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Parametric Reduced Order Models for the Generalized Kuramoto--Sivashinsky Equations

arXiv CS Thursday 04 June 2026, 04:00 UTC By Md Rezwan Bin Mizan, Maxim Olshanskii, Ilya Timofeyev 1 min read
Key Points

arXiv:2502.02718v2 Announce Type: replace Abstract: 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...

arXiv:2502.02718v2 Announce Type: replace Abstract: 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.
Kuramoto (ORG) KS (LOCATION) Sivashinsky (PERSON)
Originally published by arXiv CS Read original →

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