This conference paper was submitted for presentation at the NAFEMS World Congress 2025, held in Salzburg, Austria from May 19–22, 2025.

Abstract

Digital Twins, tightly integrating the real and the digital world, are a key enabler to support decision making for complex systems. For example, they allow informing operational decisions upfront through accepted virtual predictions of their real world counter parts'™ behavior. Many applications, such as thermal monitoring of batteries, require real-time predictions. Deriving appropriate real-time models if often a complex and tedious task. Therefore, surrogate modeling is a key technology in many real-time Digital Twin applications that require complex predictions. For highly non-linear processes, classical Reduced Order Modeling techniques, such as Krylov methods, are limited as well as require full access to solver internals. While Machine Learning technologies excel in these cases, their high data demands and lack of explainability limit their practical use. In this presentation, we review an active-learning-based Operator Inference approach to surrogate modeling. This method is built on Proper Orthogonal Decomposition combined with regression techniques. It explicitly leverages the structure of the underlying systems, making it fully explainable. Active learning ensures minimal data requirements, making the approach scalable for industrial applications. We will present the basic concept of this technology and demonstrate its application in a real-world battery thermal management case. The proof of concept was realized within a novel Surrogate Modeling Sandbox Framework for STAR-CCM+. We also quantify the storage and compute requirements for realistic applications with millions of degrees of freedom, which are significantly smaller compared to classical Deep Learning methods. This underlines the practicability of the approach for real world applications. The corresponding real-time models are simple explicit Ordinary Differential Equations, which can be exported via the Functional Mock-up Interface standard as well easily directly implemented in system simulation and control tools. At the same time Proper Orthogonal Decomposition allows to retrieve the full 3D fields at any point in time by means of simple matrix multiplications. References: [1] Hartmann (2021): Real-time Digital Twins '“ https://doi.org/10.5281/zenodo.5470479 [2] Zhuang, Lorenzi, Bungartz, Hartmann (2021): Model Order Reduction based on Runge-Kutta Neural Network '“ https://doi.org/10.1017/dce.2021.15 [3] Zhuang, Hartmann, Bungartz, Lorenzi (2023): Active-learning-based nonintrusive model order reduction '“ https://doi.org/10.1017/dce.2022.39 [4] Uy, Hartmann, Peherstorfer (2023): Operator inference with roll outs for learning reduced models from scarce and low-quality data '“ https://doi.org/10.1016/j.camwa.2023.06.012