Eman Mohamed Ahmed

A Hybrid Legendre Polynomial–Physics-Informed Neural Network for Predicting Solutions of Laplace's Equation in Spherical Coordinates

 Boundary value problems for Laplace's equation on spherical and shell-shaped domains arise in potential theory, heat conduction, electrostatics, and gravitation, with classical solutions expressed as series in spherical harmonics. Standard physics-informed neural networks (PINNs) represent such solutions with a generi...