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

TL;DR

This paper introduces MRPWI, a novel mode realignment interpolation method that enhances the efficiency of POD-Galerkin parametric reduced-order models without sacrificing accuracy.

Contribution

The paper proposes MRPWI, a new two-step mode realignment technique that improves computational efficiency of POD-Galerkin PROMs while maintaining accuracy.

Findings

MRPWI achieves similar accuracy to GMI in flow over a cylinder.

PROMs with MRPWI are significantly more computationally efficient.

Demonstrated high fidelity compared to direct numerical simulation.

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.