computational fluid dynamics

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

arXiv:2607.27433

summary

The paper develops and compares two parametric data-driven reduced models—a physics-informed neural network and a tensorial reduced-order model—for the one-dimensional shallow-water dam-break problem, focusing on direct solution mapping without time integration and evaluating performance on out-of-sample and extrapolated parameters.

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.

Topics & keywords

#physics-informed neural networks#reduced-order modeling#shallow water equations#dam break problem#tensor methods#shock-aware collocationPINNTROMparametric reduced modelshock-aware collocationdirect solution mapout-of-sample extrapolation
Comparison of a Parametric Physics-Informed Neural Network and a Tensorial Reduced-Order Model for the Shallow-Water Dam-Break Problem · wovepaper