Product-based topological Lagrangian neural network for learning articulated 2D multi-rigid-body system

Abstract Lagrangian neural networks (LNN) is a physical-informed data-driven framework for learning the dynamics of physical systems. The incorporation of strong inductive biases enables LNN to outperform purely data-driven methods. However, its application has predominantly been confined to simple systems like pendulums, springs, or single rigid bodies such as gyroscopes or rigid rotors. In this paper, we present a so-called product-based topological Lagrangian neural network (PTLNN) that can learn the dynamics of articulated multi-rigid-body system by exploiting the coupling nonlinearity and the topological relation of system. Compared to other improved Lagrangian neural networks, such as Lagrangian graph neural network and Constraint Lagrangian neural network, the additional prior-knowledges in PTLNN do not need to be measured, which make PTLNNs easier to use. We demonstrate the performance of PTLNN by learning the dynamics of articulated systems with different degrees of freedom. The testing results illustrates that PTLNN outperforms other physical-informed neural networks such as LNN, HNN and NODE, which only encode prior knowledge without measurement.