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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
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 t…
math.NA2026
Subgrid-Scale Parameterization in Burgers' Equation Using Structure-Preserving Neural Networks and Entropy Variables
Aijaz Nazir, Ilya Timofeyev
We present a machine learning approach for developing subgrid-scale (SGS) parametrizations in coarse simulations of partial differential equations. We utilize structure-preserving…
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…