Solving practical multi-body dynamics problems using a single neural operator

As a fundamental design tool in many engineering disciplines, multi-body dynamics (MBD) models a complex structure with a differential equation group containing multiple physical quantities. Engineers must constantly adjust structures at the design stage, which requires a highly efficient solver. The rise of deep learning technologies has offered new perspectives on MBD. Unfortunately, existing black-box models suffer from poor accuracy and robustness, while the advanced methodologies of single-output operator regression cannot deal with multiple quantities simultaneously. To address these challenges, we propose PINO-MBD, a deep learning framework for solving practical MBD problems based on the theory of physics-informed neural operator (PINO). PINO-MBD uses a single network for all quantities in a multi-body system, instead of training dozens, or even hundreds of networks as in the existing literature. We demonstrate the flexibility and feasibility of PINO-MBD for one toy example and two practical applications: vehicle-track coupled dynamics (VTCD) and reliability analysis of a four-storey building. The performance of VTCD indicates that our framework outperforms existing software and machine learning-based methods in terms of efficiency and precision, respectively. For the reliability analysis, PINO-MBD can provide higher-resolution results in less than a quarter of the time incurred when using the probability density evolution method (PDEM). This framework integrates mechanics and deep learning technologies and may reveal a new concept for MBD and probabilistic engineering.