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

Anton Myshak; Md Rezwan Bin Mizan; Ilya Timofeyev

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

Numerical Analysis 2026-07-29 v1 Machine Learning Fluid Dynamics

Authors: Anton Myshak , Md Rezwan Bin Mizan , Ilya Timofeyev

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.

Keywords

physics-informed neural network tensorial reduced-order model shallow-water dam-break problem parametric reduced model out-of-sample extrapolation shock-aware collocation

Cite

@article{arxiv.2607.27433,
  title  = {Comparison of a Parametric Physics-Informed Neural Network and a Tensorial Reduced-Order Model for the Shallow-Water Dam-Break Problem},
  author = {Anton Myshak and Md Rezwan Bin Mizan and Ilya Timofeyev},
  journal= {arXiv preprint arXiv:2607.27433},
  year   = {2026}
}