scimba_torch.numerical_solvers.collocation_projector¶

Collocation-based projectors for approximation spaces.

Functions

plot(f, sampler[, n_visu])

Plot the function f over a 2D domain using sampled points.

Classes

`AnagramProjector`(space[, rhs])	Subclass of CollocationProjector using anagram-based optimization.
`CollocationProjector`(space[, rhs])	A collocation-based nonlinear projection method.
`LinearProjector`(space, rhs, **kwargs)	Subclass of CollocationProjector for linear projection problems.
`NaturalGradientProjector`(space[, rhs])	Subclass of CollocationProjector using natural gradient optimization.

class CollocationProjector(space, rhs=None, **kwargs)[source]¶

Bases: AbstractNonlinearProjector

A collocation-based nonlinear projection method.

This subclass implements methods to assemble the input and output tensors for a specific nonlinear projection problem using collocation points. It computes the approximation of a nonlinear problem by sampling collocation points and evaluating the corresponding function values.

Parameters:

space (AbstractApproxSpace) – The approximation space where the projection will take place.
rhs (Optional[Callable[..., Tensor]]) – The function representing the right-hand side of the problem.
**kwargs – Additional parameters for the projection, including collocation points and losses.

set_rhs(rhs)[source]¶

Sets the right-hand side function for the projection.

Parameters:: rhs (Callable[..., Tensor]) – The function representing the right-hand side of the problem.

get_dof(flag_scope='all', flag_format='list')[source]¶

Retrieves the degrees of freedom (DoF) of the approximation space.

Parameters:

flag_scope (str) – Specifies the scope of the parameters to return.
flag_format (str) – The format for returning the parameters.

Returns:

The degrees of freedom in the specified format.

metric_matrix(x, mu, t=None, v=None, **kwargs)[source]¶

Computes the metric matrix for the given tensors.

Parameters:

x (LabelTensor) – Input tensor from the spatial domain.
mu (LabelTensor) – Input tensor from the parameter domain.
t (LabelTensor | None) – Input tensor from the time domain (optional).
v (LabelTensor | None) – Input tensor from the velocity domain (optional).
**kwargs – Additional arguments.

Return type:

Tensor

Returns:

The computed metric matrix.

Raises:

NotImplementedError – If the metric matrix is not defined for the current space type.

sample_all_vars(**kwargs)[source]¶

Samples values in the domains of the arguments of the function to project.

Parameters:: **kwargs (Any) – Additional arguments for sampling.
Return type:: tuple[LabelTensor, ...]
Returns:: A tuple containing the sampled tensors.

assembly_post_sampling(data, **kwargs)[source]¶

Assemble the I/O tensors for the nonlinear projection problem after sampling.

Parameters:

data (tuple[LabelTensor, ...]) – The sampled data.
**kwargs – Additional arguments for assembly, including flag_scope.

Return type:

tuple[tuple[Tensor, ...], tuple[Tensor, ...]]

Returns:

A tuple of tuples containing the assembled left and right-hand sides.

assembly(**kwargs)[source]¶

Assembles the system of equations for the projection problem.

Parameters:: **kwargs (Any) – Additional arguments for assembly, including the number of collocation points.
Return type:: tuple[tuple[Tensor, ...], tuple[Tensor, ...]]
Returns:: A tuple of tuples containing the assembled left and right-hand sides.

update_parameter_bounds(new_bounds)[source]¶

Updates the bounds of the parameters in the approximation space.

Parameters:: new_bounds (list[tuple[float, float]]) – A list of tuples containing the new bounds for each parameter.
Return type:: None

class NaturalGradientProjector(space, rhs=None, **kwargs)[source]¶

Bases: CollocationProjector

Subclass of CollocationProjector using natural gradient optimization.

This class extends the CollocationProjector to use natural gradient optimization for solving the projection problem.

Parameters:

space (AbstractApproxSpace) – The approximation space where the projection will take place.
rhs (Optional[Callable[..., Tensor]]) – The function representing the right-hand side of the problem.
**kwargs – Additional parameters for the projection, including collocation points and losses.

Keyword Arguments:

ng_algo (str) – The algorithm for computing the natural gradient preconditioning matrix. Default : “ENG”.
default_lr (float) – The default learning rate used when linesearch fails. Default : 1e-2.
type_linesearch (str) – The linesearch algorithm: either “armijo” or “logarithmic_grid”. Default: “armijo”
data_linesearch (dict) – optional parameters for the linesearch. For logarithmic grid: “m” (nb nodes in the grid), “interval” (min max values of the grid), “log_basis” the logarithmic basis. For armijo: “n_step_max” (the max number of steps), “alpha” and “beta” (the alpha and beta parameters).

Raises:

ValueError – value for ng_algo keyword argument is not correct.

class AnagramProjector(space, rhs=None, **kwargs)[source]¶

Bases: CollocationProjector

Subclass of CollocationProjector using anagram-based optimization.

This class extends the CollocationProjector to use anagram-based optimization for solving the projection problem.

Parameters:

space (AbstractApproxSpace) – The approximation space where the projection will take place.
rhs (Optional[Callable[..., Tensor]]) – The function representing the right-hand side of the problem.
**kwargs – Additional parameters for the projection, including collocation points and losses.

class LinearProjector(space, rhs, **kwargs)[source]¶

Bases: CollocationProjector

Subclass of CollocationProjector for linear projection problems.

This class extends the CollocationProjector to handle linear projection problems.

Parameters:

space (AbstractApproxSpace) – The approximation space where the projection will take place.
rhs (Callable) – The function representing the right-hand side of the problem.
**kwargs – Additional parameters for the projection, including collocation points and losses.

plot(f, sampler, n_visu=500)[source]¶

Plot the function f over a 2D domain using sampled points.

Parameters:

f (Callable) – The function to plot, which takes in sampled points and parameters.
sampler (Callable) – A callable that samples points from the domain.
n_visu (int) – The number of points along each axis for visualization.