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 correspond 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. Our code is available at https://github.com/yuyudeep/hcmt.

翻译：近期，众多基于网格的图神经网络模型被提出用于模拟复杂高维物理系统，相较于传统数值求解器，这些方法在显著降低求解时间方面取得了显著成效。此类方法通常致力于：（i）降低物理动力学求解的计算成本，及/或（ii）提升流体与刚体动力学中解的精度的技术。然而，针对柔性体动力学中瞬时碰撞在极短时间内发生的挑战，这些方法的有效性尚待深入探究。本文提出分层接触网格Transformer（HCMT），该模型利用分层网格结构，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——高层网格中邻近的位置对应低层网格中相距较远的位置。HCMT实现了长程交互，其分层网格结构能快速将碰撞效应传播至远端位置。为此，模型由接触网格Transformer与分层网格Transformer（分别简称为CMT和HMT）组成。最后，我们构建了一个柔性体动力学数据集，其中包含反映显示行业产品设计中常用实验设置的轨迹。同时，我们使用知名基准数据集对比了多种基线模型的性能。实验结果表明，HCMT相比现有方法实现了显著性能提升。代码已开源至https://github.com/yuyudeep/hcmt。