Burgers equation 1coarse simulation 1dam break problem 1entropy variables 1physics-informed neural networks 1reduced-order modeling 1shallow water equations 1shock-aware collocation 1structure-preserving neural networks 1subgrid-scale modeling 1tensor methods 1
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math.NA2026
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
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-wate…
math.NA2026
Subgrid-Scale Parameterization in Burgers' Equation Using Structure-Preserving Neural Networks and Entropy Variables
Aijaz Nazir, Ilya Timofeyev
The paper introduces a machine‑learning method that uses structure‑preserving neural networks and entropy variables to create subgrid‑scale parameterizations for coarse simulations…
math.NA2025
A parametric tensor ROM for the shallow water dam break problem
Md Rezwan Bin Mizan, Maxim Olshanskii, Ilya Timofeyev
We develop a variant of a tensor reduced-order model (tROM) for the parameterized shallow-water dam-break problem. This hyperbolic system presents multiple challenges for model red…