scimba_torch.physical_models.temporal_pde.abstract_temporal_pde

Module for abstract temporal PDEs.

Classes

FirstOrderTemporalPDE(space[, linear])	Base class for representing elliptic Partial Differential Equations (PDEs).
SecondOrderTemporalPDE(space[, linear])	Base class for representing elliptic Partial Differential Equations (PDEs).
TemporalPDE(space[, linear])	Base class for representing elliptic Partial Differential Equations (PDEs).

class TemporalPDE(space, linear=False, **kwargs)

Bases: ABC

Base class for representing elliptic Partial Differential Equations (PDEs).

Parameters:

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

• linear (bool) – Whether the PDE is linear

• **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

abstract rhs(w, t, x, mu)

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

Parameters:

• w (MultiLabelTensor) – Solution tensor

• t (LabelTensor) – Temporal coordinate tensor

• x (LabelTensor) – Spatial coordinate tensor

• mu (LabelTensor) – Parameter tensor

Return type:

Tensor | tuple[Tensor, ...]

Returns:

RHS tensor

abstract space_operator(w, t, x, mu)

Apply the PDE operator.

Parameters:

• w (MultiLabelTensor) – Solution tensor

• t (LabelTensor) – Temporal coordinate tensor

• x (LabelTensor) – Spatial coordinate tensor

• mu (LabelTensor) – Parameter tensor

Return type:

Tensor | tuple[Tensor, ...]

Returns:

Operator tensor

abstract time_operator(w, t, x, mu)

Apply the PDE operator.

Parameters:

• w (MultiLabelTensor) – Solution tensor

• t (LabelTensor) – Temporal coordinate tensor

• x (LabelTensor) – Spatial coordinate tensor

• mu (LabelTensor) – Parameter tensor

Return type:

Tensor | tuple[Tensor, ...]

Returns:

Operator tensor

operator(w, t, x, mu)

Apply the PDE operator.

Parameters:

• w (MultiLabelTensor) – Solution tensor

• t (LabelTensor) – Temporal coordinate tensor

• x (LabelTensor) – Spatial coordinate tensor

• mu (LabelTensor) – Parameter tensor

Return type:

Tensor | tuple[Tensor, ...]

Returns:

Operator tensor

abstract bc_rhs(w, t, x, n, mu)

Compute the boundary condition RHS.

Parameters:

• w (MultiLabelTensor) – Solution tensor

• t (LabelTensor) – Temporal coordinate tensor

• x (LabelTensor) – Spatial coordinate tensor

• n (LabelTensor) – Normal vector tensor

• mu (LabelTensor) – Parameter tensor

Return type:

Tensor

Returns:

Boundary condition RHS tensor

abstract bc_operator(w, t, x, n, mu)

Apply the boundary condition operator.

Parameters:

• w (MultiLabelTensor) – Solution tensor

• t (LabelTensor) – Temporal coordinate tensor

• x (LabelTensor) – Spatial coordinate tensor

• n (LabelTensor) – Normal vector tensor

• mu (LabelTensor) – Parameter tensor

Return type:

Tensor

Returns:

Boundary condition operator tensor

abstract initial_condition(x, mu)

Compute the initial condition.

Parameters:

• x (LabelTensor) – Spatial coordinate tensor

• mu (LabelTensor) – Parameter tensor

Return type:

tuple[Tensor, ...]

Returns:

Initial condition tensor

class FirstOrderTemporalPDE(space, linear=False, **kwargs)

Bases: TemporalPDE

Base class for representing elliptic Partial Differential Equations (PDEs).

Parameters:

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

• linear (bool) – Whether the PDE is linear

• **kwargs – Additional keyword arguments

time_operator(w, t, x, mu)

Apply the PDE operator.

Parameters:

• w (MultiLabelTensor) – Solution tensor

• t (LabelTensor) – Temporal coordinate tensor

• x (LabelTensor) – Spatial coordinate tensor

• mu (LabelTensor) – Parameter tensor

Return type:

Tensor | tuple[Tensor, ...]

Returns:

Operator tensor

class SecondOrderTemporalPDE(space, linear=False, **kwargs)

Bases: TemporalPDE

Base class for representing elliptic Partial Differential Equations (PDEs).

Parameters:

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

• linear (bool) – Whether the PDE is linear

• **kwargs – Additional keyword arguments

time_operator(w, t, x, mu)

Apply the PDE operator.

Parameters:

• w (MultiLabelTensor) – Solution tensor

• t (LabelTensor) – Temporal coordinate tensor

• x (LabelTensor) – Spatial coordinate tensor

• mu (LabelTensor) – Parameter tensor

Return type:

Tensor | tuple[Tensor, ...]

Returns:

Operator tensor