Physics informed neural networks: A case study for gas transport problems

• DOI: 10.1016/j.jcp.2023.112041
• Publication Date: 2023-03-05T07:01:55Z
• Authors: Erik Laurin Strelow; Alf Gerisch; Jens Lang; Marc E. Pfetsch
• Keywords: Broyden–Fletcher–Goldfarb–Shanno algorithm

Physics informed neural networks have been recently proposed and offer a new promising method to solve differential equations. They adapted many more scenarios different variations of the original proposed. In this case study we review these variations. We focus on variants that can compensate for imbalances in loss function perform comprehensive numerical comparison with application gas transport problems. Our includes formulations function, algorithmic balancing methods, optimization schemes numbers parameters sampling points. conclude PINN approach specifically chosen constant weights gives best results our tests. These obtained by computationally expensive random-search scheme. further test methods which were developed other equations no benefit problems, control volume physics formulation has against initial strategy is L-BFGS method.