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In multi-body dynamics, the motion of a complicated physical object isdescribed as a coupled ordinary differential equation system with multipleunknown solutions. Engineers need to constantly adjust the object to meetrequirements at the design stage, where a highly efficient solver is needed.The rise of machine learning-based partial differential equation solvers canmeet this need. These solvers can be classified into two categories:approximating the solution function (Physics-informed neural network) andlearning the solution operator (Neural operator). The recently proposedphysics-informed neural operator (PINO) gains advantages from both categoriesby embedding physics equations into the loss function of a neural operator.Following this state-of-art concept, we propose the physics-informed neuraloperator for coupled ODEs in multi-body dynamics (PINO-MBD), which learns themapping between parameter spaces and solution spaces. Once PINO-MBD is trained,only one forward pass of the network is required to obtain the solutions for anew instance with different parameters. To handle the difficulty that coupledODEs contain multiple solutions (instead of only one in normal PDE problems),two new physics embedding methods are also proposed. The experimental resultson classic vehicle-track coupled dynamics problem show state-of-art performancenot only on solutions but also the first and second derivatives of solutions.

PINO-MBD: Physics-informed Neural Operator for Solving Coupled ODEs in Multi-body Dynamics