# Unsupervised full-field Bayesian inference of orthotropic hyperelasticity from a single biaxial test: a myocardial case study

arXiv: https://arxiv.org/abs/2510.09498 · HTML: https://mlsanity.com/paper/2510.09498/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 82 references that are in the map.
- First posted on arXiv 10 Oct 2025.

## Builds on (most cited first, 11 of 11)

- [Composable Effects for Flexible and Accelerated Probabilistic Programming in NumPyro](https://mlsanity.com/paper/1912.11554/) (2019)
- [Unsupervised discovery of interpretable hyperelastic constitutive laws](https://mlsanity.com/paper/2010.13496/) (2020)
- [A new family of Constitutive Artificial Neural Networks towards automated model discovery](https://mlsanity.com/paper/2210.02202/) (2022)
- [NN-EUCLID: deep-learning hyperelasticity without stress data](https://mlsanity.com/paper/2205.06664/) (2022)
- [Bayesian-EUCLID: discovering hyperelastic material laws with uncertainties](https://mlsanity.com/paper/2203.07422/) (2022)
- [Can KAN CANs? Input-convex Kolmogorov-Arnold Networks (KANs) as hyperelastic constitutive artificial neural networks (CANs)](https://mlsanity.com/paper/2503.05617/) (2025)
- [Generative Hyperelasticity with Physics-Informed Probabilistic Diffusion Fields](https://mlsanity.com/paper/2310.03745/) (2023)
- [A topology optimisation framework to design test specimens for one-shot identification or discovery of material models](https://mlsanity.com/paper/2501.12756/) (2025)
- [A universal material model subroutine for soft matter systems](https://mlsanity.com/paper/2404.13144/) (2024)
- [Strain energy density as a Gaussian process and its utilization in stochastic finite element analysis: application to planar soft tissues](https://mlsanity.com/paper/2210.00868/) (2022)
- [Deterministic and statistical calibration of constitutive models from full-field data with parametric physics-informed neural networks](https://mlsanity.com/paper/2405.18311/) (2024)

## Built on by (most cited first, 2 of 2)

- [CANN-EUCLID: unsupervised constitutive artificial neural network model discovery from full-field data](https://mlsanity.com/paper/2606.14565/) (2026)
- [Uncertainty quantification in mechanics: A unified Bayesian perspective](https://mlsanity.com/paper/2607.18734/) (2026)

## Abstract (arXiv)

Cardiac muscle tissue exhibits highly non-linear hyperelastic and orthotropic material behavior during passive deformation. Traditional constitutive identification protocols therefore combine multiple loading modes and typically require multiple specimens and substantial handling. In soft living tissues, such protocols are challenged by inter- and intra-sample variability and by manipulation-induced alterations of mechanical response, which can bias inverse calibration. In this work we exploit spatially heterogeneous full-field kinematics as an information-rich alternative to multimodal testing. We recast EUCLID, an unsupervised method for the automated discovery of constitutive models, towards Bayesian parameter inference for highly nonlinear, orthotropic constitutive models. Using synthetic myocardial tissue slabs, we demonstrate that a single heterogeneous biaxial experiment, combined with sparse reaction-force measurements, enables robust recovery of Holzapfel-Ogden parameters with quantified uncertainty, across multiple noise levels. The inferred responses agree closely with ground-truth simulations and yield credible intervals that reflect the impact of measurement noise on orthotropic material model inference. Our work supports single-shot, uncertainty-aware characterization of nonlinear orthotropic material models from a single biaxial test, reducing sample demand and experimental manipulation.