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import torch
import numpy as np
from torch import Tensor
import torch.nn as nn
import torch.nn.functional as F
from ..base_model import AutoCfdModel
from onescience.modules.fourier.fno_layers import SpectralConv2d
torch.manual_seed(0)
np.random.seed(0)
class FnoBlock(nn.Module):
"""
FNO 块 (Fourier Neural Operator Block)。
包含一个 2D 频域卷积路径和一个 1x1 的空间卷积残差路径，
最后加上可选的激活函数。
"""
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(
in_channels=self.in_chan,
out_channels=self.out_chan,
modes1=self.modes1,
modes2=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
# +1 for mask, +2 for coordinates
self.fc0 = nn.Conv2d(
in_chan + 1 + 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)
- mask: (b, h, w), a binary mask for indicating the geometry
1 for interior, 0 for obstacles.
Returns: a tensor of shape (b, c, h, w), the solution at
the next timestep
"""
batch_size, n_chan, height, width = inputs.shape
if mask is None:
# When there is no mask, we assume that there is no obstacles.
mask = torch.ones((batch_size, 1, height, width)).to(inputs.device)
else:
if mask.dim() == 3: # (B, h, w)
mask = mask.unsqueeze(1) # (B, 1, h, w)
inputs = torch.cat([inputs, mask], dim=1) # (B, c + 1, h, w)
# Physical properties
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)
# Masked locations are not prediction
preds = preds * mask
if label is not None:
label = label * mask
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:
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), 1 for interior, 0 for obstacles.
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=mask
)
preds.append(cur_frame)
return preds
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