Solving the wave equation with physics-informed deep learning

• DOI: 10.48550/arxiv.2006.11894
• Publication Date: 2020-01-01
• Authors: Ben Moseley; Andrew Markham; Tarje Nissen‐Meyer
• Keywords: Acoustic wave equation

We investigate the use of Physics-Informed Neural Networks (PINNs) for solving wave equation. Whilst PINNs have been successfully applied across many physical systems, equation presents unique challenges due to multi-scale, propagating and oscillatory nature its solutions, it is unclear how well they perform in this setting. a deep neural network learn solutions equation, using boundary condition as direct constraints loss function when training network. test approach by 2D acoustic spatially-varying velocity models increasing complexity, including homogeneous, layered Earth-realistic models, find able accurately simulate wavefield these cases. By physics constraint solve far outside data, offering way reduce generalisation issues existing learning approaches. extend case conditioning on source location that generalise over initial condition, removing need retrain each solution. In contrast traditional numerical simulation very efficient computing arbitrary space-time points wavefield, once trained carries out inference single step without needing compute entire wavefield. discuss potential applications, limitations further research directions work.