scimba_torch.numerical_solvers.pinn_preconditioners.sketchy_ng

Preconditioner for pinns.

Classes

SketchyNaturalGradientPreconditioner(space, ...)

Sketchy natural gradient preconditioner.

class SketchyNaturalGradientPreconditioner(space, pde, **kwargs)

Bases: MatrixPreconditionerPinn

Sketchy natural gradient preconditioner.

Implements [McKay and al. 2025].

Parameters:

• space (AbstractApproxSpace) – The approximation space.

• pde (EllipticPDE | TemporalPDE | KineticPDE | LinearOrder2PDE | RitzFormEllipticPDE | DivAGradUPDE) – The PDE to be solved, which can be an instance of EllipticPDE, TemporalPDE, KineticPDE, or LinearOrder2PDE.

• **kwargs – Additional keyword arguments:

Keyword Arguments:

• tol (float) – The threshold for deciding the size of the sketch matrix, r in the paper. (default: 1e-13).

• single_pass (bool) – single pass or two pass (default False, means two pass).

[McKay and al. 2025] Near-optimal Sketchy Natural Gradients

for Physics-Informed Neural Networks, M. B. McKay, A. Kaur, C. Greif, B. Wetton Proceedings of the 42 nd International Conference on Machine Learning, Vancouver, Canada. PMLR 267, 2025

compute_preconditioning_matrix(labels, *args, **kwargs)

Compute the preconditioning matrix using the main operator.

Parameters:

• labels (Tensor) – The labels tensor.

• *args (Tensor) – Additional arguments.

• **kwargs – Additional keyword arguments.

Return type:

Tensor

Returns:

The preconditioning matrix.

compute_preconditioning_matrix_bc(labels, *args, **kwargs)

Compute the boundary condition preconditioning matrix.

Parameters:

• labels (Tensor) – The labels tensor.

• *args (Tensor) – Additional arguments.

• **kwargs – Additional keyword arguments.

Return type:

Tensor

Returns:

The boundary condition preconditioning matrix.

compute_preconditioning_matrix_ic(labels, *args, **kwargs)

Compute the initial condition preconditioning matrix.

Parameters:

• labels (Tensor) – The labels tensor.

• *args (Tensor) – Additional arguments.

• **kwargs – Additional keyword arguments.

Return type:

Tensor

Returns:

The initial condition preconditioning matrix.

compute_preconditioning_matrix_dl(*args, **kwargs)

Computes the Gram matrix of the network for the given input tensors.

Parameters:

• *args (Tensor) – Input tensors for computing the Gram matrix.

• **kwargs – Additional keyword arguments.

Return type:

Tensor

Returns:

The computed Gram matrix.