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

arXiv 2607.27433 ↗First posted 29 Jul 2026math.NA cs.LG cs.NAcited by 0

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Abstract (arXiv)

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. Neither reduced model requires time integration: both learn a direct parameter-to-solution map from space, time, and dam-break parameters to the physical state, with the PINN providing predictions at arbitrary times and the TROM reconstructing solutions at the stored snapshot times. 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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References · 10

  1. 2014Adam: A Method for Stochastic Optimizationcited by 37,240
  2. 2018On the Spectral Bias of Neural Networkscited by 1,341
  3. 2019Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networkscited by 368
  4. 2020hp-VPINNs: Variational Physics-Informed Neural Networks With Domain Decompositioncited by 236
  5. 2019Variational Physics-Informed Neural Networks For Solving Partial Differential Equationscited by 148
  6. 2022Overview frequency principle/spectral bias in deep learningcited by 69
  7. 2021Physics-informed neural networks for the shallow-water equations on the spherecited by 32
  8. 2022Quadratic Approximation Manifold for Mitigating the Kolmogorov Barrier in Nonlinear Projection-Based Model Order Reductioncited by 30
  9. 2022wPINNs: Weak Physics informed neural networks for approximating entropy solutions of hyperbolic conservation lawscited by 29
  10. 2026Parametrization of subgrid scales in long-term simulations of the shallow-water equations using machine learning and convex limitingcited by 2

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