scimba_torch.physical_models.ode.simple_ode

Implementation of a simple 1D ODE.

Classes

SimpleODE(space, init, **kwargs)

Implementation of a 1D simple ODE.

class SimpleODE(space, init, **kwargs)

Bases: AbstractODE

Implementation of a 1D simple ODE.

\[\begin{split}\frac{du}{dt} = \\mu u, \\quad t \\in (0, T),\end{split}\]

with an initial condition given by the function init.

Parameters:

• space (AbstractApproxSpace) – The approximation space for the problem

• init (Callable) – Callable for the initial condition

• **kwargs – Additional keyword arguments

time_operator(w, t, mu)

Apply the ODE operator.

Parameters:

• w (MultiLabelTensor) – Solution tensor

• t (LabelTensor) – Temporal coordinate tensor

• mu (LabelTensor) – Parameter tensor

Return type:

Tensor | tuple[Tensor, ...]

Returns:

Operator tensor

functional_operator(func, t, mu, theta)

Compute the functional operator.

Parameters:

• func (VarArgCallable) – Callable representing the function

• t (Tensor) – Temporal coordinate tensor

• mu (Tensor) – Parameter tensor

• theta (Tensor) – Additional parameters tensor

Return type:

Tensor

Returns:

Functional operator tensor