Particle-based systems provide a flexible and unified way to simulate physics
systems with complex dynamics. Most existing data-driven simulators for
particle-based systems adopt graph neural networks (GNNs) as their network
backbones, as particles and their interactions can be naturally represented by
graph nodes and graph edges. However, while particle-based systems usually
contain hundreds even thousands of particles, the explicit modeling of particle
interactions as graph edges inevitably leads to a significant computational
overhead, due to the increased number of particle interactions. Consequently,
in this paper we propose a novel Transformer-based method, dubbed as
Transformer with Implicit Edges (TIE), to capture the rich semantics of
particle interactions in an edge-free manner. The core idea of TIE is to
decentralize the computation involving pair-wise particle interactions into
per-particle updates. This is achieved by adjusting the self-attention module
to resemble the update formula of graph edges in GNN. To improve the
generalization ability of TIE, we further amend TIE with learnable
material-specific abstract particles to disentangle global material-wise
semantics from local particle-wise semantics. We evaluate our model on diverse
domains of varying complexity and materials. Compared with existing GNN-based
methods, without bells and whistles, TIE achieves superior performance and
generalization across all these domains. Codes and models are available at
this https URL

本论文提出了一种新的基于 Transformer 的方法 ——Transformer with Implicit Edges (TIE)，以无边的方式捕捉粒子相互作用的丰富语义，最终在领域多样性和材料多样性方面获得卓越表现和泛化能力。