Modeling System Dynamics with Physics-Informed Neural Networks Based on Lagrangian Mechanics
This work addresses the need for interpretable and efficient dynamic models in mechanical system control and identification, representing an incremental improvement over existing hybrid approaches.
The authors tackled the problem of accurately modeling system dynamics by developing PINODE, a hybrid model that integrates Lagrangian mechanics into neural ODEs, achieving accurate and data-efficient results with physical plausibility in a real-world test case.
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.