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Funder: RWTH Aachen (3131), Data-driven models are becoming increasingly popular in engineering, on their own or in combination with mechanistic models. Commonly, the trained models are subsequently used in model-based optimization of design and/or operation of processes. Thus, it is critical to ensure that data-driven models are not evaluated outside their validity domain during process optimization. We propose a method to learn this validity domain and encode it as constraints in process optimization. We first perform a topological data analysis using persistent homology identifying potential holes or separated clusters in the training data. In case clusters or holes are identified, we train a one-class classifier, i.e., a one-class support vector machine, on the training data domain and encode it as constraints in the subsequent process optimization. Otherwise, we construct the convex hull of the data and encode it as constraints. We finally perform deterministic global process optimization with the data-driven models subject to their respective validity constraints. To ensure computational tractability, we develop a reduced-space formulation for trained one-class support vector machines and show that our formulation outperforms common full-space formulations by a factor of over 3000, making it a viable tool for engineering applications. The method is ready-to-use and available open-source as part of our MeLOn toolbox (https://git.rwth-aachen.de/avt.svt/public/MeLOn).

The increasing presence of renewables in today's power systems leads to more power electronics devices. Therefore, it is becoming critical to integrate analysis and design of power electronics and power systems. This paper presents a multi-level approach to use Modelica models to interface these two domains and to enable experts to work with consistent models and simulation environments. Furthermore, the multilevel approach requires coherent initialization of all levels of the models. To this aim, this paper demonstrated how the results of static phasor simulation can be utilized to automatically generate correct initial conditions for electromagnetic transient simulations that include switching power electronic devices.