Accelerated estimation of quantities of interest via adjoint-based model reduction

2026-07-06

AI Summary

This work addresses the challenge of efficiently and accurately estimating quantities of interest (QoI) in multi-query linear problems, where conventional approaches suffer from high computational costs and strong dependence on load configurations. The authors propose a novel reduced-order modeling paradigm based on the adjoint problem, shifting the focus of model reduction from the primal to the adjoint equation for the first time. By introducing a parameterized kernel function to replace the full external load, the method constructs a load-independent surrogate model. Demonstrated on Poisson’s equation and plane-stress elasticity problems, the approach achieves rapid convergence and significantly outperforms traditional primal-based reduction strategies. It enables high-fidelity QoI estimation while supporting fast multi-scenario evaluation and virtual chart generation, thereby greatly enhancing the generality and efficiency of early-stage design optimization.

Abstract

We introduce an adjoint-based reduced-order model framework for fast and accurate estimation of quantities of interest for many-query linear problems. The method builds a reduced-order model with respect to the adjoint problem, thus bypassing the solution of the primal problem and drastically reducing computational cost. It creates a surrogate model that is independent of the loading configurations. It enables fast evaluation across multiple load cases and the generation of virtual charts to support decision-making. Numerical experiments on the Poisson equation and a plane-stress elasticity problem demonstrate that the adjoint reduced-order model converges rapidly, outperforms its primal counterpart, and provides reliable estimates of the quantities of interest. Importantly, it is often more practical to parameterize a kernel function than an entire set of external loads, making the method generic and particularly suited for early-stage prototyping and design optimization.

Problem

• quantities of interest
• many-query problems
• computational cost
• model reduction
• adjoint problem

Innovation

• adjoint-based model reduction
• reduced-order modeling
• quantities of interest estimation
• multi-query problems
• surrogate modeling