Traveling Wave Solutions of Partial Differential Equations Via Neural Networks

This paper focuses on how to approximate traveling wave solutions for various kinds of partial differential equations via artificial neural networks. A solution is hard obtain with traditional numerical methods when the corresponding speed unknown in advance. We propose a novel method both and network an additional free parameter. proved that under mild assumption, converges analytic parameter accurately approximates as loss tends zero Keller–Segel equation. also demonstrate experiments reducing through training assures accurate approximation equation, Allen–Cahn model relaxation, Lotka–Volterra competition model.