Application of a parallel physics-informed neural network to solve the multi-body dynamic equations for full-scale train collisions

Abstract

The prohibitive cost of acquiring data from full-scale train collision experiments limits the applicability of data-driven machine learning methods in train collision simulation. Physics-informed neural networks (PINN) attempt to address this challenge by incorporating physics equations as part of the loss function construction. However, the PINN approach is relatively time-consuming when it comes to solving a large number of physical equations. In this paper, a parallel physics-informed neural network (PPINN) methodology is developed for the solution of multibody dynamics equations to further reduce the computational cost. As well, a PPINN-based framework for engineering applications is proposed, investigating the dynamic responses, absorbed energy, collision forces, and wheel vertical rises of the full-scale train collision. Automatic differentiation and parallelization algorithms are applied to the multi-body dynamic equations including mass, damping, and stiffness matrices, as well as the. The residuals and the initial conditions are included in the loss function. The dynamic responses, absorbed energy, collision forces, and wheel vertical rise of the full-scale train collision are simulated and studied in detail. The results obtained from the PPINN method are in excellent agreement with those obtained from the finite element method (FEM), Newmark-β, and fourth-order Runge–Kutta methods for all four train collision scenarios. Additionally, the PPINN methodology keeps better stability even under large time steps which implies a big potential for computational cost reduction.