Sym-ML: A symplectic machine learning framework for stable dynamic prediction of mechanical system

Abstract

Due to the complexity and nonlinearity of mechanical system, traditional dynamic analysis methods are often struggle to balance computational efficiency and accuracy. In order to overcome the challenges existing in the current numerical methods, this paper proposes a novel mechanism-data hybrid-driven method for dynamic analysis of mechanical system via symplectic mathematical theory, machine learning theory and multibody system theory. The proposed method introduces the variational principle into neural network to establish a symplectic machine learning framework, which leverages the high precision advantages of symplectic theory and the efficient and strong generalization ability of neural network, thereby achieving efficient and high precision dynamic prediction of constrained mechanical system. And the characteristic of symplectic conservation of the proposed strategy is proved both in mathematical and numerical perspectives. In addition, three numerical examples are studied, the comparison results indicate that the proposed strategy can perform outstanding advantages in terms of numerical accuracy and computational efficiency, and the proposed method can also predict high precision results without the need for retraining when certain parameters change of the mechanical system.