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28d9c3b | 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 | from __future__ import annotations
import math
from collections.abc import Mapping, Sequence
import torch
import torch.nn as nn
class FCN(nn.Module):
"""Fully connected network used by the BPINN solution model."""
def __init__(
self,
layer_sizes: Sequence[int],
activation: str = "tanh",
dtype: torch.dtype = torch.float64,
stddev: float | None = None,
) -> 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}")
if stddev is None:
stddev = math.sqrt(50.0 / layer_sizes[1])
if stddev <= 0:
raise ValueError("stddev must be positive")
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)
)
for linear in self.linears:
nn.init.trunc_normal_(
linear.weight,
mean=0.0,
std=stddev,
a=-2.0 * stddev,
b=2.0 * stddev,
)
nn.init.zeros_(linear.bias)
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 PhysNet(nn.Module):
"""Physics-informed network with solution and optional parameter outputs."""
def __init__(
self,
input_dim: int = 1,
n_layers: int = 4,
n_neurons: int = 50,
n_out_sol: int = 1,
n_out_par: int = 0,
activation: str = "tanh",
dtype: torch.dtype = torch.float64,
) -> None:
super().__init__()
if min(input_dim, n_layers, n_neurons, n_out_sol) <= 0 or n_out_par < 0:
raise ValueError("network dimensions must be positive")
self.n_out_sol = n_out_sol
self.n_out_par = n_out_par
output_dim = n_out_sol + n_out_par
self.fcn = FCN(
[input_dim, *([n_neurons] * n_layers), output_dim],
activation=activation,
dtype=dtype,
)
def forward(self, inputs: torch.Tensor) -> tuple[torch.Tensor, torch.Tensor | None]:
outputs = self.fcn(inputs)
solution = outputs[..., : self.n_out_sol]
parameters = outputs[..., self.n_out_sol :] if self.n_out_par else None
return solution, parameters
def predict_u(self, inputs: torch.Tensor) -> torch.Tensor:
return self.forward(inputs)[0]
class BPINN(nn.Module):
"""Physics-informed neural network used by the BPINNs workflow."""
def __init__(
self,
input_dim: int = 1,
n_layers: int = 4,
n_neurons: int = 50,
n_out_sol: int = 1,
n_out_par: int = 0,
activation: str = "tanh",
dtype: torch.dtype = torch.float64,
) -> None:
super().__init__()
self.net = PhysNet(
input_dim=input_dim,
n_layers=n_layers,
n_neurons=n_neurons,
n_out_sol=n_out_sol,
n_out_par=n_out_par,
activation=activation,
dtype=dtype,
)
def forward(self, inputs: torch.Tensor) -> tuple[torch.Tensor, torch.Tensor | None]:
return self.net(inputs)
def predict_u(self, inputs: torch.Tensor) -> torch.Tensor:
return self.net.predict_u(inputs)
def build_model(config: Mapping, dtype: torch.dtype = torch.float64) -> BPINN:
return BPINN(
input_dim=int(config["input_dim"]),
n_layers=int(config["n_layers"]),
n_neurons=int(config["n_neurons"]),
n_out_sol=int(config["n_out_sol"]),
n_out_par=int(config["n_out_par"]),
activation=str(config["activation"]),
dtype=dtype,
)
def laplace1d_loss_components(
model: BPINN,
x_solution: torch.Tensor,
u_solution: torch.Tensor,
x_boundary: torch.Tensor,
u_boundary: torch.Tensor,
x_pde: torch.Tensor,
) -> dict[str, torch.Tensor]:
solution_prediction = model.predict_u(x_solution)
boundary_prediction = model.predict_u(x_boundary)
pde_points = x_pde.detach().requires_grad_(True)
pde_prediction = model.predict_u(pde_points)
first_derivative = torch.autograd.grad(
pde_prediction,
pde_points,
torch.ones_like(pde_prediction),
create_graph=True,
)[0]
second_derivative = torch.autograd.grad(
first_derivative,
pde_points,
torch.ones_like(first_derivative),
create_graph=True,
)[0]
source = torch.pi**2 * torch.sin(torch.pi * pde_points)
residual = second_derivative + source
return {
"data": torch.mean((solution_prediction - u_solution).square()),
"boundary": torch.mean((boundary_prediction - u_boundary).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["boundary"]) * components["boundary"]
+ float(weights["pde"]) * components["pde"]
)
def posterior_predict(
model: BPINN,
states: Sequence[Mapping[str, torch.Tensor]],
inputs: torch.Tensor,
) -> tuple[torch.Tensor, torch.Tensor, torch.Tensor]:
"""Compute predictive mean and standard deviation from parameter-state samples."""
if not states:
raise ValueError("posterior prediction requires at least one parameter state")
original_state = {
key: value.detach().clone() for key, value in model.state_dict().items()
}
predictions = []
try:
for state in states:
model.load_state_dict(state, strict=True)
with torch.no_grad():
predictions.append(model.predict_u(inputs))
finally:
model.load_state_dict(original_state, strict=True)
samples = torch.stack(predictions)
return samples.mean(dim=0), samples.std(dim=0, unbiased=False), samples
|