scimba_torch.numerical_solvers.ode.pinns¶

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

It is designed to solve ordinary differential equations (ODEs) using physics-informed neural networks (PINNs).

Classes

`NaturalGradientODEPinns`(ode[, ic_type])	A class extending ODEPinns with natural gradient preconditioning.
`ODEPinns`(ode[, ic_type])	A class to solve ODEs using Physics-Informed Neural Networks.
`PreconditionedODEPinns`(**kwargs)	A class extending ODEPinns with preconditioning.

class ODEPinns(ode, ic_type='strong', **kwargs)[source]¶

Bases: CollocationProjector

A class to solve ODEs using Physics-Informed Neural Networks.

Parameters:

ode (AbstractODE) – The ODE to be solved
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 ic_weights does not match residual_size or ic_residual_size

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, mu)[source]¶

Evaluates the approximation at given points.

Parameters:

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

Return type:

MultiLabelTensor

Returns:

The evaluated solution.

sample_all_vars(**kwargs)[source]¶

Samples collocation points for the ODE 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(tmu, **kwargs)[source]¶

Assembles the system of equations post-sampling.

Parameters:

tmu (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 ODE.

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

class PreconditionedODEPinns(**kwargs)[source]¶

Bases: ABC

A class extending ODEPinns with preconditioning.

Parameters:

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

Keyword Arguments:

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).

class NaturalGradientODEPinns(ode, ic_type='strong', **kwargs)[source]¶

Bases: ODEPinns, PreconditionedODEPinns

A class extending ODEPinns with natural gradient preconditioning.

Parameters:

ode (AbstractODE) – The ODE to be solved.
ic_type (str) – Type of initial condition (“strong” or “weak”). Defaults to “strong”.
**kwargs – Additional keyword arguments for customization.

Keyword Arguments:

ng_algo (str) – The algorithm for computing the natural gradient preconditioning matrix. Default : “ENG”.

Raises:

ValueError – value for ng_algo keyword argument is not correct.
NotImplementedError – value for ng_algo keyword argument is not implemented.