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fno2d.py
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fno2d.py
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from typing import List, Dict, Optional
import torch
import numpy as np
from torch import Tensor
import torch.nn as nn
import torch.nn.functional as F
from .Adam import Adam
from .utilities3 import MatReader, count_params
from ..base_model import AutoCfdModel
torch.manual_seed(0)
np.random.seed(0)
class SpectralConv2d_fast(nn.Module):
def __init__(self, in_channels, out_channels, modes1, modes2):
super(SpectralConv2d_fast, 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( # type: ignore
self.scale
* torch.rand(
in_channels, out_channels, self.modes1, self.modes2, dtype=torch.cfloat
)
)
self.weights2 = nn.Parameter( # type: ignore
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 FnoBlock(nn.Module):
def __init__(
self,
in_chan: int,
out_chan: int,
modes1: int,
modes2: int,
act_fn: Optional[nn.Module] = None,
):
super().__init__()
self.in_chan = in_chan
self.out_chan = out_chan
self.modes1 = modes1
self.modes2 = modes2
self.act_fn = act_fn
self.conv0 = SpectralConv2d_fast(
self.in_chan, self.out_chan, self.modes1, self.modes2
)
self.w0 = nn.Conv2d(self.in_chan, self.out_chan, 1)
def forward(self, x: Tensor) -> Tensor:
x1 = self.conv0(x)
x2 = self.w0(x)
x = x1 + x2
if self.act_fn is not None:
x = self.act_fn(x)
return x
class Fno2d(AutoCfdModel):
def __init__(
self,
in_chan: int,
out_chan: int,
n_case_params: int,
loss_fn: nn.Module,
num_layers: int,
modes1: int = 12,
modes2: int = 12,
hidden_dim: int = 20,
padding: Optional[int] = None,
):
super().__init__(loss_fn)
"""
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 .
"""
self.in_chan = in_chan
self.out_chan = out_chan
self.n_case_params = n_case_params
self.num_layers = num_layers
self.modes1 = modes1
self.modes2 = modes2
self.hidden_dim = hidden_dim
self.padding = padding # pad the domain if input is non-periodic
self.act_fn = nn.GELU()
# Channel projection into `hidden_dim` channels
# +7 because of coordinates (+2) and case params (+5)
self.fc0 = nn.Conv2d(in_chan + 2 + n_case_params, self.hidden_dim, 1, 1, 0)
# input channel is 12: the solution of the previous 10 timesteps + 2 locations
# (u(t-10, x, y), ..., u(t-1, x, y), x, y)
# FNO blocks
blocks = []
for _ in range(self.num_layers):
blocks.append(
FnoBlock(
self.hidden_dim,
self.hidden_dim,
self.modes1,
self.modes2,
self.act_fn,
)
)
self.blocks = nn.Sequential(*blocks)
self.fc1 = nn.Conv2d(self.hidden_dim, 128, 1, 1, 0)
self.fc2 = nn.Conv2d(128, self.out_chan, 1, 1, 0)
def forward(
self,
inputs: Tensor,
case_params: Tensor,
mask: Optional[Tensor] = None,
label: Optional[Tensor] = None,
) -> Dict:
"""
Args:
input: (b, c, h, w)
labels: (b, c, h, w)
Returns:
output: (b, c, h, w), the solution of the next timestep
"""
batch_size, _, height, width = inputs.shape
# 物性
props = case_params # (B, p)
props = props.unsqueeze(-1).unsqueeze(-1) # (B, p, 1, 1)
props = props.repeat(1, 1, height, width) # (B, p, H, W)
# Append (x, y) coordinates to every location
grid = self.get_coords(inputs.shape, inputs.device) # (b, 2, h, w)
inputs = torch.cat((inputs, grid, props), dim=1) # (b, c + 2 + 2, h, w)
# Project channels
inputs = self.fc0(inputs) # (b, hidden_dim, h, w)
# x = x.permute(0, 3, 1, 2) # (b, c, h, w)?
if self.padding is not None:
# pad the domain if input is non-periodic
inputs = F.pad(inputs, [0, self.padding, 0, self.padding])
inputs = self.blocks(inputs) # (b, hidden_dim, h, w)
if self.padding is not None:
# pad the domain if inputis non-periodic
inputs = inputs[..., : -self.padding, : -self.padding]
inputs = self.fc1(inputs) # (b, 128, h, w)
inputs = self.act_fn(inputs)
preds = self.fc2(inputs) # (b, c_out, h, w)
if label is not None:
loss = self.loss_fn(preds=preds, labels=label)
return dict(
preds=preds,
loss=loss,
)
return dict(preds=preds)
def get_coords(self, shape, device):
"""
Return a tensor of shape (b, 2, h, w) such that the element at
[:, :, i, j] is the (x, y) coordinates at the grid location (i, j).
"""
bsz, c, size_x, size_y = shape
grid_x = torch.tensor(np.linspace(0, 1, size_x), dtype=torch.float)
grid_x = grid_x.reshape(1, 1, size_x, 1).repeat([bsz, 1, 1, size_y])
grid_y = torch.tensor(np.linspace(0, 1, size_y), dtype=torch.float)
grid_y = grid_y.reshape(1, 1, 1, size_y).repeat([bsz, 1, size_x, 1])
coords = torch.cat([grid_x, grid_y], dim=1).to(device) # (b, 2, h, w)
return coords
def generate(
self,
inputs: Tensor,
case_params: Tensor,
mask: Optional[Tensor] = None,
) -> Tensor:
"""
Args:
x (Tensor):
case_params (dict):
Returns:
output: (steps, c, h, w)
"""
outputs = self.forward(
inputs=inputs, case_params=case_params, mask=mask
) # (b, c, h, w)
preds = outputs["preds"]
return preds
def generate_many(
self, inputs: Tensor, case_params: Tensor, mask: Tensor, steps: int
) -> List[Tensor]:
"""
Args:
x (Tensor): (c, h, w)
case_params (Tensor): (p)
mask (Tensor): (h, w)
Returns:
output: (steps, c, h, w)
"""
assert len(inputs.shape) == len(case_params.shape) + 2
if inputs.dim() == 3:
# Add a dimension for batch size of 1
inputs = inputs.unsqueeze(0)
case_params = case_params.unsqueeze(0)
mask = mask.unsqueeze(0)
assert inputs.shape[0] == case_params.shape[0] == mask.shape[0]
cur_frame = inputs # (b, c, h, w)
preds = []
for _ in range(steps):
cur_frame = self.generate(
inputs=cur_frame, case_params=case_params, mask=None
)
preds.append(cur_frame)
return preds
if __name__ == "__main__":
TRAIN_PATH = "data/ns_data_V100_N1000_T50_1.mat"
TEST_PATH = "data/ns_data_V100_N1000_T50_2.mat"
ntrain = 1000
ntest = 200
modes = 12
width = 20
batch_size = 20
batch_size2 = batch_size
epochs = 500
learning_rate = 0.001
scheduler_step = 100
scheduler_gamma = 0.5
print(epochs, learning_rate, scheduler_step, scheduler_gamma)
path = (
"ns_fourier_2d_rnn_V10000_T20_N"
+ str(ntrain)
+ "_ep"
+ str(epochs)
+ "_m"
+ str(modes)
+ "_w"
+ str(width)
)
path_model = "model/" + path
path_train_err = "results/" + path + "train.txt"
path_test_err = "results/" + path + "test.txt"
path_image = "image/" + path
sub = 1
S = 64
T_in = 10
T = 10
step = 1
################################################################
# load data
################################################################
reader = MatReader(TRAIN_PATH)
train_a = reader.read_field("u")[:ntrain, ::sub, ::sub, :T_in]
train_u = reader.read_field("u")[:ntrain, ::sub, ::sub, T_in : T + T_in]
reader = MatReader(TEST_PATH)
test_a = reader.read_field("u")[-ntest:, ::sub, ::sub, :T_in]
test_u = reader.read_field("u")[-ntest:, ::sub, ::sub, T_in : T + T_in]
print(train_u.shape)
print(test_u.shape)
assert S == train_u.shape[-2]
assert T == train_u.shape[-1]
train_a = train_a.reshape(ntrain, S, S, T_in)
test_a = test_a.reshape(ntest, S, S, T_in)
train_loader = torch.utils.data.DataLoader(
torch.utils.data.TensorDataset(train_a, train_u),
batch_size=batch_size,
shuffle=True,
)
test_loader = torch.utils.data.DataLoader(
torch.utils.data.TensorDataset(test_a, test_u),
batch_size=batch_size,
shuffle=False,
)
################################################################
# training and evaluation
################################################################
model = Fno2d(modes, modes, width).cuda()
# model = torch.load('model/ns_fourier_V100_N1000_ep100_m8_w20')
print(count_params(model))
optimizer = Adam(model.parameters(), lr=learning_rate, weight_decay=1e-4)
scheduler = torch.optim.lr_scheduler.StepLR(
optimizer, step_size=scheduler_step, gamma=scheduler_gamma
)