat(ntrain,1,1)], dim=2)
x_test = torch.cat([x_test.reshape(ntest,s,1), grid.repeat(ntest,1,1)], dim=2)

train_loader = torch.utils.data.DataLoader(torch.utils.data.TensorDataset(x_train, y_train), batch_size=batch_size, shuffle=True)
test_loader = torch.utils.data.DataLoader(torch.utils.data.TensorDataset(x_test, y_test), batch_size=batch_size, shuffle=False)

# model
model = Net1d(modes, width).cuda()
print(model.count_params())


################################################################
# training and evaluation
################################################################
optimizer = torch.optim.Adam(model.parameters(), lr=learning_rate, weight_decay=1e-4)
scheduler = torch.optim.lr_scheduler.StepLR(optimizer, step_size=step_size, gamma=gamma)

myloss = LpLoss(size_average=False)
for ep in range(epochs):
    model.train()
    t1 = default_timer()
    train_mse = 0
    train_l2 = 0
    for x, y in train_loader:
        x, y = x.cuda(), y.cuda()

        optimizer.zero_grad()
        out = model(x)

        mse = F.mse_loss(out, y, reduction='mean')
        # mse.backward()
        l2 = myloss(out.view(batch_size, -1), y.view(batch_size, -1))
        l2.backward()

        optimizer.step()
        train_mse += mse.item()
        train_l2 += l2.item()

    scheduler.step()
    model.eval()
    test_l2 = 0.0
    with torch.no_grad():
        for x, y in test_loader:
            x, y = x.cuda(), y.cuda()

            out = model(x)
            test_l2 += myloss(out.view(batch_size, -1), y.view(batch_size, -1)).item()

    train_mse /= len(train_loader)
    train_l2 /= ntrain
    test_l2 /= ntest

    t2 = default_timer()
    print(ep, t2-t1, train_mse, train_l2, test_l2)

# torch.save(model, 'model/ns_fourier_burgers_8192')
pred = torch.zeros(y_test.shape)
index = 0
test_loader = torch.utils.data.DataLoader(torch.utils.data.TensorDataset(x_test, y_test), batch_size=1, shuffle=False)
with torch.no_grad():
    for x, y in test_loader:
        test_l2 = 0
        x, y = x.cuda(), y.cuda()

        out = model(x)
        pred[index] = out

        test_l2 += myloss(out.view(1, -1), y.view(1, -1)).item()
        print(index, test_l2)
        index = index + 1

# scipy.io.savemat('pred/burger_test.mat', mdict={'pred': pred.cpu().numpy()})