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

2025-07-17

AI Summary

To address challenges in surrogate modeling for deformable-body contact mechanics—including nonlinearity arising from geometric deformation and inaccurate contact detection—this paper proposes a novel graph neural network (GNN)-based surrogate modeling framework. Methodologically, it introduces, for the first time, a *sufficient contact detection condition*, integrating continuous collision detection with necessary contact verification to ensure physically consistent and robust contact logic. A contact-term regularization loss is designed to enforce physical plausibility, and the framework supports multi-platform training and inference. Evaluated on biomechanical tissue modeling benchmarks, the method achieves up to 1000× speedup in inference while generalizing across diverse geometric configurations. Although training overhead remains substantial, the approach achieves significant co-optimization of accuracy, computational efficiency, and generalizability.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Search and Optimization: Sampling/Simulation-based Search
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

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.

Problem

• Modeling contact between deformable bodies with varying geometries
• Incorporating sufficient conditions for soft body contact detection
• Balancing computational cost and inference speed in surrogate models

Innovation

• Graph neural network for deformable body contact
• Continuous collision detection with sufficient conditions
• Handles varying geometries and complex contact scenarios