An optimization-based coupling of reduced order models with efficient reduced adjoint basis generation approach

• Main Authors: Hawkins, Elizabeth, Kuberry, Paul, Bochev, Pavel
• Format: Journal Article
• Language: English
• Published: 26-08-2024
• Subjects: Computer Science - Computational Engineering, Finance, and Science
• DOI: 10.48550/arxiv.2408.14450

Optimization-based coupling (OBC) is an attractive alternative to traditional
Lagrange multiplier approaches in multiple modeling and simulation contexts.
However, application of OBC to time-dependent problem has been hindered by the
computational costs of finding the stationary points of the associated
Lagrangian, which requires primal and adjoint solves. This issue can be
mitigated by using OBC in conjunction with computationally efficient reduced
order models (ROM). To demonstrate the potential of this combination, in this
paper we develop an optimization-based ROM-ROM coupling for a transient
advection-diffusion transmission problem. The main challenge in this
formulation is the generation of adjoint snapshots and reduced bases for the
adjoint systems required by the optimizer. One of the main contributions of the
paper is a new technique for efficient adjoint snapshot collection for
gradient-based optimizers in the context of optimization-based ROM-ROM
couplings. We present numerical studies demonstrating the accuracy of the
approach along with comparison between various approaches for selecting a
reduced order basis for the adjoint systems, including decay of snapshot
energy, iteration counts, and timings.