Recently, many mesh-based graph neural network (GNN) models have been proposed for modeling complex high-dimensional physical systems. Remarkable achievements have been made in significantly reducing the solving time compared to traditional numerical solvers. These methods are typically designed to i) reduce the computational cost in solving physical dynamics and/or ii) propose techniques to enhance the solution accuracy in fluid and rigid body dynamics. However, it remains under-explored whether they are effective in addressing the challenges of flexible body dynamics, where instantaneous collisions occur within a very short timeframe. In this paper, we present Hierarchical Contact Mesh Transformer (HCMT), which uses hierarchical mesh structures and can learn long-range dependencies (occurred by collisions) among spatially distant positions of a body -- two close positions in a higher-level mesh corresponds to two distant positions in a lower-level mesh. HCMT enables long-range interactions, and the hierarchical mesh structure quickly propagates collision effects to faraway positions. To this end, it consists of a contact mesh Transformer and a hierarchical mesh Transformer (CMT and HMT, respectively). Lastly, we propose a flexible body dynamics dataset, consisting of trajectories that reflect experimental settings frequently used in the display industry for product designs. We also compare the performance of several baselines using well-known benchmark datasets. Our results show that HCMT provides significant performance improvements over existing methods.

翻译：近年来，基于网格的图神经网络模型被广泛提出用于模拟复杂高维物理系统。与传统数值求解器相比，这些方法在显著缩短求解时间方面取得了显著成就。典型方法通常致力于：i)降低物理动力学求解的计算成本；ii)提出提升流体与刚体动力学求解精度的技术。然而，当前研究尚未充分探索这些方法是否能有效应对柔性体动力学中瞬时碰撞的挑战。本文提出层级接触网格Transformer，该模型利用层级网格结构，能够学习物体空间远距离位置间（由碰撞引发的）长程依赖关系——高层级网格中的邻近位置对应低层级网格中的远距离位置。HCMT实现了长程交互，其层级网格结构可将碰撞效应快速传播至远距离位置。为此，模型由接触网格Transformer与层级网格Transformer两部分构成。最后，我们构建了柔性体动力学数据集，其中包含反映显示行业产品设计常用实验设置的轨迹数据，并采用基准数据集对多个基线模型进行性能对比。实验结果表明，HCMT相较于现有方法取得了显著的性能提升。