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Physics-Informed Neural Networks: A Case Study for Gas Transport Problems

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

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Metadaten
Author:Erik Laurin Strelow, Alf Gerisch, Jens Lang, Marc E. Pfetsch
Document Type:Article
Language:English
Date of Publication (online):2024/03/21
Release Date:2024/03/25
Volume:Journal of Computational Physics
Issue:Vol. 481
First Page:112041
Institutes:Technische Universität Darmstadt
Subprojects:A01
B01
Licence (German):License LogoCreative Commons - CC BY - Namensnennung 4.0 International