# Automated Model Discovery for Tensional Homeostasis: Constitutive Machine Learning in Growth and Remodeling

arXiv: https://arxiv.org/abs/2410.13645 · HTML: https://mlsanity.com/paper/2410.13645/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 104 references that are in the map.
- First posted on arXiv 17 Oct 2024.

## Builds on (most cited first, 20 of 20)

- [Deep Learning of Vortex Induced Vibrations](https://mlsanity.com/paper/1808.08952/) (2018)
- [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)
- [Neural networks meet hyperelasticity: A guide to enforcing physics](https://mlsanity.com/paper/2302.02403/) (2023)
- [Automated discovery of generalized standard material models with EUCLID](https://mlsanity.com/paper/2211.04453/) (2022)
- [Discovering plasticity models without stress data](https://mlsanity.com/paper/2202.04916/) (2022)
- [On physics-informed data-driven isotropic and anisotropic constitutive models through probabilistic machine learning and space-filling sampling](https://mlsanity.com/paper/2109.11028/) (2021)
- [Viscoelasticty with physics-augmented neural networks: Model formulation and training methods without prescribed internal variables](https://mlsanity.com/paper/2401.14270/) (2024)
- [On sparse regression, Lp-regularization, and automated model discovery](https://mlsanity.com/paper/2310.06872/) (2023)
- [Viscoelastic Constitutive Artificial Neural Networks (vCANNs) - a framework for data-driven anisotropic nonlinear finite viscoelasticity](https://mlsanity.com/paper/2303.12164/) (2023)
- [Theory and implementation of inelastic Constitutive Artificial Neural Networks](https://mlsanity.com/paper/2311.06380/) (2023)
- [Evolution TANN and the identification of internal variables and evolution equations in solid mechanics](https://mlsanity.com/paper/2209.13269/) (2022)
- [Model-free Data-Driven Computational Mechanics Enhanced by Tensor Voting](https://mlsanity.com/paper/2004.02503/) (2020)
- [Physics-informed Data-driven Discovery of Constitutive Models with Application to Strain-Rate-sensitive Soft Materials](https://mlsanity.com/paper/2304.13897/) (2023)
- [Accounting for plasticity: An extension of inelastic Constitutive Artificial Neural Networks](https://mlsanity.com/paper/2407.19326/) (2024)
- [A macroscopic approach for stress driven anisotropic growth in bioengineered soft tissues](https://mlsanity.com/paper/2107.03698/) (2021)
- [A multiphysics modeling approach for in-stent restenosis: Theoretical aspects and finite element implementation](https://mlsanity.com/paper/2204.02301/) (2022)
- [A computational framework for modeling cell-matrix interactions in soft biological tissues](https://mlsanity.com/paper/2103.13110/) (2021)
- [What do cells regulate in soft tissues on short time scales?](https://mlsanity.com/paper/2104.05580/) (2021)
- [Mechanical modeling of the maturation process for tissue-engineered implants: application to biohybrid heart valves](https://mlsanity.com/paper/2307.12439/) (2023)

## Built on by (most cited first, 6 of 6)

- [Inelastic Constitutive Kolmogorov-Arnold Networks: A generalized framework for automated discovery of interpretable inelastic material models](https://mlsanity.com/paper/2602.17750/) (2026)
- [A Complement to Neural Networks for Anisotropic Inelasticity at Finite Strains](https://mlsanity.com/paper/2510.04187/) (2025)
- [A Convex Route to Thermoelasticity: Learning Internal Energy and Dissipation](https://mlsanity.com/paper/2603.28707/) (2026)
- [LLM-driven design of physics-constrained constitutive models: two agents are better than one](https://mlsanity.com/paper/2605.23754/) (2026)
- [Automatic-Differentiation-Enabled Finite Element Model Updating: Learning Constitutive Neural Networks from Structural Deformation Data](https://mlsanity.com/paper/2606.05199/) (2026)
- [CANN-EUCLID: unsupervised constitutive artificial neural network model discovery from full-field data](https://mlsanity.com/paper/2606.14565/) (2026)

## Abstract (arXiv)

Soft biological tissues exhibit a tendency to maintain a preferred state of tensile stress, known as tensional homeostasis, which is restored even after external mechanical stimuli. This macroscopic behavior can be described using the theory of kinematic growth, where the deformation gradient is multiplicatively decomposed into an elastic part and a part related to growth and remodeling. Recently, the concept of homeostatic surfaces was introduced to define the state of homeostasis and the evolution equations for inelastic deformations. However, identifying the optimal model and material parameters to accurately capture the macroscopic behavior of inelastic materials can only be accomplished with significant expertise, is often time-consuming, and prone to error, regardless of the specific inelastic phenomenon. To address this challenge, built-in physics machine learning algorithms offer significant potential. In this work, we extend our inelastic Constitutive Artificial Neural Networks (iCANNs) by incorporating kinematic growth and homeostatic surfaces to discover the scalar model equations, namely the Helmholtz free energy and the pseudo potential. The latter describes the state of homeostasis in a smeared sense. We evaluate the ability of the proposed network to learn from experimentally obtained tissue equivalent data at the material point level, assess its predictive accuracy beyond the training regime, and discuss its current limitations when applied at the structural level. Our source code, data, examples, and an implementation of the corresponding material subroutine are made accessible to the public at https://doi.org/10.5281/zenodo.13946282.