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.
翻译:在多体动态中,复杂的物理物体的动作被描述为具有多种未知的解决方案的普通普通差异方程式系统。 工程师需要不断调整对象,以满足设计阶段的需求, 需要高效的求解器。 机器学习的局部偏差方程式的崛起可以满足这一需求。 这些解答器可以分为两类: 接近解答功能( 物理- 知情神经网络) 和学习解答操作器( 神经操作器 ) 。 最近提议的物理知情神经操作器( PINO) 通过将物理方程式嵌入神经操作器的丢失功能而从这两个类别中获取优势。 在设计阶段需要高效的解答器的阶段, 工程师需要不断调整对象。 根据这个最新设计的概念, 我们建议为多体动态中混合的极点( PINO- MBD) 建立物理知情的神经操作器操作器操作器( IPNO- MBD), 在进行 PINO- MBD 培训后, 网络只需过一个前端通道, 才能获得具有不同参数的新实例解决方案的解决方案。 要处理同时含有多种解决方案的困难( 而不是仅是常规的常规驱动驱动工具的双物理学演示结果) 。