Abstract
Hybrid modeling, the combination of first principle and machine learning models, is an emerging research field that gathers more and more attention. Even if hybrid models produce formidable results for academic examples, there are still different technical challenges that hinder the use of hybrid modeling in real-world applications. By presenting NeuralFMUs, the fusion of a Functional Mock-up Unit (FMU), a numerical ODE solver and an artifical neural network, we are paving the way for the use of a variety of first principle models from different modeling tools as parts of hybrid models. This contribution handles the hybrid modeling of a complex, real-world example: Starting with a simplified 1D-fluid model of the human cardiovascular system (arterial side), the aim is to learn neglected physical effects like arterial elasticity from data. We will show that the hybrid modeling process is more comfortable, needs less system knowledge and is therefore less error-prone compared to modeling solely based on first principle. Further, the resulting hybrid model has improved in computation performance, compared to a pure first principle white-box model, while still fulfilling the requirements regarding accuracy of the considered hemodynamic quantities. The use of the presented techniques is explained in a general manner and the considered use-case can serve as example for other modeling and simulation applications in and beyond the medical domain.
Highlights
The structural integration of physical white-box models into artifical neural networks (ANNs) to retrieve a hybrid model is a growing research field, see [1] or [2]
By presenting NeuralFMUs, the fusion of a Functional Mock-up Unit (FMU), a numerical ordinary differential equations (ODEs) solver and an artifical neural network, we are paving the way for the use of a variety of first principle models from different modeling tools as parts of hybrid models
The use of the presented techniques is explained in a general manner and the considered use-case can serve as example for other modeling and simulation applications in and beyond the medical domain
Summary
The structural integration of physical white-box models into artifical neural networks (ANNs) to retrieve a hybrid model is a growing research field, see [1] or [2]. One of the core challenges in hybrid modeling, the fusion of data driven and first principle models, is to provide an efficient training process for the resulting heterogeneous structure. The main reason for the difference between reference and simplified Modelica model is the lack of arterial dynamics: The system pressure inside the simplified model is the same at any location inside the arterial network, but varies over time with the heart pulse wave.
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