Abstract: Physics-informed neural networks (PINNs) offer a flexible framework for solving differential equations using physical constraints and data. This study focuses on second-order ...

Abstract: In this paper, we give a simple theorem on the waveform relaxation (WR) solution for a system of nonlinear second-order differential equations. It is shown that if the norm of certain ...

Can neural networks learn to solve partial differential equations (PDEs)? We investigate this question for two (systems of) PDEs, namely, the Poisson equation and the ...

[1] M. Raissi, P. Perdikaris, and G. E. Karniadakis. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving ...