collaborators

5 papers

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…

physics.flu-dyn2026

Reduced-Order Modeling of Parameterized Visco-Plastic Shallow Flows

Md Rezwan Bin Mizan, Ilya Timofeyev, Maxim Olshanskii

We propose a non-intrusive reduced-order modeling framework for parametrized visco-plastic free-surface flows governed by a shallow-water formulation of Herschel--Bulkley fluids. T…

physics.flu-dyn2026

Parametrization of subgrid scales in long-term simulations of the shallow-water equations using machine learning and convex limiting

Md Amran Hossan Mojamder, Zhihang Xu, Min Wang +1

We present a method for parametrizing sub-grid processes in the Shallow Water equations. We define coarse variables and local spatial averages and use a feed-forward neural network…

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…