  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
https://github.com/ftbabi/TIE_ECCV2022.git.
