Accelerated estimation of quantities of interest via adjoint-based model reduction
2026-07-06 • Computational Engineering, Finance, and Science
Computational Engineering, Finance, and Science
AI summaryⓘ
The authors present a new method that uses an adjoint-based reduced-order model to quickly estimate important results for many similar linear problems. Their approach skips solving the main problem directly, which saves a lot of computing time. This method can quickly handle different input conditions and helps create virtual charts to aid decisions. Tests on standard equations show the model works well and is often easier to apply than traditional methods, making it useful for early design stages.
adjoint problemreduced-order modellinear problemsPoisson equationplane-stress elasticitysurrogate modelparameterizationquantities of interestmany-query problemsdesign optimization
Authors
Clément Vella, Serge Prudhomme
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.