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

2026-07-29

AI Summary

This work proposes a time-integration-free direct mapping surrogate model for efficiently predicting physical states in parametric one-dimensional shallow water dam-break problems. The approach constructs and compares two data-driven models—Physics-Informed Neural Networks (PINNs) and non-intrusive Tensorized Reduced Order Models (TROMs)—both trained to directly map spatial coordinates, time, and dam-break parameters to flow field states. A novel shock-aware collocation strategy is introduced to enhance the robustness and accuracy of PINNs, particularly under parameter extrapolation scenarios. Numerical experiments demonstrate that both models accurately capture the dam-break evolution in out-of-sample and parameter extrapolation tests, with the shock-aware PINN exhibiting superior stability and precision.

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.

Problem

• shallow-water
• dam-break
• reduced-order model
• physics-informed neural network
• parameterized problem

Innovation

• physics-informed neural network
• tensorial reduced-order model
• shallow-water equations
• parameterized modeling
• shock-aware collocation