Parametric Reduced Order Models for the Generalized Kuramoto--Sivashinsky Equations
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916597918072832 |
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| author | Mizan, Md Rezwan Bin Olshanskii, Maxim Timofeyev, Ilya |
| author_facet | Mizan, Md Rezwan Bin Olshanskii, Maxim Timofeyev, Ilya |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2502_02718 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Parametric Reduced Order Models for the Generalized Kuramoto--Sivashinsky Equations Mizan, Md Rezwan Bin Olshanskii, Maxim Timofeyev, Ilya Numerical Analysis Analysis of PDEs 65M22, 65M60 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. |
| title | Parametric Reduced Order Models for the Generalized Kuramoto--Sivashinsky Equations |
| topic | Numerical Analysis Analysis of PDEs 65M22, 65M60 |
| url | https://arxiv.org/abs/2502.02718 |