A boundary-only holomorphic KAN framework solves Laplace, Helmholtz, and elasticity problems on simply and multiply connected 2D domains, outperforming standard PINNs in the tested cases.
Vekua theory for the helmholtz operator.Zeitschrift f¨ ur angewandte Mathematik und Physik, 62(5):779–807, 2011
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A holomorphic Kolmogorov-Arnold network framework for solving elliptic problems on arbitrary 2D domains
A boundary-only holomorphic KAN framework solves Laplace, Helmholtz, and elasticity problems on simply and multiply connected 2D domains, outperforming standard PINNs in the tested cases.