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

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.