scimba_torch.numerical_solvers.temporal_pde.pinns¶

Define the TemporalPinns class, which is a subclass of CollocationProjector.

It is designed to solve time-dependent partial differential equations (PDEs) using physics-informed neural networks (PINNs).

Classes

`AnagramTemporalPinns`(pde[, bc_type, ic_type])	A class extending TemporalPinns with Anagram preconditioning.
`NaturalGradientTemporalPinns`(pde[, bc_type, ...])	A class extending TemporalPinns with natural gradient preconditioning.
`TemporalPinns`(pde[, bc_type, ic_type])	A class to solve time-dependent PDEs using Physics-Informed Neural Networks.

class TemporalPinns(pde, bc_type='strong', ic_type='strong', **kwargs)[source]¶

Bases: CollocationProjector

A class to solve time-dependent PDEs using Physics-Informed Neural Networks.

Parameters:

pde (TemporalPDE) – The time-dependent PDE to be solved
bc_type (str) – The type of boundary condition to be applied (“strong” or “weak”). (default: “strong”)
ic_type (str) – The type of initial condition to be applied (“strong” or “weak”). (default: “strong”)
**kwargs – Additional keyword arguments for customization.

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

Gets the parameters of the approximation space in use.

Parameters:

flag_scope (str) – Scope of the degrees of freedom to retrieve.
flag_format (str) – Format of the output, either “list” or “tensor”.

Return type:

Tensor | list

Returns:

Degrees of freedom in the specified format.

evaluate(t, x, mu)[source]¶

Evaluates the approximation at given points.

Parameters:

t (Tensor) – Input tensor for time coordinates.
x (Tensor) – Input tensor for spatial coordinates.
mu (Tensor) – Input tensor for parameters.

Return type:

MultiLabelTensor

Returns:

The evaluated solution.

sample_all_vars(**kwargs)[source]¶

Samples collocation points for the PDE, BCs, and initial conditions.

Parameters:: **kwargs (Any) – Additional keyword arguments for sampling.
Return type:: dict[str, tuple[LabelTensor, ...]]
Returns:: Dictionary of sampled tensors.

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

Assembles the system of equations post-sampling.

Parameters:

txmu (dict) – dictionary of sampled tensors.
**kwargs – Additional keyword arguments.

Return type:

tuple

Returns:

Tuple containing the assembled operator and right-hand side.

assembly(**kwargs)[source]¶

Assembles the system of equations for the PDE.

Assembles also weak boundary conditions if needed.

Parameters:: **kwargs (Any) – Additional keyword arguments.
Return type:: tuple
Returns:: Tuple containing the assembled operator and right-hand side.

class NaturalGradientTemporalPinns(pde, bc_type='strong', ic_type='strong', **kwargs)[source]¶

Bases: TemporalPinns

A class extending TemporalPinns with natural gradient preconditioning.

Parameters:

pde (TemporalPDE) – The time-dependent PDE to be solved.
bc_type (str) – Type of boundary condition (“strong” or “weak”). Defaults to “strong”.
ic_type (str) – Type of initial condition (“strong” or “weak”). Defaults to “strong”.
**kwargs – Additional keyword arguments for customization.

class AnagramTemporalPinns(pde, bc_type='strong', ic_type='strong', **kwargs)[source]¶

Bases: TemporalPinns

A class extending TemporalPinns with Anagram preconditioning.

Parameters:

pde (TemporalPDE) – The time-dependent PDE to be solved.
bc_type (str) – Type of boundary condition (“strong” or “weak”). Defaults to “strong”.
ic_type (str) – Type of initial condition (“strong” or “weak”). Defaults to “strong”.
**kwargs – Additional keyword arguments for customization.