Bi-Directional Dynamic Neural Networks with Physical Analyzability

Abstract

The rapid growth of research in exploiting deep learning to predict mechanical systems has revealed a new route for system identification, however, the analytic model as a white-box has not been replaced in applications because of its open physical information. In contrast, the models generated by end-to-end learning usually lack the ability of physical analysis, which makes them inapplicable in many situations. Consequently, high-precision modeling with physical analyzability becomes a necessity. In this paper, we introduce Bi-Directional Dynamic Neural Networks (BDDN), a deep learning framework that can infer the dynamics of physical systems from control signals and observed state trajectories. Based on Lagrangian Mechanics, we train the neural ordinary differential equations (ODEs) in a trajectory backtracking algorithm. As a result, the model can seamlessly incorporate with prior knowledge, learn unknown dynamics without human intervention, and provide information as transparent as analytic models, including forward and inverse dynamics as well as inertia, Coriolis and centrifugal forces, and gravity. We demonstrate our method on a simulated 2-axis and a 6-axis robot respectively, the experimental results show that this method outperforms existing methods in terms of precision. This framework provides new ideas for system identification by providing interpretable, physically-consistent models for physical systems.

Keywords: Deep learning, physics-based priors, forward dynamics, inverse dynamic, parameters estimation