Emulation of Cardiac Mechanics Using E(3) Equivariant Graph Neural Networks

Finite-element-based simulations of cardiac electromechanics, though accurate, remain prohibitively computationally expensive, often requiring hours per beat using high-performance computing resources. We present a deep learning-based emulator leveraging E(3) equivariant graph neural networks (GNNs) to approximate cardiac passive mechanics, enabling fast and generalizable predictions of myocardial deformations. Our architecture encodes both geometric and physiological features in an E(3)-equivariant form and introduces a multi-resolution graph augmentation strategy to model long-range dependencies. The proposed method achieves substantial acceleration while maintaining good accuracy.