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PreprintarXiv licencearXiv

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
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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. 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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Cite

BibTeXRIS
BibTeX
@misc{myshak2026comparison,
  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},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2607.27433},
  eprint = {2607.27433},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.27433},
}
RIS
TY  - UNPB
TI  - Comparison of a Parametric Physics-Informed Neural Network and a Tensorial Reduced-Order Model for the Shallow-Water Dam-Break Problem
AU  - Anton Myshak
AU  - Md Rezwan Bin Mizan
AU  - Ilya Timofeyev
PY  - 2026
DA  - 2026/10/05
PB  - arXiv
DO  - 10.48550/arxiv.2607.27433
UR  - https://arxiv.org/abs/2607.27433
AB  - 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.
ER  -