An online-adaptive hyperreduced reduced basis element method for parameterized component-based nonlinear systems using hierarchical error estimation

TL;DR

This paper introduces an online-adaptive hyperreduced basis element method for efficient model order reduction of parameterized nonlinear systems, utilizing hierarchical error estimation for adaptive fidelity selection and component-wise hyperreduction.

Contribution

It develops a hierarchical error estimation framework and adaptive refinement strategy for component-based reduced models, improving accuracy and efficiency over uniform approaches.

Findings

Achieves approximately 100-fold computational speedup at 1% error level.

Demonstrates effective error control with adaptive component refinement.

Validates the method on nonlinear thermal fin systems with up to 225 components.

Abstract

We present an online-adaptive hyperreduced reduced basis element method for model order reduction of parameterized, component-based nonlinear systems. The method, in the offline phase, prepares a library of hyperreduced archetype components of various fidelity levels and, in the online phase, assembles the target system using instantiated components whose fidelity is adaptively selected to satisfy a user-prescribed system-level error tolerance. To achieve this, we introduce a hierarchical error estimation framework that compares solutions at successive fidelity levels and drives a local refinement strategy based on component-wise error indicators. We also provide an efficient estimator for the system-level error to ensure that the adaptive strategy meets the desired accuracy. Component-wise hyperreduction is performed using an empirical quadrature procedure, with the training accuracy guided by the Brezzi--Rappaz--Raviart theorem. The proposed method is demonstrated on a family of nonlinear thermal fin systems comprising up to 225 components and 68 parameters. Numerical results show that the hyperreduced basis element model achieves O(100) computational reduction at 1% error level relative to the truth finite-element model. In addition, the adaptive refinement strategy provides more effective error control than uniform refinement by selectively enriching components with higher local errors.