Bidirectional dynamic neural networks with physical analyzability

The rapid growth in research 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-accuracy modeling with physical analyzability becomes a necessity. In this paper, we introduce bidirectional dynamic neural networks, a deep learning framework that can infer the dynamics of physical systems from control signals and observed state trajectories. Based on forward dynamics, we train the neural ordinary differential equations in a trajectory backtracking algorithm. With the trained model, the inverse dynamics can be calculated and based on $$\textit{Lagrangian}$$ $$\textit{Mechanics}$$ , the physical parameters of the mechanical system can be estimated, including inertia, Coriolis and centrifugal forces, and gravity. As a result, the model can seamlessly incorporate prior knowledge, learn unknown dynamics without human intervention, and provide information as transparent as analytic models. We demonstrate our method on simulated 2-axis and 6-axis robots to evaluate model accuracy, including physical parameters and verified its applicability on real 7-axis robots. The experimental results show that this method is superior to the existing methods. This framework provides a new idea for system identification by providing interpretable, physically consistent models for physical systems.