Hybrid modelling and identification of mechanical systems using Physics-Enhanced Machine Learning

Obtaining mathematical models for mechanical systems is a key subject in engineering. These models are essential for calculation, simulation and design tasks, and they are usually obtained from physical principles or by fitting a black-box parametric input-output model to experimental data. However, both methodologies have some limitations: physics based models may not take some phenomena into account and black-box models are complicated to interpretate. In this work, we develop a novel methodology based on discrepancy modelling, which combines physical principles with neural networks to model mechanical systems with partially unknown or unmodelled physics. Two different mechanical systems with partially unknown dynamics are successfully modelled and the values of their physical parameters are obtained. Furthermore, the obtained models enable numerical integration for future state prediction, linearization and the possibility of varying the values of the physical parameters. The results show how a hybrid methodology provides accurate and interpretable models for mechanical systems when some physical information is missing. In essence, the presented methodology is a tool to obtain better mathematical models, which could be used for analysis, simulation and design tasks.