Solution to the wave equation using physics-informed machine learning

Authors

  • Sean Brendan L. Guansing ⋅ PH National Institute of Physics, University of the Philippines Diliman
  • Reinabelle C. Reyes ⋅ PH National Institute of Physics, University of the Philippines Diliman

Abstract

We developed and optimised an artificial neural network (ANN) solution for the linear homogeneous hyperbolic wave partial differential equation (PDE) and analysed its errors against an approximated finite difference method (FDM) solution. The wave PDE formulated has constant coefficients and is well-posed with physical initial and boundary conditions. The ANN formulated has a fully-connected feed-forward architecture. The PDE residual and conditions are embedded into the ANN solution on rectangular domains through physics-informed machine learning, gradient-based optimisation, regularisation, and hyperparameter tuning. We found that the ANN solution achieved lower errors, demonstrating the potential of physics-informed machine learning models as better and flexible approximators to PDE solutions for modelling physical phenomena.

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Issue

Article ID

SPP-2024-1H-02

Section

Theoretical and Mathematical Physics

Published

2024-06-26

How to Cite

[1]
SBL Guansing and RC Reyes, Solution to the wave equation using physics-informed machine learning, Proceedings of the Samahang Pisika ng Pilipinas 42, SPP-2024-1H-02 (2024). URL: https://proceedings.spp-online.org/article/view/SPP-2024-1H-02.