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arXiv · 2604.25955

Mode-realigned pointwise interpolation (MRPWI) for efficient POD-Galerkin parametric reduced-order models

Lei Du·Shengqi Zhang
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Abstract

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.

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Lei Du, Shengqi Zhang. 2026-04-26. Mode-realigned pointwise interpolation (MRPWI) for efficient POD-Galerkin parametric reduced-order models. https://arxiv.org/abs/2604.25955

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