TY - JOUR A1 - Strelow, Erik Laurin A1 - Gerisch, Alf A1 - Lang, Jens A1 - Pfetsch, Marc E. T1 - Physics-Informed Neural Networks: A Case Study for Gas Transport Problems N2 - 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. Y1 - VL - Journal of Computational Physics IS - Vol. 481 SP - 112041 ER - TY - CHAP A1 - Börner, Pascal A1 - Pfetsch, Marc E. A1 - Ulbrich, Stefan T1 - Modeling and optimization of gas mixtures on networks N2 - This paper presents a model for the mixture of gases on networks in the stationary case. The model is based on an equation of state for the mixture, the stationary isothermal Euler equations and coupling conditions for the flow and mixture. The equation of state or pressure law is based on the change of the speed of sound in a mixture of gases. We use this model to solve stationary gas flow problems to global optimality on large networks and present computational results. Y1 - 2024 ER -