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from collections.abc import Sequence
import numpy as np
import torch
import torch.autograd as autograd
import torch.nn as nn
class SubNet(nn.Module):
"""Fully connected network with trainable adaptive activations."""
def __init__(self, layers: Sequence[int], activation: str = "tanh") -> None:
super().__init__()
if len(layers) < 2:
raise ValueError("layers must contain at least an input and an output size")
if activation not in {"tanh", "sin", "cos"}:
raise ValueError(f"unsupported activation: {activation}")
self.activation = activation
self.linears = nn.ModuleList(
nn.Linear(layers[index], layers[index + 1], dtype=torch.float64)
for index in range(len(layers) - 1)
)
# Keep one value per layer for compatibility with the published checkpoints.
self.a = nn.ParameterList(
nn.Parameter(torch.tensor(0.05, dtype=torch.float64))
for _ in range(len(layers) - 1)
)
def forward(self, inputs: torch.Tensor) -> torch.Tensor:
hidden = inputs
for index, linear in enumerate(self.linears[:-1]):
hidden = 20.0 * self.a[index] * linear(hidden)
hidden = getattr(torch, self.activation)(hidden)
return self.linears[-1](hidden)
class gPINN(nn.Module):
"""Gradient-enhanced physics-informed neural network backbone."""
def __init__(self, layers: Sequence[int], activation: str = "tanh") -> None:
super().__init__()
self.net = SubNet(layers, activation)
def forward(self, inputs: torch.Tensor) -> torch.Tensor:
return self.net(inputs)
class gPINNPoisson2D(nn.Module):
"""2D Poisson model whose output transform enforces zero boundaries."""
def __init__(self, layers: Sequence[int]) -> None:
super().__init__()
self.net = gPINN(layers)
def forward(self, coordinates: torch.Tensor) -> torch.Tensor:
x = coordinates[:, 0:1]
y = coordinates[:, 1:2]
return x * y * (1.0 - x) * (1.0 - y) * self.net(coordinates)
def exact_poisson1d(x: np.ndarray) -> np.ndarray:
solution = x + np.sin(8.0 * x) / 8.0
for frequency in range(1, 5):
solution += np.sin(frequency * x) / frequency
return solution
def gpinn_loss_poisson1d(
model: nn.Module,
interior: torch.Tensor,
boundary: torch.Tensor,
boundary_values: torch.Tensor,
gradient_weight: float,
) -> tuple[torch.Tensor, dict[str, float]]:
x = interior.detach().requires_grad_(True)
prediction = model(x)
first = autograd.grad(prediction, x, torch.ones_like(prediction), create_graph=True)[0]
second = autograd.grad(first, x, torch.ones_like(first), create_graph=True)[0]
third = autograd.grad(second, x, torch.ones_like(second), create_graph=True)[0]
source = 8.0 * torch.sin(8.0 * x) + sum(
frequency * torch.sin(frequency * x) for frequency in range(1, 5)
)
source_gradient = (
torch.cos(x)
+ 4.0 * torch.cos(2.0 * x)
+ 9.0 * torch.cos(3.0 * x)
+ 16.0 * torch.cos(4.0 * x)
+ 64.0 * torch.cos(8.0 * x)
)
residual = -second - source
residual_gradient = -third - source_gradient
residual_loss = torch.mean(residual.square())
boundary_loss = torch.mean((model(boundary) - boundary_values).square())
gradient_loss = torch.mean(residual_gradient.square())
loss = residual_loss + boundary_loss + gradient_weight * gradient_loss
return loss, {
"residual": residual_loss.item(),
"boundary": boundary_loss.item(),
"gradient": gradient_loss.item(),
}
def exact_poisson2d(x: np.ndarray, y: np.ndarray, exponent: float) -> np.ndarray:
return (16.0 * x * y * (1.0 - x) * (1.0 - y)) ** exponent
def _poisson2d_source(coordinates: torch.Tensor, exponent: float) -> torch.Tensor:
x = coordinates[:, 0:1]
y = coordinates[:, 1:2]
exact = (16.0 * x * y * (1.0 - x) * (1.0 - y)) ** exponent
exact_gradient = autograd.grad(
exact, coordinates, torch.ones_like(exact), create_graph=True
)[0]
exact_xx = autograd.grad(
exact_gradient[:, 0:1],
coordinates,
torch.ones_like(exact_gradient[:, 0:1]),
create_graph=True,
)[0][:, 0:1]
exact_yy = autograd.grad(
exact_gradient[:, 1:2],
coordinates,
torch.ones_like(exact_gradient[:, 1:2]),
create_graph=True,
)[0][:, 1:2]
return -(exact_xx + exact_yy)
def gpinn_loss_poisson2d(
model: nn.Module,
interior: torch.Tensor,
gradient_weight: float,
exponent: float,
) -> tuple[torch.Tensor, dict[str, float]]:
coordinates = interior.detach().requires_grad_(True)
prediction = model(coordinates)
prediction_gradient = autograd.grad(
prediction, coordinates, torch.ones_like(prediction), create_graph=True
)[0]
prediction_xx = autograd.grad(
prediction_gradient[:, 0:1],
coordinates,
torch.ones_like(prediction_gradient[:, 0:1]),
create_graph=True,
)[0][:, 0:1]
prediction_yy = autograd.grad(
prediction_gradient[:, 1:2],
coordinates,
torch.ones_like(prediction_gradient[:, 1:2]),
create_graph=True,
)[0][:, 1:2]
residual = prediction_xx + prediction_yy + _poisson2d_source(coordinates, exponent)
residual_gradient = autograd.grad(
residual, coordinates, torch.ones_like(residual), create_graph=True
)[0]
residual_loss = torch.mean(residual.square())
gradient_loss = torch.mean(residual_gradient[:, 0:1].square()) + torch.mean(
residual_gradient[:, 1:2].square()
)
loss = residual_loss + gradient_weight * gradient_loss
return loss, {"residual": residual_loss.item(), "gradient": gradient_loss.item()}
def output_transform_burgers(
coordinates: torch.Tensor, raw_prediction: torch.Tensor
) -> torch.Tensor:
x = coordinates[:, 0:1]
t = coordinates[:, 1:2]
return (
(1.0 - x) * (1.0 + x) * (1.0 - torch.exp(-t)) * raw_prediction
- torch.sin(torch.pi * x)
)
class gPINNBurgers(nn.Module):
"""Burgers model with hard initial and boundary constraints."""
def __init__(self, layers: Sequence[int]) -> None:
super().__init__()
self.net = gPINN(layers)
def forward(self, coordinates: torch.Tensor) -> torch.Tensor:
return output_transform_burgers(coordinates, self.net(coordinates))
def burgers_residual(
model: nn.Module, coordinates: torch.Tensor, create_graph: bool = True
) -> tuple[torch.Tensor, torch.Tensor]:
inputs = coordinates.detach().requires_grad_(True)
prediction = model(inputs)
prediction_gradient = autograd.grad(
prediction, inputs, torch.ones_like(prediction), create_graph=True
)[0]
prediction_x = prediction_gradient[:, 0:1]
prediction_t = prediction_gradient[:, 1:2]
prediction_xx = autograd.grad(
prediction_x,
inputs,
torch.ones_like(prediction_x),
create_graph=create_graph,
)[0][:, 0:1]
viscosity = 0.01 / torch.pi
residual = prediction_t + prediction * prediction_x - viscosity * prediction_xx
return residual, inputs
def burgers_gpinn_terms(
model: nn.Module, coordinates: torch.Tensor
) -> tuple[torch.Tensor, torch.Tensor, torch.Tensor]:
residual, inputs = burgers_residual(model, coordinates, create_graph=True)
residual_gradient = autograd.grad(
residual, inputs, torch.ones_like(residual), create_graph=True
)[0]
return residual, residual_gradient[:, 0:1], residual_gradient[:, 1:2]
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