Understanding machine learning approaches for partial differential equations
Recent works in computational physics have been successful in the super-resolution of numerical solutions of partial differential equations (PDEs) via neural networks. In this paper we explore the possibilities and limitations of the data-driven discretization approach implemented by Bar-Sinai et. al., while contrasting it with a simpler yet weaker approach utilizing the nangs Python library. The results demonstrate what neural network parameters optimize accuracy and performance, as well as what conditions on PDEs are necessary to maintain convergence.
97 MATHEMATICS AND COMPUTING↗