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. Our code is available at \url{https://github.com/yuyudeep/hcmt}.

翻译：近期，多项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。相比传统数值求解器，这些方法在显著降低求解时间方面取得了显著进展。此类方法通常旨在：i)降低物理动力学求解的计算成本，以及/或ii)提出提升流体与刚体动力学求解精度的技术。然而，对于极短时间尺度内发生瞬时碰撞的柔性体动力学挑战，这些方法的有效性尚待深入探究。本文提出层级接触网格Transformer，该模型采用层级网格结构，能够学习物体空间远距离位置间因碰撞产生的长程依赖关系——高层网格中相邻位置对应低层网格中相距较远的位置。该模型实现了长程交互，并通过层级网格结构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，其轨迹数据反映了显示产业产品设计中常用的实验场景。同时，我们采用经典基准数据集对比了多种基线模型的性能。结果表明，本方法在性能上显著优于现有方法。代码已开源至\url{https://github.com/yuyudeep/hcmt}。