Mode-realigned pointwise interpolation (MRPWI) for efficient POD-Galerkin parametric reduced-order models
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917444736516096 |
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| author | Du, Lei Zhang, Shengqi |
| author_facet | Du, Lei Zhang, Shengqi |
| contents | As a cornerstone of reduced-order modeling, the POD-Galerkin framework has garnered widespread attention and remains one of the most widely adopted approaches. Constructing POD-Galerkin PROMs involves integrating this framework with advanced interpolation techniques to obtain POD modes at target (unseen) parameters. While Grassmann manifold interpolation (GMI) serves as an accurate baseline, mode-realigned pointwise interpolation (MRPWI) is proposed to develop highly efficient PROMs that maintain comparable accuracy. Notably, the MRPWI employs a two-step mode realignment procedure, consisting of sign alignment and rotation alignment, to effectively synchronize the POD modes. Demonstration and evaluation of the constructed POD-Galerkin PROMs are conducted by examining flow over a cylinder. These models exhibit high fidelity in comparison to direct numerical simulation and standard POD-Galerkin ROMs. PROMs constructed via MRPWI achieve accuracy comparable to those using GMI, while providing significantly higher computational efficiency. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_25955 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Mode-realigned pointwise interpolation (MRPWI) for efficient POD-Galerkin parametric reduced-order models Du, Lei Zhang, Shengqi Numerical Analysis Fluid Dynamics As a cornerstone of reduced-order modeling, the POD-Galerkin framework has garnered widespread attention and remains one of the most widely adopted approaches. Constructing POD-Galerkin PROMs involves integrating this framework with advanced interpolation techniques to obtain POD modes at target (unseen) parameters. While Grassmann manifold interpolation (GMI) serves as an accurate baseline, mode-realigned pointwise interpolation (MRPWI) is proposed to develop highly efficient PROMs that maintain comparable accuracy. Notably, the MRPWI employs a two-step mode realignment procedure, consisting of sign alignment and rotation alignment, to effectively synchronize the POD modes. Demonstration and evaluation of the constructed POD-Galerkin PROMs are conducted by examining flow over a cylinder. These models exhibit high fidelity in comparison to direct numerical simulation and standard POD-Galerkin ROMs. PROMs constructed via MRPWI achieve accuracy comparable to those using GMI, while providing significantly higher computational efficiency. |
| title | Mode-realigned pointwise interpolation (MRPWI) for efficient POD-Galerkin parametric reduced-order models |
| topic | Numerical Analysis Fluid Dynamics |
| url | https://arxiv.org/abs/2604.25955 |