# Transformer with Implicit Edges for Particle-based Physics Simulation

arXiv: https://arxiv.org/abs/2207.10860 · HTML: https://mlsanity.com/paper/2207.10860/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 31 references that are in the map.
- First posted on arXiv 22 Jul 2022.

## Builds on (most cited first, 23 of 23)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [End-to-End Object Detection with Transformers](https://mlsanity.com/paper/2005.12872/) (2020)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Non-local Neural Networks](https://mlsanity.com/paper/1711.07971/) (2017)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [A Generalization of Transformer Networks to Graphs](https://mlsanity.com/paper/2012.09699/) (2020)
- [Interaction Networks for Learning about Objects, Relations and Physics](https://mlsanity.com/paper/1612.00222/) (2016)
- [MaX-DeepLab: End-to-End Panoptic Segmentation with Mask Transformers](https://mlsanity.com/paper/2012.00759/) (2020)
- [PolyGen: An Autoregressive Generative Model of 3D Meshes](https://mlsanity.com/paper/2002.10880/) (2020)
- [Learning Particle Dynamics for Manipulating Rigid Bodies, Deformable Objects, and Fluids](https://mlsanity.com/paper/1810.01566/) (2018)
- [Towards Physics-informed Deep Learning for Turbulent Flow Prediction](https://mlsanity.com/paper/1911.08655/) (2019)
- [Graph-Bert: Only Attention is Needed for Learning Graph Representations](https://mlsanity.com/paper/2001.05140/) (2020)
- [Deep Learning Methods for Reynolds-Averaged Navier-Stokes Simulations of Airfoil Flows](https://mlsanity.com/paper/1810.08217/) (2018)
- [Flexible Neural Representation for Physics Prediction](https://mlsanity.com/paper/1806.08047/) (2018)
- [Scalable Differentiable Physics for Learning and Control](https://mlsanity.com/paper/2007.02168/) (2020)
- [SPNets: Differentiable Fluid Dynamics for Deep Neural Networks](https://mlsanity.com/paper/1806.06094/) (2018)
- [Graph-based Task-specific Prediction Models for Interactions between Deformable and Rigid Objects](https://mlsanity.com/paper/2103.02932/) (2021)

## Built on by (most cited first, 15 of 15)

- [Neural Material Adaptor for Visual Grounding of Intrinsic Dynamics](https://mlsanity.com/paper/2410.08257/) (2024)
- [Towards Multi-Layered 3D Garments Animation](https://mlsanity.com/paper/2305.10418/) (2023)
- [Latent Intuitive Physics: Learning to Transfer Hidden Physics from A 3D Video](https://mlsanity.com/paper/2406.12769/) (2024)
- [PGODE: Towards High-quality System Dynamics Modeling](https://mlsanity.com/paper/2311.06554/) (2023)
- [FD-Bench: A Modular and Fair Benchmark for Data-driven Fluid Simulation](https://mlsanity.com/paper/2505.20349/) (2025)
- [GausSim: Foreseeing Reality by Gaussian Simulator for Elastic Objects](https://mlsanity.com/paper/2412.17804/) (2024)
- [Learning Physical Simulation with Message Passing Transformer](https://mlsanity.com/paper/2406.06060/) (2024)
- [FluidFormer: Transformer with Continuous Convolution for Particle-based Fluid Simulation](https://mlsanity.com/paper/2508.01537/) (2025)
- [ClothTransformer: Unified Latent-Space Transformers for Scalable Cloth Simulation](https://mlsanity.com/paper/2605.27852/) (2026)
- [PhysiFormer: Learning to Simulate Mechanics in World Space](https://mlsanity.com/paper/2606.27364/) (2026)
- [Learning Physics-Guided Residual Dynamics for Deformable Object Simulation](https://mlsanity.com/paper/2607.13451/) (2026)
- [A Pioneering Neural Network Method for Efficient and Robust Fluid Simulation](https://mlsanity.com/paper/2412.10748/) (2024)
- [Reversible GNS for Dissipative Fluids with Consistent Bidirectional Dynamics](https://mlsanity.com/paper/2509.22207/) (2025)
- [MAVEN: A Mesh-Aware Volumetric Encoding Network for Simulating 3D Flexible Deformation](https://mlsanity.com/paper/2604.04474/) (2026)
- [MeshPriorDiT: Hierarchical Modeling for Action-Conditioned Cloth Dynamics](https://mlsanity.com/paper/2608.26766/) (2026)

## Abstract (arXiv)

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.