scimba_torch.physical_models.temporal_pde.heat_equation

Heat equation in strong form.

Classes

HeatEquation1DDirichletStrongForm(space, init)

Implementation of a 1D heat equation with Dirichlet BCs in strong form.

HeatEquation1DStrongForm(space, init[, f, g])

Implementation of a 1D heat equation with Neumann BCs in strong form.

HeatEquation2DStrongForm(space, init[, f, g])

Implementation of a 2D Laplacian problem with Dirichlet BCs in strong form.

HeatEquation2DStrongFormImplicit(space, init)

2D heat equation for implicit discrete_pinns.
class HeatEquation1DStrongForm(space, init, f=None, g=None, **kwargs)[source]

Bases: GenericFirstOrderTemporalPDE

Implementation of a 1D heat equation with Neumann BCs in strong form.

Parameters:

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

  • init (Callable) – Callable for the initial condition

  • f (Optional[Callable]) – Source term function (default is zero)

  • g (Optional[Callable]) – Neumann boundary condition function (default is zero)

  • **kwargs – Additional keyword arguments

class HeatEquation1DDirichletStrongForm(space, init, f=None, g=None, **kwargs)[source]

Bases: GenericFirstOrderTemporalPDE

Implementation of a 1D heat equation with Dirichlet BCs in strong form.

Parameters:

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

  • init (Callable) – Callable for the initial condition

  • f (Optional[Callable]) – Source term function (default is zero)

  • g (Optional[Callable]) – Dirichlet boundary condition function (default is zero)

  • **kwargs – Additional keyword arguments

class HeatEquation2DStrongForm(space, init, f=None, g=None, **kwargs)[source]

Bases: GenericFirstOrderTemporalPDE

Implementation of a 2D Laplacian problem with Dirichlet BCs in strong form.

Parameters:

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

  • init (Callable) – Callable for the initial condition

  • f (Optional[Callable]) – Source term function (default is zero)

  • g (Optional[Callable]) – Dirichlet boundary condition function (default is zero)

  • **kwargs – Additional keyword arguments

class HeatEquation2DStrongFormImplicit(space, init, f=None, g=None, **kwargs)[source]

Bases: GenericFirstOrderTemporalPDE

2D heat equation for implicit discrete_pinns.

Parameters:

  • space (AbstractApproxSpace) – the approx. space.

  • init (Callable) – the rhs of the initial condition.

  • f (Optional[Callable]) – the rhs of the residual (default is zero).

  • g (Optional[Callable]) – the rhs of the boundary condition (default is zero).

  • **kwargs – Additional keyword arguments.

functional_operator(func, x, mu, theta)[source]

Compute the functional operator.

Parameters:

  • func (VarArgCallable) – Callable representing the function

  • x (Tensor) – Spatial coordinate tensor

  • mu (Tensor) – Parameter tensor

  • theta (Tensor) – Additional parameters tensor

Return type:

Tensor

Returns:

Functional operator tensor

functional_operator_bc(func, t, x, n, mu, theta)[source]

Compute the functional operator for boundary conditions.

Parameters:

  • func (VarArgCallable) – Callable representing the function

  • t (LabelTensor) – Temporal coordinate tensor

  • x (Tensor) – Spatial coordinate tensor

  • n (Tensor) – Normal vector tensor

  • mu (Tensor) – Parameter tensor

  • theta (Tensor) – Additional parameters tensor

Return type:

Tensor

Returns:

Functional operator tensor for boundary conditions

functional_operator_ic(func, x, mu, theta)[source]

Compute the functional operator for initial conditions.

Parameters:

  • func (VarArgCallable) – Callable representing the function

  • x (Tensor) – Spatial coordinate tensor

  • mu (Tensor) – Parameter tensor

  • theta (Tensor) – Additional parameters tensor

Return type:

Tensor

Returns:

Functional operator tensor for initial conditions