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eac1b4e | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 | """HO-FNO model for the Pipe horizontal velocity experiment.
This module implements the order-2 higher-order spectral mixer described in
the HO-FNO paper. The model uses channel-last tensors at the public interface:
``[batch, height, width, channels]``.
"""
from __future__ import annotations
from typing import Sequence
import torch
from torch import nn
class RMSNorm2d(nn.Module):
"""RMS normalization over the channel dimension for channel-last fields."""
def __init__(self, channels: int, eps: float = 1e-6) -> None:
super().__init__()
self.weight = nn.Parameter(torch.ones(channels))
self.eps = eps
def forward(self, x: torch.Tensor) -> torch.Tensor:
scale = torch.rsqrt(x.pow(2).mean(dim=-1, keepdim=True) + self.eps)
return x * scale * self.weight.view(1, 1, 1, -1)
class DropPath(nn.Module):
def __init__(self, probability: float = 0.0) -> None:
super().__init__()
self.probability = float(probability)
def forward(self, x: torch.Tensor) -> torch.Tensor:
if not self.training or self.probability <= 0.0:
return x
keep = 1.0 - self.probability
mask_shape = (x.shape[0],) + (1,) * (x.ndim - 1)
mask = torch.empty(mask_shape, device=x.device, dtype=x.dtype).bernoulli_(keep)
return x * mask / keep
class DepthwiseSpectralConv2d(nn.Module):
"""Depthwise complex Fourier convolution on retained low modes."""
def __init__(self, channels: int, modes: Sequence[int]) -> None:
super().__init__()
if len(modes) != 2:
raise ValueError("modes must contain exactly two integers")
self.channels = int(channels)
self.modes1 = int(modes[0])
self.modes2 = int(modes[1])
scale = 1.0 / max(1, self.channels)
self.weights_pos = nn.Parameter(
scale * torch.randn(self.channels, self.modes1, self.modes2, dtype=torch.cfloat)
)
self.weights_neg = nn.Parameter(
scale * torch.randn(self.channels, self.modes1, self.modes2, dtype=torch.cfloat)
)
@staticmethod
def _mul_modes(x_ft: torch.Tensor, weights: torch.Tensor) -> torch.Tensor:
return torch.einsum("bchw,chw->bchw", x_ft, weights)
def forward(self, x: torch.Tensor) -> torch.Tensor:
batch, channels, height, width = x.shape
if channels != self.channels:
raise ValueError(f"expected {self.channels} channels, got {channels}")
x_ft = torch.fft.rfft2(x.float())
out_ft = torch.zeros(
batch,
self.channels,
height,
width // 2 + 1,
device=x.device,
dtype=torch.cfloat,
)
m1 = min(self.modes1, height)
m2 = min(self.modes2, width // 2 + 1)
out_ft[:, :, :m1, :m2] = self._mul_modes(
x_ft[:, :, :m1, :m2], self.weights_pos[:, :m1, :m2]
)
out_ft[:, :, -m1:, :m2] = self._mul_modes(
x_ft[:, :, -m1:, :m2], self.weights_neg[:, :m1, :m2]
)
return torch.fft.irfft2(out_ft, s=(height, width))
class HigherOrderSpectralMixer2d(nn.Module):
"""Order-m HO spectral mixer.
The input is projected by ``m`` independent 1x1 maps, their outputs are
multiplied channelwise in physical space, then a retained-mode spectral
convolution is applied.
"""
def __init__(self, channels: int, modes: Sequence[int], order: int = 2) -> None:
super().__init__()
if order < 1:
raise ValueError("order must be positive")
self.order = int(order)
self.factor_projection = nn.Conv2d(channels, channels * self.order, kernel_size=1)
self.spectral = DepthwiseSpectralConv2d(channels, modes)
def forward(self, x: torch.Tensor) -> torch.Tensor:
x_cf = x.permute(0, 3, 1, 2).contiguous()
factors = self.factor_projection(x_cf).chunk(self.order, dim=1)
product = factors[0]
for factor in factors[1:]:
product = product * factor
mixed = self.spectral(product)
return mixed.permute(0, 2, 3, 1).contiguous()
class HOFNOBlock(nn.Module):
def __init__(
self,
width: int,
modes: Sequence[int],
order: int,
mlp_expansion: int = 4,
mlp_dropout: float = 0.0,
drop_path: float = 0.0,
) -> None:
super().__init__()
self.norm_mixer = RMSNorm2d(width)
self.mixer = HigherOrderSpectralMixer2d(width, modes, order)
self.norm_ffn = RMSNorm2d(width)
hidden = int(width * mlp_expansion)
self.ffn = nn.Sequential(
nn.Linear(width, hidden),
nn.GELU(),
nn.Dropout(mlp_dropout),
nn.Linear(hidden, width),
nn.Dropout(mlp_dropout),
)
self.drop_path = DropPath(drop_path)
def forward(self, x: torch.Tensor) -> torch.Tensor:
x = x + self.drop_path(self.mixer(self.norm_mixer(x)))
x = x + self.drop_path(self.ffn(self.norm_ffn(x)))
return x
class HOFNOPipe(nn.Module):
"""HO-FNO Pipe model with paper Table 13 defaults."""
def __init__(
self,
input_channels: int = 2,
output_channels: int = 1,
order: int = 2,
layers: int = 8,
width: int = 128,
modes: Sequence[int] = (50, 24),
add_unit_grid: bool = True,
mlp_expansion: int = 4,
mlp_dropout: float = 0.0,
drop_path_rate: float = 0.0,
) -> None:
super().__init__()
self.add_unit_grid = bool(add_unit_grid)
lift_channels = int(input_channels) + (2 if self.add_unit_grid else 0)
self.lift = nn.Linear(lift_channels, width)
if layers <= 1:
drop_rates = [0.0] * layers
else:
drop_rates = torch.linspace(0.0, float(drop_path_rate), layers).tolist()
self.blocks = nn.ModuleList(
[
HOFNOBlock(
width=width,
modes=modes,
order=order,
mlp_expansion=mlp_expansion,
mlp_dropout=mlp_dropout,
drop_path=drop_rates[idx],
)
for idx in range(layers)
]
)
self.project = nn.Linear(width, output_channels)
@staticmethod
def unit_grid(batch: int, height: int, width: int, device: torch.device, dtype: torch.dtype) -> torch.Tensor:
gx = torch.linspace(0.0, 1.0, height, device=device, dtype=dtype).view(1, height, 1, 1)
gy = torch.linspace(0.0, 1.0, width, device=device, dtype=dtype).view(1, 1, width, 1)
gx = gx.expand(batch, height, width, 1)
gy = gy.expand(batch, height, width, 1)
return torch.cat((gx, gy), dim=-1)
def forward(self, x: torch.Tensor) -> torch.Tensor:
if x.ndim != 4:
raise ValueError("HOFNOPipe expects [batch, height, width, channels]")
if self.add_unit_grid:
grid = self.unit_grid(x.shape[0], x.shape[1], x.shape[2], x.device, x.dtype)
x = torch.cat((x, grid), dim=-1)
x = self.lift(x)
for block in self.blocks:
x = block(x)
return self.project(x)
def count_parameters(model: nn.Module) -> int:
return sum(param.numel() for param in model.parameters() if param.requires_grad)
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