scimba_torch.numerical_solvers.preconditioner_pinns¶

Preconditioners for pinns.

Classes

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

class MatrixPreconditionerPinn(space, pde, **kwargs)[source]¶

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”)

class EnergyNaturalGradientPreconditioner(space, pde, is_operator_linear=False, **kwargs)[source]¶

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.
is_operator_linear (bool) – Whether the operator is linear (default: False).
**kwargs –
Additional keyword arguments:
- matrix_regularization: Regularization parameter for the preconditioning matrix (default: 1e-6).

eval_and_jactheta(*args)[source]¶

Evaluate the Jacobian of the network with respect to its parameters.

Parameters:: *args (Tensor | dict[str, Parameter]) – Arguments to be passed to the network, with the last argument being the parameters of the network.
Return type:: Tensor
Returns:: The Jacobian matrix of the network with respect to its parameters.

eval_and_jactheta_and_func(func, *args)[source]¶

Evaluate the Jacobian of a given function.

With respect to the network parameters.

Parameters:

func (Callable) – The function whose Jacobian is to be computed.
*args (Tensor | dict[str, Parameter]) – Arguments to be passed to the function, with the last argument being the parameters of the network.

Return type:

Tensor

Returns:

The Jacobian matrix of the function with respect to the network parameters.s

compute_preconditioning_matrix(labels, *args, **kwargs)[source]¶

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)[source]¶

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)[source]¶

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)[source]¶

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)[source]¶

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).

Raises:

AttributeError – If the residual_size, bc_residual_size, or ic_residual_size attributes are not integers.

compute_preconditioning_matrix(labels, *args, **kwargs)[source]¶

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)[source]¶

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)[source]¶

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)[source]¶

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)[source]¶

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)[source]¶

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.