# Physics-Encoded Graph Neural Networks for Deformation Prediction under Contact

arXiv: https://arxiv.org/abs/2402.03466 · HTML: https://mlsanity.com/paper/2402.03466/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 40 references that are in the map.
- First posted on arXiv 5 Feb 2024.

## Builds on (most cited first, 20 of 20)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Objaverse: A Universe of Annotated 3D Objects](https://mlsanity.com/paper/2212.08051/) (2022)
- [Point Transformer](https://mlsanity.com/paper/2011.00931/) (2020)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [A Compositional Object-Based Approach to Learning Physical Dynamics](https://mlsanity.com/paper/1612.00341/) (2016)
- [Topology Adaptive Graph Convolutional Networks](https://mlsanity.com/paper/1710.10370/) (2017)
- [Physics-Informed Machine Learning: A Survey on Problems, Methods and Applications](https://mlsanity.com/paper/2211.08064/) (2022)
- [SyncSpecCNN: Synchronized Spectral CNN for 3D Shape Segmentation](https://mlsanity.com/paper/1612.00606/) (2016)
- [Rotation-Invariant Transformer for Point Cloud Matching](https://mlsanity.com/paper/2303.08231/) (2023)
- [Bending Graphs: Hierarchical Shape Matching using Gated Optimal Transport](https://mlsanity.com/paper/2202.01537/) (2022)
- [PhysGNN: A Physics-Driven Graph Neural Network Based Model for Predicting Soft Tissue Deformation in Image-Guided Neurosurgery](https://mlsanity.com/paper/2109.04352/) (2021)
- [Graphite: GRAPH-Induced feaTure Extraction for Point Cloud Registration](https://mlsanity.com/paper/2010.09079/) (2020)
- [Dynamic Hyperbolic Attention Network for Fine Hand-object Reconstruction](https://mlsanity.com/paper/2309.02965/) (2023)
- [Physics-informed deep learning for flow and deformation in poroelastic media](https://mlsanity.com/paper/2010.15426/) (2020)
- [Robotic Navigation Autonomy for Subretinal Injection via Intelligent Real-Time Virtual iOCT Volume Slicing](https://mlsanity.com/paper/2301.07204/) (2023)
- [CloudAttention: Efficient Multi-Scale Attention Scheme For 3D Point Cloud Learning](https://mlsanity.com/paper/2208.00524/) (2022)

## Built on by (most cited first, 6 of 6)

- [Learning 3D-Gaussian Simulators from RGB Videos](https://mlsanity.com/paper/2503.24009/) (2025)
- [SoMA: A Real-to-Sim Neural Simulator for Robotic Soft-body Manipulation](https://mlsanity.com/paper/2602.02402/) (2026)
- [Neural-Augmented Kelvinlet for Real-Time Soft Tissue Deformation Modeling](https://mlsanity.com/paper/2506.08043/) (2025)
- [Recurrent U-Net-Based Graph Neural Network (RUGNN) for Accurate Deformation Predictions in Sheet Material Forming](https://mlsanity.com/paper/2507.11547/) (2025)
- [MIXPINN: Mixed-Material Simulations by Physics-Informed Neural Network](https://mlsanity.com/paper/2503.13123/) (2025)
- [ODeform: Learning Continuous 4D Motion for Shape Deformation with Neural ODEs](https://mlsanity.com/paper/2607.20670/) (2026)

## Abstract (arXiv)

In robotics, it's crucial to understand object deformation during tactile interactions. A precise understanding of deformation can elevate robotic simulations and have broad implications across different industries. We introduce a method using Physics-Encoded Graph Neural Networks (GNNs) for such predictions. Similar to robotic grasping and manipulation scenarios, we focus on modeling the dynamics between a rigid mesh contacting a deformable mesh under external forces. Our approach represents both the soft body and the rigid body within graph structures, where nodes hold the physical states of the meshes. We also incorporate cross-attention mechanisms to capture the interplay between the objects. By jointly learning geometry and physics, our model reconstructs consistent and detailed deformations. We've made our code and dataset public to advance research in robotic simulation and grasping.