Taper-based scattering formulation of the Helmholtz equation to improve the training process of Physics-Informed Neural Networks

arXiv:2404.09794v1 Announce Type: new
Abstract: This work addresses the scattering problem of an incident wave at a junction connecting two semi-infinite waveguides, which we intend to solve using Physics-Informed Neural Networks (PINNs). As with other deep learning-based approaches, PINNs are known to suffer from a spectral bias and from the hyperbolic nature of the Helmholtz equation. This makes the training process challenging, especially for higher wave numbers. We show an example where these limitations are present. In order to improve …

abstract arxiv cs.lg deep learning equation incident networks neural networks physics physics.comp-ph physics-informed process solve training type waveguides work