Learning Flexible Body Collision Dynamics with Hierarchical Contact Mesh Transformer

TL;DR

H Hierarchical Contact Mesh Transformer (HCMT) is presented, which uses hierarchical mesh structures and can learn long-range dependencies among spatially distant positions of a body and provides significant performance improvements over existing methods.

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.

Figures (20)

• Figure 1: Relationship between velocity and non-linearity in various physical systems. Typically, implicit methods are used in static system, while explicit methods chang2007improved are employed in dynamic domain. Flexible dynamics solve problems with highly non-linear characteristics and occur quickly in a very short time.
• Figure 2: An illustration of the contact propagation via one-hop propagation in various levels. Level $i$ is the $i$-th level mesh (after pooling nodes from the previous level) in our hierarchical mesh structure. After node pooling, our Transformer accelerates contact propagation, which is a key in simulating flexible body collision dynamics.
• Figure 3: Overview of Hierarchical Contact Mesh Transformer (HCMT) with four layers: encoder, CMT, HMT, and decoder. The light blue graph in $G_0$ corresponds to a ball in the Impact Plate dataset, while the green graph represents a plate.
• Figure 4: Hierarchical architecture of HMT layer in Fig. \ref{['fig:overview']}. The overall process of HMT layer is constructed by repetitively stacking HMT blocks and pooling. Utilizing this hierarchical structure is highly effective in reducing computational complexity.
• Figure 5: (a) depicts our proposed CMT block and dual self-attention blocks. The mesh attention on the left only computes attention weights $\mathbf{a}_{ij}$ for each of the edges of two colliding objects nodes. The contact attention on the right only considers the weights $\mathbf{b}_{iq}$ of contact edges. (b) describes our proposed HMT module. The mesh self-attention in HMT is the same as mesh attention in CMT.