A Differentiable Solver Approach to Operator Inference

2021/07/05 by Dirk Hartmann, Hartmann, Dirk, Lukas Failer +1
Computer Science · Decision Sciences · Physics and Astronomy · #Advanced Multi-Objective Optimization Algorithms #FOS: Mathematics #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Probabilistic and Robust Engineering Design

paper · pdf · doi:10.48550/arxiv.2107.02093

openalex publication_date 2021/07/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Neural Ordinary Differential Equations
• Characterising the Digital Twin: A systematic literature review
• Physics-informed machine learning

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