scimba_torch.numerical_solvers.preconditioner_deep_ritz¶

Deep Ritz preconditioners.

Classes

`EnergyNaturalGradientPreconditioner`(space, ...)	Energy Natural Gradient preconditioner for Deep Ritz methods.
`MatrixPreconditionerDeepRitz`(space, pde, ...)	Matrix-based preconditioner for pinns.

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

Bases: MatrixPreconditionerSolver

Matrix-based preconditioner for pinns.

Parameters:

space (AbstractApproxSpace) – The approximation space.
pde (RitzFormEllipticPDE | DivAGradUPDE) – The PDE to be solved.
**kwargs – Additional keyword arguments.

Raises:

AttributeError – If the input PDE does not have the required attributes.

vectorize_along_physical_variables(func)[source]¶

Vectorizes a function along physical variables based on the type of space.

Parameters:: func (VarArgAnyCallable) – The function to be vectorized.
Return type:: VarArgAnyCallable
Returns:: The vectorized function.
Raises:: NotImplementedError – If the type of space is not supported.

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

Bases: MatrixPreconditionerDeepRitz

Energy Natural Gradient preconditioner for Deep Ritz methods.

Parameters:

space (AbstractApproxSpace) – The approximation space used in the Deep Ritz method.
pde (RitzFormEllipticPDE | DivAGradUPDE) – The elliptic PDE represented as an instance of RitzForm_Elliptic
**kwargs – Additional keyword arguments.

Raises:

ValueError – If the number of unknowns in the space is greater than 1.

eval_and_gradx(*args)[source]¶

Evaluate the function and compute its gradient.

Parameters:: *args (Tensor | dict[str, Parameter]) – Input arguments where the last argument is the parameters of the network.
Returns:: A tensor containing the function evaluation and its gradient.

eval_and_gradx_and_jactheta(*args)[source]¶

Evaluate the function, compute its gradient, and the Jacobian.

Parameters:: *args (Tensor | dict[str, Parameter]) – Input arguments where the last argument is the parameters of the network.
Returns:: A tensor containing the function evaluation, its gradient, and the Jacobian

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

Compute the preconditioning matrix.

Parameters:

labels (Tensor) – Tensor of labels corresponding to the input data.
*args (Tensor) – Additional arguments required for computing the matrix.
**kwargs – Additional keyword arguments.

Return type:

Tensor

Returns:

The computed preconditioning matrix as a tensor.

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

Compute the boundary condition preconditioning matrix.

Parameters:

labels (Tensor) – Tensor of labels corresponding to the boundary condition data.
*args (Tensor) – Additional arguments required for computing the matrix.
**kwargs – Additional keyword arguments.

Return type:

Tensor

Returns:

The computed boundary condition preconditioning matrix as a tensor.

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

Compute the initial condition preconditioning matrix.

Parameters:

labels (Tensor) – Tensor of labels corresponding to the boundary condition data.
*args (Tensor) – Additional arguments required for computing the matrix.
**kwargs – Additional keyword arguments.

Return type:

Tensor

Returns:

NotImplementedError.