Learning Flexible Body Collision Dynamics with Hierarchical Contact Mesh Transformer

TL;DR

This paper introduces HCMT, a hierarchical mesh transformer model that effectively captures long-range collision dependencies in flexible body dynamics, significantly improving simulation accuracy and efficiency.

Contribution

The paper proposes HCMT, a novel hierarchical contact mesh transformer that models long-range dependencies in flexible body collisions, addressing a gap in existing mesh-based GNN methods.

Findings

HCMT outperforms existing methods on benchmark datasets.

Hierarchical mesh structure accelerates collision effect propagation.

Model effectively captures long-range dependencies in flexible body dynamics.

Abstract

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.