fourier_2d.py

"""
@author: Zongyi Li
This file is the Fourier Neural Operator for 2D problem such as the Darcy Flow discussed in Section 5.2 in the [paper](https://arxiv.org/pdf/2010.08895.pdf).
"""
import os
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 *
import scipy

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


################################################################
# fourier layer
################################################################
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, 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.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.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, 128)
        self.fc2 = nn.Linear(128, 1)

    def forward(self, x):
        batchsize = x.shape[0]
        size_x, size_y = x.shape[1], x.shape[2]

        x = self.fc0(x)
        x = x.permute(0, 3, 1, 2)

        x1 = self.conv0(x)
        x2 = self.w0(x.view(batchsize, self.width, -1)).view(batchsize, self.width, size_x, size_y)
        x = x1 + x2
        x = F.relu(x)

        x1 = self.conv1(x)
        x2 = self.w1(x.view(batchsize, self.width, -1)).view(batchsize, self.width, size_x, size_y)
        x = x1 + x2
        x = F.relu(x)

        x1 = self.conv2(x)
        x2 = self.w2(x.view(batchsize, self.width, -1)).view(batchsize, self.width, size_x, size_y)
        x = x1 + x2
        x = F.relu(x)

        x1 = self.conv3(x)
        x2 = self.w3(x.view(batchsize, self.width, -1)).view(batchsize, self.width, size_x, size_y)
        x = x1 + x2

        x = x.permute(0, 2, 3, 1)
        x = self.fc1(x)
        x = F.relu(x)
        x = self.fc2(x)
        return x



def FNO_main(train_data_res, save_index):
    """
    Parameters
    ----------
    train_data_res : resolution of the training data
    save_index : index of the saving folder
    """

    
    ################################################################
    # configs
    ################################################################
    TRAIN_PATH = 'piececonst_r421_N1024_smooth1.mat'
    TEST_PATH = 'piececonst_r421_N1024_smooth2.mat'
    
    ntrain = 1000   # first 1000 of smooth1.mat 
    ntest = 200     # first 100 of smooth1.mat 
    
    batch_size = 20
    learning_rate = 0.001
    
    epochs = 500
    step_size = 100
    gamma = 0.5
    
    modes = 12
    width = 32
    
    s = train_data_res
    r = (421-1) // (s-1) 
    # r = 5
    # h = int(((421 - 1)/r) + 1)
    # s = h
    
    ################################################################
    # load data and data normalization
    ################################################################
    reader = MatReader(TRAIN_PATH)
    x_train = reader.read_field('coeff')[:ntrain,::r,::r][:,:s,:s]
    y_train = reader.read_field('sol')[:ntrain,::r,::r][:,:s,:s]
    
    reader.load_file(TEST_PATH)
    x_test = reader.read_field('coeff')[:ntest,::r,::r][:,:s,:s]
    y_test = reader.read_field('sol')[:ntest,::r,::r][:,:s,:s]
    
    
    x_normalizer = UnitGaussianNormalizer(x_train)
    x_train = x_normalizer.encode(x_train)
    x_test = x_normalizer.encode(x_test)
    
    y_normalizer = UnitGaussianNormalizer(y_train)
    y_train = y_normalizer.encode(y_train)
    
    grids = []
    grid_all = np.linspace(0, 1, 421).reshape(421, 1).astype(np.float64)
    grids.append(grid_all[::r,:])
    grids.append(grid_all[::r,:])
    grid = np.vstack([xx.ravel() for xx in np.meshgrid(*grids)]).T
    grid = grid.reshape(1,s,s,2)
    grid = torch.tensor(grid, dtype=torch.float)
    x_train = torch.cat([x_train.reshape(ntrain,s,s,1), grid.repeat(ntrain,1,1,1)], dim=3)
    x_test = torch.cat([x_test.reshape(ntest,s,s,1), grid.repeat(ntest,1,1,1)], dim=3)
    
    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)
    
    ################################################################
    # training and evaluation
    ################################################################
    model = FNO2d(modes, modes, width).cuda()
    print(count_params(model))
    
    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)
    
    start_time = default_timer()
    myloss = LpLoss(size_average=False)
    y_normalizer.cuda()
    for ep in range(epochs):
        model.train()
        t1 = default_timer()
        train_l2 = 0
        train_mse = 0
        for x, y in train_loader:
            x, y = x.cuda(), y.cuda()
    
            optimizer.zero_grad()
            out = model(x).reshape(batch_size, s, s)
            
            
            mse = F.mse_loss(out.view(batch_size, -1), y.view(batch_size, -1), reduction='mean')
            mse.backward()
            
            out = y_normalizer.decode(out)
            y = y_normalizer.decode(y)
            loss = myloss(out.view(batch_size,-1), y.view(batch_size,-1))
            # loss.backward()
    
            optimizer.step()
            train_mse += mse.item()
            train_l2 += loss.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).reshape(batch_size, s, s)
                out = y_normalizer.decode(out)
                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_l2, test_l2)
        print("Epoch: %d, time: %.3f, Train Loss: %.3e, Train l2: %.4f, Test l2: %.4f" 
                  % ( ep, t2-t1, train_mse, train_l2, test_l2) )

    elapsed = default_timer() - start_time
    print("\n=============================")
    print("Training done...")
    print('Training time: %.3f'%(elapsed))
    print("=============================\n")
    
    # ====================================
    # saving settings
    # ====================================
    current_directory = os.getcwd()
    resolution = "TrainRes_"+str(train_data_res)
    folder_index = str(save_index)
    
    results_dir = "/results/" + resolution +"/" + folder_index +"/"
    save_results_to = current_directory + results_dir
    if not os.path.exists(save_results_to):
        os.makedirs(save_results_to)
        
    model_dir = "/model/" + resolution +"/" + folder_index +"/"
    save_models_to = current_directory + model_dir
    if not os.path.exists(save_models_to):
        os.makedirs(save_models_to)
        
    ################################################################
    # testing
    ################################################################
    torch.save(model, save_models_to+'fourier_darcy')
    
    test_data_res = train_data_res
    s = test_data_res
    r = (421-1) // (s-1) 
    
    reader.load_file(TEST_PATH)
    x_test = reader.read_field('coeff')[:ntest,::r,::r][:,:s,:s]
    y_test = reader.read_field('sol')[:ntest,::r,::r][:,:s,:s]
    x_test = x_normalizer.encode(x_test)
    
    grids = []
    grids.append(grid_all[::r,:])
    grids.append(grid_all[::r,:])
    grid = np.vstack([xx.ravel() for xx in np.meshgrid(*grids)]).T
    grid = grid.reshape(1,s,s,2)
    grid = torch.tensor(grid, dtype=torch.float)
    x_test = torch.cat([x_test.reshape(ntest,s,s,1), grid.repeat(ntest,1,1,1)], dim=3)
    test_loader = torch.utils.data.DataLoader(torch.utils.data.TensorDataset(x_test, y_test), batch_size=1, shuffle=False)
    
    pred = torch.zeros(y_test.shape)
    index = 0
    t1 = default_timer()
    test_l2 = 0
    with torch.no_grad():
        for x, y in test_loader:
            x, y = x.cuda(), y.cuda()
            out = model(x).reshape(1, s, s)
            out = y_normalizer.decode(out)
            
            pred[index:index+1,:,:] = out
    
            # test_l2 += myloss(out.view(1, -1), y.view(1, -1)).item()
            # print(index, test_l2)
            test_l2 += np.linalg.norm(out.view(1, -1).cpu().numpy() 
                                      - y.view(1, -1).cpu().numpy()) / np.linalg.norm(y.view(1, -1).cpu().numpy())
            index = index + 1
    t2 = default_timer()
    testing_time = t2-t1
     
    test_l2 = test_l2/index
    print("\n=============================")
    print('Testing error: %.3e'%(test_l2))
    print("=============================\n")
    
    
    # scipy.io.savemat(save_results_to+'darcy_test_'+str(test_data_res)+'.mat', 
    #                     mdict={'x_test': reader.read_field('coeff')[:ntest,::r,::r][:,:s,:s].numpy(),
    #                            'y_test': y_test.numpy(), 
    #                            'y_pred': pred.cpu().numpy(),
    #                            'testing_time': testing_time})
    
    

if __name__ == "__main__":
    
    training_data_resolution = 29
    run_index = 0
    FNO_main(training_data_resolution, run_index)