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

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.

Accepted for publication at the 21st IFAC World Congress 2020

References in corpus (4)

• Artificial Neural Networks for Solving Ordinary and Partial Differential Equations
• Discovering physical concepts with neural networks
• Symplectic ODE-Net: Learning Hamiltonian Dynamics with Control
• Deep Lagrangian Networks: Using Physics as Model Prior for Deep Learning

Cited by in corpus (8)

• A Physics-Informed Deep Learning Paradigm for Car-Following Models
• A Review of Machine Learning Methods Applied to Structural Dynamics and Vibroacoustic
• Implicit energy regularization of neural ordinary-differential-equation control
• Forecasting the outcome of spintronic experiments with Neural Ordinary Differential Equations
• Neural modal ordinary differential equations: Integrating physics-based modeling with neural ordinary differential equations for modeling high-dimensional monitored structures
• Control of Dual-Sourcing Inventory Systems using Recurrent Neural Networks
• Spectrally Adapted Physics-Informed Neural Networks for Solving Unbounded Domain Problems
• A Two-Stage Training Method for Modeling Constrained Systems With Neural Networks