Comparison of a Parametric Physics-Informed Neural Network and a Tensorial Reduced-Order Model for the Shallow-Water Dam-Break Problem

2026/07/29 by Anton Myshak, Md Rezwan Bin Mizan, Ilya Timofeyev
Mathematics · Computer Science · Physics and Astronomy · #math.NA #cs.LG #cs.NA #physics.flu-dyn #msc:65M22 #msc:65M60 #msc:68T07 #msc:35L65

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arxiv created 2026/07/29 · arxiv updated 2026/07/31

Abstract

We develop two parametric data-driven reduced models: a physics-informed neural network (PINN) and a non-intrusive tensorial reduced-order model (TROM), and apply both approaches to the parametrized one-dimensional shallow-water dam-break problem. Both reduced models do not require time integration and learn a direct solution map from space, time, and dam-break parameters to the physical state. We present a detailed comparison for out-of-sample and extrapolated parameter values. In addition, we demonstrate that it is essential to introduce shock-aware collocation to improve the robustness of the PINN model.

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