scimba_torch.numerical_solvers.preconditioner_pinns

Preconditioners for pinns.

Classes

AnagramPreconditioner(space, pde, **kwargs)	Anagram preconditioner.
EnergyNaturalGradientPreconditioner(space, ...)	Energy-based natural gradient preconditioner.
MatrixPreconditionerPinn(space, pde, **kwargs)	Matrix-based preconditioner for pinns.

class MatrixPreconditionerPinn(space, pde, **kwargs)

Bases: MatrixPreconditionerSolver

Matrix-based preconditioner for pinns.

Parameters:

• space (AbstractApproxSpace) – The approximation space.

• pde (EllipticPDE | TemporalPDE | KineticPDE | LinearOrder2PDE) – The PDE to be solved.

• **kwargs –

  Additional keyword arguments:

  • in_lhs_name: Name of the operator to be used in the left-hand side assembly. (default: “functional_operator”)

Raises:

ValueError – residual size (bc, ic) is not a multiple of the number of labels

class EnergyNaturalGradientPreconditioner(space, pde, **kwargs)

Bases: MatrixPreconditionerPinn

Energy-based natural gradient preconditioner.

Parameters:

• space (AbstractApproxSpace) – The approximation space.

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

• **kwargs –

  Additional keyword arguments:

  • matrix_regularization: Regularization parameter for the preconditioning matrix (default: 1e-6).

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_full_preconditioning_matrix(data, **kwargs)

Compute the full preconditioning matrix.

Include contributions from the main operator, boundary conditions, and initial conditions.

Parameters:

• data (tuple | dict) – Input data, either as a tuple or a dictionary.

• **kwargs – Additional keyword arguments.

Return type:

Tensor

Returns:

The full preconditioning matrix.

class AnagramPreconditioner(space, pde, **kwargs)

Bases: MatrixPreconditionerPinn

Anagram preconditioner.

This preconditioner is based on the anagram method, which aims to improve convergence by transforming the problem into a more favorable form.

Parameters:

• space (AbstractApproxSpace) – The approximation space.

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

• **kwargs –

  Additional keyword arguments:

  • svd_threshold (float): Threshold for singular value decomposition (default: 1e-6).

  • bc_weight (float): Weight for boundary condition contributions (default: 1.0).

  • ic_weight (float): Weight for initial condition contributions (default: 1.0).

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.

assemble_right_member(data, res_l, res_r)

Assemble the right-hand side of the equation.

Parameters:

• data (tuple | dict) – Input data, either as a tuple or a dictionary.

• res_l (tuple) – Left residuals.

• res_r (tuple) – Right residuals.

Return type:

Tensor

Returns:

The assembled right-hand side tensor.

assemble_right_member_bc(data, res_l, res_r)

Assemble the right-hand side for boundary conditions.

Parameters:

• data (tuple | dict) – Input data, either as a tuple or a dictionary.

• res_l (tuple) – Left residuals.

• res_r (tuple) – Right residuals.

Return type:

Tensor

Returns:

The assembled right-hand side tensor for boundary conditions.

assemble_right_member_ic(data, res_l, res_r)

Assemble the right-hand side for initial conditions.

Parameters:

• data (tuple | dict) – Input data, either as a tuple or a dictionary.

• res_l (tuple) – Left residuals.

• res_r (tuple) – Right residuals.

Return type:

Tensor

Returns:

The assembled right-hand side tensor for initial conditions.