Generalizing Soft Tissue Deformation and Force Prediction Across Material Stiffness and Geometry

Accurate soft tissue simulation is essential for surgical training, pre-operative planning, and haptic feedback systems. While learning-based surrogate models trained on data using the finite element method (FEM) offer a promising path to real-time inference, their reliability depends on well-calibrated constitutive models. Existing approaches neither provide systematic guidance on model selection across stiffness levels, nor generalize across different tissue stiffnesses or geometries. We perform a comprehensive calibration of hyperelastic constitutive models in the SOFA Framework using gravity-loaded silicone beams with different stiffnesses. Using calibrated simulations as training data, we use a softness conditioned equivariant graph neural network, enabling deformation and force prediction across multiple tissue types and unseen geometries. Our model achieves sub-millimeter mean deformation accuracy at 0.010s inference time, while showing that force prediction quality is directly tied to upstream calibration consistency.