Modeling System Dynamics with Physics-Informed Neural Networks Based on Lagrangian Mechanics

• URL: http://arxiv.org/abs/2005.14617v1
• Date: Fri, 29 May 2020 15:10:43 GMT
• Title: Modeling System Dynamics with Physics-Informed Neural Networks Based on Lagrangian Mechanics
• Authors: Manuel A. Roehrl, Thomas A. Runkler, Veronika Brandtstetter, Michel Tokic, Stefan Obermayer
• Abstract summary: Two main modeling approaches often fail to meet requirements: first principles methods suffer from high bias, whereas data-driven modeling tends to have high variance. We present physics-informed neural ordinary differential equations (PINODE), a hybrid model that combines the two modeling techniques to overcome the aforementioned problems. Our findings are of interest for model-based control and system identification of mechanical systems.
• Score: 3.214927790437842
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Identifying accurate dynamic models is required for the simulation and control of various technical systems. In many important real-world applications, however, the two main modeling approaches often fail to meet requirements: first principles methods suffer from high bias, whereas data-driven modeling tends to have high variance. Additionally, purely data-based models often require large amounts of data and are often difficult to interpret. In this paper, we present physics-informed neural ordinary differential equations (PINODE), a hybrid model that combines the two modeling techniques to overcome the aforementioned problems. This new approach directly incorporates the equations of motion originating from the Lagrange Mechanics into a deep neural network structure. Thus, we can integrate prior physics knowledge where it is available and use function approximation--e. g., neural networks--where it is not. The method is tested with a forward model of a real-world physical system with large uncertainties. The resulting model is accurate and data-efficient while ensuring physical plausibility. With this, we demonstrate a method that beneficially merges physical insight with real data. Our findings are of interest for model-based control and system identification of mechanical systems.

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