3 papers
math.NA2026
Enhancing Future Prediction of Linear and Nonlinear Reduced-Order Models for Transport-Dominated Problems Using Lagrangian Data
Meng Li, Yang Xiang, Zhichao Peng
Designing effective reduced-order models (ROMs) for parametrized transport-dominated problems remains challenging because of the well-known Kolmogorov barrier. Autoencoder-based no…
math.NA2025
Adaptive and hybrid reduced order models to mitigate Kolmogorov barrier in a multiscale kinetic transport equation
Tianyu Jin, Zhichao Peng, Yang Xiang
In this work, we develop reduced order models (ROMs) to predict solutions to a multiscale kinetic transport equation with a diffusion limit under the parametric setting. When the u…
math.NA2025
A fast neural hybrid Newton solver adapted to implicit methods for nonlinear dynamics
Tianyu Jin, Georg Maierhofer, Katharina Schratz +1
The use of implicit time-stepping schemes for the numerical approximation of solutions to stiff nonlinear time-evolution equations brings well-known advantages including, typically…