pihnn.nn.L_PIHKAN

class pihnn.nn.L_PIHKAN(PDE, units, degree, singularities, material={'lambda': 1, 'mu': 1}, has_bias=True, rhs_solution=None)

Bases: L_PIHNN

Laurent physics-informed holomorphic Kolmogorov-Arnold network (L-PIHKAN).

Combination of pihnn.nn.PIHKAN and pihnn.nn.L_PIHNN, in order to extend the applicability of PIHKANs to multiply-connected domains.

Parameters:

• PDE (str) – Problem to solve, either ‘laplace’, ‘biharmonic’, ‘km’ or ‘km-so’.

• units (list of int) – List containing number of units at each layer, e.g., [1,10,10,1].

• degree (int) – KAN polynomial degree \(D\).

• singularities (List of dictionaries) – List with the information about singularities. Each element of the list (\(s=1,\dots,S\)) is a dictionary containing \(z_s\) (“location”) and units of \(NN_s\) (“units”).

• material (dict) – Properties of the material, dictionary with ‘lambda’ (first Lamé coefficient), ‘mu’ (second Lamé coefficient).

• has_bias (bool) – Whether to include the bias vector.

• rhs_solution (callable) – Particular solution to the non-homogeneous problem. E.g., \(x^2+y^2\) for \(\nabla^2u=4\).