Data-driven Model Reduction for Parameter-Dependent Matrix Equations via Operator Inference

TL;DR

This paper introduces a data-driven, non-intrusive surrogate modeling approach using Operator Inference to efficiently solve parameter-dependent matrix equations, bypassing costly computations in high-dimensional problems.

Contribution

It reformulates matrix equations into a polynomial form to enable efficient model reduction via regression on solution data, avoiding intrusive methods.

Findings

Accurate reduced-order models for parameter-dependent equations.

Significant computational speedups demonstrated.

Scalable approach suitable for high-dimensional problems.

Abstract

This work develops a non-intrusive, data-driven surrogate modeling framework based on Operator Inference (OpInf) for rapidly solving parameter-dependent matrix equations in many-query settings. Motivated by the requirements of the OpInf methodology, we reformulate the matrix equations into a structured representation that explicitly shows the parameter dependence in polynomial form. This reformulation is crucial for efficient model reduction. This approach constructs reduced-order models via regression on solution snapshots, bypassing the need for expensive full-order operators and thus overcoming the primary bottlenecks of intrusive methods in high-dimensional contexts. Numerical experiments confirm their accuracy and computational efficiency, demonstrating that our work is a scalable and practical solution for parameter-dependent matrix equations.