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.
PreconditionedTemporalPinns(**kwargs)	A class extending TemporalPinns with 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)

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.

Raises:

ValueError – when the lengths of in_weights or bc_weights of ic_weights does not match residual_size or bc_residual_size or ic_residual_size

get_dof(flag_scope='all', flag_format='list')

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)

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)

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)

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)

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 PreconditionedTemporalPinns(**kwargs)

Bases: ABC

A class extending TemporalPinns with preconditioning.

Parameters:

**kwargs (Any) – Additional keyword arguments for customization.

class NaturalGradientTemporalPinns(pde, bc_type='strong', ic_type='strong', **kwargs)

Bases: TemporalPinns, PreconditionedTemporalPinns

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)

Bases: TemporalPinns, PreconditionedTemporalPinns

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.