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

arXiv: https://arxiv.org/abs/2608.20967 · HTML: https://mlsanity.com/paper/2608.20967/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 21 references that are in the map.
- First posted on arXiv 21 Aug 2026.

## Builds on (most cited first, 6 of 6)

- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Simulation of hyperelastic materials in real-time using Deep Learning](https://mlsanity.com/paper/1904.06197/) (2019)
- [MAgNET: A Graph U-Net Architecture for Mesh-Based Simulations](https://mlsanity.com/paper/2211.00713/) (2022)
- [Soft Tissue Simulation and Force Estimation from Heterogeneous Structures using Equivariant Graph Neural Networks](https://mlsanity.com/paper/2509.10125/) (2025)
- [Inverse deformation analysis: an experimental and numerical assessment using the FEniCS Project](https://mlsanity.com/paper/2102.13455/) (2021)
- [Conditional Graph Neural Network for Predicting Soft Tissue Deformation and Forces](https://mlsanity.com/paper/2507.05315/) (2025)

## Abstract (arXiv)

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.