A Differentiable Solver Approach to Operator Inference

TL;DR

This paper introduces a differentiable solver approach to operator inference, reformulating it as a constrained optimization problem to improve robustness and usability in model order reduction for industrial applications.

Contribution

It presents a novel reformulation of operator inference as a constrained optimization problem, reducing the need for regularization and enhancing robustness.

Findings

Validated on a complex 3D cooling process of a multi-tubular reactor

Achieved improved robustness and usability in model order reduction

Demonstrated effectiveness with commercial software package

Abstract

Model Order Reduction is a key technology for industrial applications in the context of digital twins. Key requirements are non-intrusiveness, physics-awareness, as well as robustness and usability. Operator inference based on least-squares minimization combined with the Discrete Empirical Interpolation Method captures most of these requirements, though the required regularization limits usability. Within this contribution we reformulate the problem of operator inference as a constrained optimization problem allowing to relax on the required regularization. The result is a robust model order reduction approach for real-world industrial applications, which is validated along a dynamics complex 3D cooling process of a multi-tubular reactor using a commercial software package.