Adaptive goal-oriented hierarchical surrogate modeling for port-Hamiltonian multiphysical systems

• Applicants: Professor Dr.-Ing. Jörg Fehr; Professor Dr. Bernard Haasdonk
• Subject Area: Mathematics ; Mechanics
• Term: since 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 566234291

For the optimization and control of technical systems, quick simulation responses are essential, which is why model reduction and surrogate modeling are utilized, in which detailed full order models (FOMs) are approximated by reduced order models (ROMs). Current developments focus on structure-preserving methods. The energy-based modeling of port-Hamiltonian (pH) systems ensures passivity, thereby guaranteeing stable simulation results for coupled domains. Currently, it is not possible to automate, reliably, efficiently, and simultaneously certify the simulation of multiphysical pH systems (mpHs). Error estimators that quantify the accuracy of subsystem surrogates are essential for certification. The unclear influence of subsystem error bounds on the global model result prevents automated model adaptation. In this project, we aim to develop, analyze, implement, and apply adaptive hierarchical certified and pH-structure-preserving surrogate models for mpHs. A specific example is a synchronous reluctance machine. It contributes to sustainable mobility since it offers high efficiency and low manufacturing and maintenance costs without using rare earths. Material optimization and real-time capable control are research questions that will be solved with the hierarchical, adaptive simulation framework. We are developing a modeling workflow that initially selects a combination of modular subsystem FOMs of different abstraction levels based on the simulation task, such as lumped-parameter or finite element (FE) models. This model configuration serves as the basis for subsequent adaptive surrogate modeling. In accordance with the overall accuracy measure desired by the user, hierarchical subsystem surrogates are calculated adaptively online to meet the global accuracy requirement. We are developing methods for determining subsystem accuracies based on the overall system accuracy. First, we select appropriate initial surrogates from a collection of static models which are subsequently adaptively refined during the simulation using structure-exploiting output error estimators. Our newly developed RB-ML-ROM approach, now extended in the current project to include structure preservation, enables the precise and adaptive refinement of "global" (therefore coarse) subsystem surrogates within the parameter subset of the actual operational range. Efficiency is achieved through the correct choice of model dimension, certification through error estimators, and reliability as well as interpretability through structure-preserving reduction with pH models. The control of submodel accuracies and the hierarchical submodel surrogates utilize machine learning (ML) methods. Through the inherent error control, our models offer guaranteed accuracies, thereby contributing to certified, reliable, and interpretable ML.

• DFG Programme: Research Grants