MIXPINN: Mixed-Material Simulations by Physics-Informed Neural Network

Simulating the complex interactions between soft tissues and rigid anatomy is critical for applications in surgical training, planning, and robotic-assisted interventions. Traditional Finite Element Method (FEM)-based simulations, while accurate, are computationally expensive and impractical for real-time scenarios. Learning-based approaches have shown promise in accelerating predictions but have fallen short in modeling soft-rigid interactions effectively. We introduce MIXPINN, a physics-informed Graph Neural Network (GNN) framework for mixed-material simulations, explicitly capturing soft-rigid interactions using graph-based augmentations. Our approach integrates Virtual Nodes (VNs) and Virtual Edges (VEs) to enhance rigid body constraint satisfaction while preserving computational efficiency. By leveraging a graph-based representation of biomechanical structures, MIXPINN learns high-fidelity deformations from FEM-generated data and achieves real-time inference with sub-millimeter accuracy. We validate our method in a realistic clinical scenario, demonstrating superior performance compared to baseline GNN models and traditional FEM methods. Our results show that MIXPINN reduces computational cost by an order of magnitude while maintaining high physical accuracy, making it a viable solution for real-time surgical simulation and robotic-assisted procedures.