  In multi-body dynamics, the motion of a complicated physical object is
described as a coupled ordinary differential equation system with multiple
unknown solutions. Engineers need to constantly adjust the object to meet
requirements at the design stage, where a highly efficient solver is needed.
The rise of machine learning-based partial differential equation solvers can
meet this need. These solvers can be classified into two categories:
approximating the solution function (Physics-informed neural network) and
learning the solution operator (Neural operator). The recently proposed
physics-informed neural operator (PINO) gains advantages from both categories
by embedding physics equations into the loss function of a neural operator.
Following this state-of-art concept, we propose the physics-informed neural
operator for coupled ODEs in multi-body dynamics (PINO-MBD), which learns the
mapping 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 a
new instance with different parameters. To handle the difficulty that coupled
ODEs contain multiple solutions (instead of only one in normal PDE problems),
two new physics embedding methods are also proposed. The experimental results
on classic vehicle-track coupled dynamics problem show state-of-art performance
not only on solutions but also the first and second derivatives of solutions.
