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

Area of Science:

• Computational Mechanics
• Machine Learning in Engineering
• Nonlinear Boundary Value Problems

Background:

• Surrogate models accelerate engineering simulations but struggle with deformable body contact, especially with changing shapes.
• Existing methods are limited to rigid bodies or simple soft-rigid contact, using incomplete collision detection.
• Accurate modeling of soft deformable body contact is crucial for applications like biomechanics.

Purpose of the Study:

• To develop a novel graph neural network (GNN) architecture for rapid inference of nonlinear boundary value problems involving soft deformable body contact.
• To incorporate sufficient conditions for contact detection, addressing limitations of existing methods.
• To evaluate the GNN's performance on benchmarks, including soft tissue mechanics, and assess its ability to handle varying geometries.

Main Methods:

• A graph neural network architecture was designed utilizing continuous collision detection.
• Sufficient conditions for contact between soft deformable bodies were integrated into the GNN.
• The model was trained and tested on benchmark problems, including bioprosthetic aortic valve simulation.
• Contact terms were added to the loss function to improve generalization.

Main Results:

• The GNN successfully models contact between soft deformable bodies, including complex scenarios with varying geometries.
• Adding contact terms to the loss function demonstrated a regularizing effect, enhancing network generalization.
• The framework handles varying reference geometries effectively.
• Significant inference speedups were achieved: 100-1000x on GPU and 20-200x on CPU.

Conclusions:

• The proposed GNN provides an effective solution for rapid inference of nonlinear mechanics problems with soft deformable body contact.
• The method offers substantial computational speedups for inference, though training remains computationally intensive.
• This approach advances surrogate modeling for complex contact scenarios in engineering and biomechanics.