Hybrid modeling – the combination of first-principle models and machine learning – offers the potential to increase model accuracy while reducing modeling effort. Although approaches for creating hybrid models from system simulation models exist, the unique characteristics of Modelica-based, object-oriented models – such as modularity and reusability – can, as of today, not be utilized. In this contribution, we explore approaches for bridging this gap to enable the use of hybrid models with Modelica. Key challenges of architecture definition, training environment and reintegration of the trained machine learning parts into a Modelica model are addressed. To illustrate our approach, we present a case study involving a SCARA robot. This example demonstrates a partially integrated workflow for hybrid modeling, intended to serve as a foundation and motivation for further research.

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The Functional Mock-up Interface (FMI) is the standard for exchanging industrial simulation models in a variety of different applications. Although sensitivity analysis for continuously differentiable systems is directly supported by the standard, for systems with state discontinuities, it is only possible to determine correct sensitivities to a limited extent. In this position paper, we investigate how sensitivity analysis for discontinuous Functional Mock-up Units (FMUs), i.e. including state and time events, works in theory and which additional steps are required to obtain correct results in practice. We further investigate that these steps are unnecessarily computationally intensive from a mathematical point of view, but cannot be implemented in a more efficient way under the current restrictions of the standard. We therefore make a concrete proposal for the new layered standard sensitivity analysis (LS-SA) that remedies the current deficits of FMI in the sensitivity analysis of discontinuous systems. In this way, LS-SA opens FMI towards a variety of next-level applications — including (scientific) machine learning and optimal control — by providing fully differentiable FMUs under high computational performance.