scimba_torch.physical_models.ode.abstract_ode

Module for abstract ODEs.

Functions

zeros_rhs(w, t, mu[, nb_func])

Function returning a zero right-hand side.

Classes

AbstractODE(space, init[, n_equations, rhs_func])

Base class for representing Ordinary Differential Equations (ODEs).

zeros_rhs(w, t, mu, nb_func=1)

Function returning a zero right-hand side.

Parameters:

• w (MultiLabelTensor) – Solution tensor.

• t (LabelTensor) – Temporal coordinates tensor.

• mu (LabelTensor) – Parameter tensor.

• nb_func (int) – Number of functions to return (default is 1).

Return type:

Tensor

Returns:

A tensor of zeros with shape (number of points, nb_func).

class AbstractODE(space, init, n_equations=1, rhs_func=None, **kwargs)

Bases: ABC

Base class for representing Ordinary Differential Equations (ODEs).

Parameters:

• space (AbstractApproxSpace) – Approximation space used for the ODE

• init (Callable) – Initial condition function

• n_equations (int) – Number of equations in the system (default is 1)

• rhs_func (Optional[Callable]) – Right-hand side function of the ODE (default is zeros_rhs)

• **kwargs – Additional keyword arguments

grad(w, y)

Compute the gradient of the tensor w with respect to the tensor y.

Parameters:

• w (Tensor | MultiLabelTensor) – Input tensor

• y (Tensor | LabelTensor) – Tensor with respect to which the gradient is computed

Return type:

Tensor | tuple[Tensor, ...]

Returns:

Gradient tensor

rhs(w, t, mu)

Compute the right-hand side (RHS) of the PDE.

Parameters:

• w (MultiLabelTensor) – Solution tensor

• t (LabelTensor) – Temporal coordinate tensor

• mu (LabelTensor) – Parameter tensor

Return type:

Tensor | tuple[Tensor, ...]

Returns:

RHS tensor

abstract time_operator(w, t, mu)

Apply the PDE operator.

Parameters:

• w (MultiLabelTensor) – Solution tensor

• t (LabelTensor) – Temporal coordinate tensor

• mu (LabelTensor) – Parameter tensor

Return type:

Tensor | tuple[Tensor, ...]

Returns:

Operator tensor

operator(w, t, mu)

Apply the PDE operator.

Parameters:

• w (MultiLabelTensor) – Solution tensor

• t (LabelTensor) – Temporal coordinate tensor

• mu (LabelTensor) – Parameter tensor

Return type:

Tensor | tuple[Tensor, ...]

Returns:

Operator tensor

initial_condition(mu)

Compute the initial condition.

Parameters:

mu (LabelTensor) – Parameter tensor

Return type:

tuple[Tensor, ...]

Returns:

Initial condition tensor

functional_operator_ic(func, mu, theta)

Compute the functional operator for initial conditions.

Parameters:

• func (VarArgCallable) – Callable representing the function

• mu (Tensor) – Parameter tensor

• theta (Tensor) – Additional parameters tensor

Return type:

Tensor

Returns:

Functional operator tensor for initial conditions