Parametric Reduced Order Models for the Generalized Kuramoto--Sivashinsky Equations
For researchers in reduced-order modeling, this work provides a practical method to handle parametric variations in complex nonlinear PDEs, though it is incremental in nature.
The paper develops parametric reduced order models (ROMs) for the Kuramoto–Sivashinsky (KS) and generalized KS equations, identifying a strategy that efficiently captures dynamics across weakly chaotic, transitional, and quasi-periodic regimes. The approach emphasizes accurate representation of short-time transient behavior.
The paper studies parametric Reduced Order Models (ROMs) for the Kuramoto--Sivashinsky (KS) and generalized Kuramoto--Sivashinsky (gKS) equations. We consider several POD and POD-DEIM projection ROMs with various strategies for parameter sampling and snapshot collection. The aim is to identify an approach for constructing a ROM that is efficient across a range of parameters, encompassing several regimes exhibited by the KS and gKS solutions: weakly chaotic, transitional, and quasi-periodic dynamics. We describe such an approach and demonstrate that it is essential to develop ROMs that adequately represent the short-time transient behavior of the gKS model.