scimba_torch.geometry.regularized_eikonal_pde

The PDE for learning a Regularized Signed Distance Function.

Classes

RegEikonalPDE(space, **kwargs)

Base class for representing a regularized Eikonal PDE.
class RegEikonalPDE(space, **kwargs)[source]

Bases: StrongFormEllipticPDE

Base class for representing a regularized Eikonal PDE.

Parameters:

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

  • **kwargs – Additional keyword arguments.

rhs(w, x, mu)[source]

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

Parameters:
Return type:

tuple[Tensor, Tensor]

Returns:

The source term ( f(x, mu) ).

operator(w, x, mu)[source]

Compute the operator of the PDE.

Parameters:
Return type:

tuple[Tensor, Tensor]

Returns:

The result of applying the operator to the state.

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

Apply the functional operator for the differential equation.

Parameters:

  • func (VarArgCallable) – The callable function to apply.

  • x (Tensor) – Spatial coordinates tensor.

  • mu (Tensor) – Parameter tensor.

  • theta (Tensor) – Theta parameter tensor.

Return type:

Tensor

Returns:

The result of applying the functional operator.

bc_rhs(w, x, n, mu)[source]

Compute the RHS for the boundary conditions.

Parameters:
Return type:

tuple[Tensor, Tensor]

Returns:

The boundary condition g(x, μ).

bc_operator(w, x, n, mu)[source]

Compute the operator for the boundary conditions.

Parameters:
Return type:

tuple[Tensor, Tensor]

Returns:

The boundary operator applied to the state.

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

Apply the functional operator for boundary conditions.

Parameters:

  • func (VarArgCallable) – The callable function to apply.

  • x (Tensor) – Spatial coordinates tensor.

  • n (Tensor) – Normal vector tensor.

  • mu (Tensor) – Parameter tensor.

  • theta (Tensor) – Theta parameter tensor.

Return type:

Tensor

Returns:

The result of applying the functional operator.