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371b59f | 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 | from __future__ import annotations
from collections.abc import Mapping, Sequence
import torch
import torch.nn as nn
class FCN(nn.Module):
"""Fully connected trunk used by the fuzzy PINN."""
def __init__(
self,
layer_sizes: Sequence[int],
activation: str = "tanh",
dtype: torch.dtype = torch.float32,
) -> None:
super().__init__()
if len(layer_sizes) < 2:
raise ValueError("layer_sizes must include input and output widths")
if activation not in {"tanh", "sin", "sine", "relu", "gelu"}:
raise ValueError(f"unsupported activation: {activation}")
self.activation = "sin" if activation == "sine" else activation
self.linears = nn.ModuleList(
nn.Linear(layer_sizes[index], layer_sizes[index + 1], dtype=dtype)
for index in range(len(layer_sizes) - 1)
)
def _activate(self, values: torch.Tensor) -> torch.Tensor:
if self.activation == "gelu":
return torch.nn.functional.gelu(values)
return getattr(torch, self.activation)(values)
def forward(self, inputs: torch.Tensor) -> torch.Tensor:
hidden = inputs
for linear in self.linears[:-1]:
hidden = self._activate(linear(hidden))
return self.linears[-1](hidden)
class FuzzyLayer(nn.Module):
"""Gaussian fuzzy membership rules followed by product inference."""
def __init__(
self,
input_dim: int,
rule_count: int,
dtype: torch.dtype = torch.float32,
) -> None:
super().__init__()
if min(input_dim, rule_count) <= 0:
raise ValueError("input_dim and rule_count must be positive")
self.input_dim = input_dim
self.rule_count = rule_count
self.centers = nn.Parameter(torch.empty(rule_count, input_dim, dtype=dtype))
self.sigma = nn.Parameter(torch.ones(rule_count, input_dim, dtype=dtype))
nn.init.xavier_uniform_(self.centers)
def forward(self, inputs: torch.Tensor) -> torch.Tensor:
differences = inputs[:, None, :] - self.centers[None, :, :]
variance = self.sigma.square().clamp_min(torch.finfo(inputs.dtype).eps)
memberships = torch.exp(-differences.square() / variance[None, :, :])
return memberships.prod(dim=-1)
class FPINNNet(nn.Module):
"""Parallel neural and fuzzy feature branches with a fused linear head."""
def __init__(
self,
hidden_layers: Sequence[int],
linear_dim: int,
fuzzy_dim: int,
activation: str = "tanh",
dtype: torch.dtype = torch.float32,
) -> None:
super().__init__()
self.fcn = FCN(
[2, *hidden_layers, linear_dim], activation=activation, dtype=dtype
)
self.fuzzy = FuzzyLayer(2, fuzzy_dim, dtype=dtype)
self.head = nn.Linear(linear_dim + fuzzy_dim, 1, dtype=dtype)
def forward(self, coordinates: torch.Tensor) -> torch.Tensor:
neural_features = torch.tanh(self.fcn(coordinates))
fuzzy_features = self.fuzzy(coordinates)
return self.head(torch.cat((neural_features, fuzzy_features), dim=1))
class FPINNForward(nn.Module):
"""Forward Allen-Cahn solver with fixed PDE parameters."""
def __init__(
self, model_config: Mapping, dtype: torch.dtype = torch.float32
) -> None:
super().__init__()
self.net = FPINNNet(
hidden_layers=model_config["hidden_layers"],
linear_dim=int(model_config["linear_dim"]),
fuzzy_dim=int(model_config["fuzzy_dim"]),
activation=str(model_config["activation"]),
dtype=dtype,
)
def forward(self, coordinates: torch.Tensor) -> torch.Tensor:
return self.net(coordinates)
def predict_u(self, coordinates: torch.Tensor) -> torch.Tensor:
return self.forward(coordinates)
class FPINNInverse(FPINNForward):
"""Inverse Allen-Cahn solver with learnable diffusion and reaction values."""
def __init__(
self,
model_config: Mapping,
initial_lambda_1: float = 1.0,
initial_lambda_2: float = 0.0,
dtype: torch.dtype = torch.float32,
) -> None:
super().__init__(model_config, dtype=dtype)
self.lambda_1 = nn.Parameter(torch.tensor(initial_lambda_1, dtype=dtype))
self.lambda_2 = nn.Parameter(torch.tensor(initial_lambda_2, dtype=dtype))
def build_model(
task: str,
model_config: Mapping,
pde_config: Mapping,
dtype: torch.dtype,
) -> FPINNForward:
if task == "forward":
return FPINNForward(model_config, dtype=dtype)
if task == "inverse":
return FPINNInverse(
model_config,
initial_lambda_1=float(pde_config["initial_lambda_1"]),
initial_lambda_2=float(pde_config["initial_lambda_2"]),
dtype=dtype,
)
raise ValueError(f"unsupported task: {task}")
def allen_cahn_residual(
model: FPINNForward,
coordinates: torch.Tensor,
lambda_1: float | torch.Tensor,
lambda_2: float | torch.Tensor,
) -> torch.Tensor:
inputs = coordinates.detach().requires_grad_(True)
prediction = model(inputs)
gradient = torch.autograd.grad(
prediction, inputs, torch.ones_like(prediction), create_graph=True
)[0]
prediction_x = gradient[:, 0:1]
prediction_t = gradient[:, 1:2]
prediction_xx = torch.autograd.grad(
prediction_x,
inputs,
torch.ones_like(prediction_x),
create_graph=True,
)[0][:, 0:1]
return (
prediction_t
- lambda_1 * prediction_xx
+ lambda_2 * (prediction.pow(3) - prediction)
)
def loss_components(
model: FPINNForward,
x_data: torch.Tensor,
u_data: torch.Tensor,
x_pde: torch.Tensor,
lambda_1: float | torch.Tensor,
lambda_2: float | torch.Tensor,
) -> dict[str, torch.Tensor]:
prediction = model(x_data)
residual = allen_cahn_residual(model, x_pde, lambda_1, lambda_2)
return {
"data": torch.mean((prediction - u_data).square()),
"pde": torch.mean(residual.square()),
}
def weighted_loss(components: Mapping[str, torch.Tensor], weights: Mapping) -> torch.Tensor:
return float(weights["data"]) * components["data"] + float(
weights["pde"]
) * components["pde"]
|