# Graph Neural Network Surrogates for Contacting Deformable Bodies with Necessary and Sufficient Contact Detection

arXiv: https://arxiv.org/abs/2507.13459 · HTML: https://mlsanity.com/paper/2507.13459/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 50 references that are in the map.
- First posted on arXiv 17 Jul 2025.

## Builds on (most cited first, 15 of 15)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [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)
- [Towards Physics-informed Deep Learning for Turbulent Flow Prediction](https://mlsanity.com/paper/1911.08655/) (2019)
- [Combining Differentiable PDE Solvers and Graph Neural Networks for Fluid Flow Prediction](https://mlsanity.com/paper/2007.04439/) (2020)
- [Flexible Neural Representation for Physics Prediction](https://mlsanity.com/paper/1806.08047/) (2018)
- [Learning rigid dynamics with face interaction graph networks](https://mlsanity.com/paper/2212.03574/) (2022)
- [The mixed deep energy method for resolving concentration features in finite strain hyperelasticity](https://mlsanity.com/paper/2104.09623/) (2021)
- [Solving Forward and Inverse Problems of Contact Mechanics using Physics-Informed Neural Networks](https://mlsanity.com/paper/2308.12716/) (2023)
- [What machine learning can do for computational solid mechanics](https://mlsanity.com/paper/2109.08419/) (2021)
- [Energy-based physics-informed neural network for frictionless contact problems under large deformation](https://mlsanity.com/paper/2411.03671/) (2024)
- [Physics-Informed Neural Networks for Solving Contact Problems in Three Dimensions](https://mlsanity.com/paper/2412.09022/) (2024)
- [Data-Driven Surrogate Modeling Techniques to Predict the Effective Contact Area of Rough Surface Contact Problems](https://mlsanity.com/paper/2504.17354/) (2025)

## Abstract (arXiv)

Surrogate models for the rapid inference of nonlinear boundary value problems in mechanics are helpful in a broad range of engineering applications. However, effective surrogate modeling of applications involving the contact of deformable bodies, especially in the context of varying geometries, is still an open issue. In particular, existing methods are confined to rigid body contact or, at best, contact between rigid and soft objects with well-defined contact planes. Furthermore, they employ contact or collision detection filters that serve as a rapid test but use only the necessary and not sufficient conditions for detection. In this work, we present a graph neural network architecture that utilizes continuous collision detection and, for the first time, incorporates sufficient conditions designed for contact between soft deformable bodies. We test its performance on two benchmarks, including a problem in soft tissue mechanics of predicting the closed state of a bioprosthetic aortic valve. We find a regularizing effect on adding additional contact terms to the loss function, leading to better generalization of the network. These benefits hold for simple contact at similar planes and element normal angles, and complex contact at differing planes and element normal angles. We also demonstrate that the framework can handle varying reference geometries. However, such benefits come with high computational costs during training, resulting in a trade-off that may not always be favorable. We quantify the training cost and the resulting inference speedups on various hardware architectures. Importantly, our graph neural network implementation results in up to a thousand-fold speedup for our benchmark problems at inference.