Fully differentiable framework for inverse identification of geometry and material parameters with application to determining stress-free configuration of soft tissues
Abstract
Medical images of soft tissues typically depict loaded configurations rather than true unloaded (stress-free) states, which can bias biomechanical simulations and inverse material identification. A gradient-based inverse finite element framework is presented that jointly reconstructs an effective unloaded reference geometry and estimates hyperelastic material parameters from two or more observed deformed configurations. The formulation is fully differentiable and leverages exact end-to-end gradients to enable unified, simultaneous optimization of geometry and constitutive parameters. The objective function combines a nodal-position misfit with a deformation-gradient-based mismatch term, improving robustness under large deformations. Benchmark studies quantify the influence of loading diversity and observation count and demonstrate reduced sensitivity to poor material initialization. Finally, application to an MRI-derived breast model shows accurate recovery of the unloaded configuration and constitutive parameters from multiple gravity-loaded states. The framework provides a unified and scalable tool for inverse biomechanics with potential applications in personalized modeling, elastography, and surgical planning.
Related
- Semiempirical Quantum Chemistry in the Age of ab initio Data and Differentiable Programming: III. Differentiable Complete Active Space Configuration Interaction
- A Differentiable Framework for Inverse Identification of Heterogeneous Cohesive Laws
- A Differentiable, GPU-Accelerated Finite-Element Formulation in JAX for Large-Deformation Shells with Contact: Application to Patient-Specific Aortic Valve Simulation
- Application and Performance Assessment of Annealing Methods for Electrostatic-Energy-Based Configuration Search in Mixed Crystals
- Inverse identification of thermal-radiative parameters for reduced effective-temperature uncertainty in an ion optical clock
BibTeX
@misc{bae2026fully,
title = {{Fully differentiable framework for inverse identification of geometry and material parameters with application to determining stress-free configuration of soft tissues}},
author = {Hyunoh Bae and Tianyi Hu and Adrian Buganza Tepole and Hector Gomez},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.18109},
eprint = {2609.18109},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.18109},
}
RIS
TY - UNPB
TI - Fully differentiable framework for inverse identification of geometry and material parameters with application to determining stress-free configuration of soft tissues
AU - Hyunoh Bae
AU - Tianyi Hu
AU - Adrian Buganza Tepole
AU - Hector Gomez
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.18109
UR - https://arxiv.org/abs/2609.18109
AB - Medical images of soft tissues typically depict loaded configurations rather than true unloaded (stress-free) states, which can bias biomechanical simulations and inverse material identification. A gradient-based inverse finite element framework is presented that jointly reconstructs an effective unloaded reference geometry and estimates hyperelastic material parameters from two or more observed deformed configurations. The formulation is fully differentiable and leverages exact end-to-end gradients to enable unified, simultaneous optimization of geometry and constitutive parameters. The objective function combines a nodal-position misfit with a deformation-gradient-based mismatch term, improving robustness under large deformations. Benchmark studies quantify the influence of loading diversity and observation count and demonstrate reduced sensitivity to poor material initialization. Finally, application to an MRI-derived breast model shows accurate recovery of the unloaded configuration and constitutive parameters from multiple gravity-loaded states. The framework provides a unified and scalable tool for inverse biomechanics with potential applications in personalized modeling, elastography, and surgical planning.
ER -