Accelerating design optimization using reduced order models

TL;DR

This paper presents a reduced order model-based approach to accelerate PDE-constrained design optimization by allowing inexact solves and reducing Krylov iteration counts, significantly speeding up topology optimization tasks.

Contribution

It introduces a novel acceleration method combining inexact linear solves and fewer Krylov iterations, applicable to general PDE-constrained optimization problems.

Findings

Achieves significant speed-up in topology optimization.

Reduces the number of linear solves compared to traditional methods.

Effective even when preconditioners fail to reduce iteration counts.

Abstract

Although design optimization has shown its great power of automatizing the whole design process and providing an optimal design, using sophisticated computational models, its process can be formidable due to a computationally expensive large-scale linear system of equations to solve, associated with underlying physics models. We introduce a general reduced order model-based design optimization acceleration approach that is applicable not only to design optimization problems, but also to any PDE-constrained optimization problems. The acceleration is achieved by two techniques: i) allowing an inexact linear solve and ii) reducing the number of iterations in Krylov subspace iterative methods. The choice between two techniques are made, based on how close a current design point to an optimal point. The advantage of the acceleration approach is demonstrated in topology optimization examples, including both compliance minimization and stress-constrained problems, where it achieves a tremendous reduction and speed-up when a traditional preconditioner fails to achieve a considerable reduction in the number of linear solve iterations.