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anypinn.catalog.heat_1d

ALPHA_KEY = 'alpha' module-attribute

TRUE_ALPHA = 0.1 module-attribute

U_KEY = 'u' module-attribute

Heat1DDataModule

Bases: PINNDataModule

DataModule for 1D heat equation inverse problem.

gen_data produces sparse interior measurements from the analytic solution u(x,t) = exp(-alpha pi^2 t) sin(pi x), with optional noise. These measurements are used by DataConstraint during training to recover alpha.

Source code in src/anypinn/catalog/heat_1d.py 
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class Heat1DDataModule(PINNDataModule):
    """DataModule for 1D heat equation inverse problem.

    gen_data produces sparse interior measurements from the analytic
    solution u(x,t) = exp(-alpha pi^2 t) sin(pi x), with optional noise.
    These measurements are used by DataConstraint during training
    to recover alpha.
    """

    def __init__(
        self,
        hp: PINNHyperparameters,
        true_alpha: float = TRUE_ALPHA,
        n_measurements: int = 200,
        noise_std: float = 0.01,
        grid_size: int = 50,
        validation: ValidationRegistry | None = None,
        callbacks: list[DataCallback] | None = None,
    ):
        self.true_alpha = true_alpha
        self.n_measurements = n_measurements
        self.noise_std = noise_std
        self.grid_size = grid_size
        super().__init__(hp, validation, callbacks)

    @override
    def gen_data(self, config: GenerationConfig) -> tuple[Tensor, Tensor]:
        """Generate analytic solution on a 2D meshgrid for training + prediction."""
        xs = torch.linspace(0, 1, self.grid_size)
        ts = torch.linspace(0, 1, self.grid_size)
        grid_x, grid_t = torch.meshgrid(xs, ts, indexing="ij")

        x_grid = torch.stack([grid_x.reshape(-1), grid_t.reshape(-1)], dim=1)  # (N, 2)

        u_analytic = torch.exp(-self.true_alpha * math.pi**2 * x_grid[:, 1]) * torch.sin(
            math.pi * x_grid[:, 0]
        )

        # Add measurement noise
        u_noisy = u_analytic + self.noise_std * torch.randn_like(u_analytic)

        # Shape: (N, 1, 1) to match codebase convention
        y_data = u_noisy.unsqueeze(-1).unsqueeze(1)

        return x_grid, y_data

grid_size = grid_size instance-attribute

n_measurements = n_measurements instance-attribute

noise_std = noise_std instance-attribute

true_alpha = true_alpha instance-attribute

__init__(hp: PINNHyperparameters, true_alpha: float = TRUE_ALPHA, n_measurements: int = 200, noise_std: float = 0.01, grid_size: int = 50, validation: ValidationRegistry | None = None, callbacks: list[DataCallback] | None = None)

Source code in src/anypinn/catalog/heat_1d.py 
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def __init__(
    self,
    hp: PINNHyperparameters,
    true_alpha: float = TRUE_ALPHA,
    n_measurements: int = 200,
    noise_std: float = 0.01,
    grid_size: int = 50,
    validation: ValidationRegistry | None = None,
    callbacks: list[DataCallback] | None = None,
):
    self.true_alpha = true_alpha
    self.n_measurements = n_measurements
    self.noise_std = noise_std
    self.grid_size = grid_size
    super().__init__(hp, validation, callbacks)

gen_data(config: GenerationConfig) -> tuple[Tensor, Tensor]

Generate analytic solution on a 2D meshgrid for training + prediction.

Source code in src/anypinn/catalog/heat_1d.py 
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@override
def gen_data(self, config: GenerationConfig) -> tuple[Tensor, Tensor]:
    """Generate analytic solution on a 2D meshgrid for training + prediction."""
    xs = torch.linspace(0, 1, self.grid_size)
    ts = torch.linspace(0, 1, self.grid_size)
    grid_x, grid_t = torch.meshgrid(xs, ts, indexing="ij")

    x_grid = torch.stack([grid_x.reshape(-1), grid_t.reshape(-1)], dim=1)  # (N, 2)

    u_analytic = torch.exp(-self.true_alpha * math.pi**2 * x_grid[:, 1]) * torch.sin(
        math.pi * x_grid[:, 0]
    )

    # Add measurement noise
    u_noisy = u_analytic + self.noise_std * torch.randn_like(u_analytic)

    # Shape: (N, 1, 1) to match codebase convention
    y_data = u_noisy.unsqueeze(-1).unsqueeze(1)

    return x_grid, y_data