An adaptive model reduction method leveraging locally supported basis functions

TL;DR

This paper introduces the CG-GL method, combining locally and globally supported basis functions for adaptive, accurate, and efficient reduced-order modeling with solution-based adaptivity and error estimation.

Contribution

The paper presents a novel CG-GL method that integrates local and global basis functions with adaptive error estimation for improved reduced-order models.

Findings

Demonstrates accurate approximations with limited training data

Shows tunable tradeoff between accuracy and computational cost

Introduces efficient nonlinear term evaluation without retraining

Abstract

We propose a new method, the continuous Galerkin method with globally and locally supported basis functions (CG-GL), to address the parametric robustness issues of reduced-order models (ROMs) by incorporating solution-based adaptivity with locally supported finite element basis functions. The CG-GL method combines the accuracy of locally supported basis functions with the efficiency of globally supported data-driven basis functions. Efficient output-based dual-weighted residual error estimates are derived and implemented for the CG-GL method and used to drive efficient online trial space adaptation. An empirical quadrature procedure is introduced for rapid evaluation of nonlinear terms that does not require retraining throughout the adaptation process. Two numerical experiments demonstrate the potential of the CG-GL method to produce accurate approximations with limited training and its tunable tradeoff between accuracy and computational cost.