# Exploring hyperelastic material model discovery for human brain cortex: multivariate analysis vs. artificial neural network approaches

arXiv: https://arxiv.org/abs/2310.10762 · HTML: https://mlsanity.com/paper/2310.10762/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 71 references that are in the map.
- First posted on arXiv 16 Oct 2023.

## Builds on (most cited first, 9 of 9)

- [Mean Absolute Percentage Error for regression models](https://mlsanity.com/paper/1605.02541/) (2016)
- [Polyconvex anisotropic hyperelasticity with neural networks](https://mlsanity.com/paper/2106.14623/) (2021)
- [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)
- [Data-driven Tissue Mechanics with Polyconvex Neural Ordinary Differential Equations](https://mlsanity.com/paper/2110.03774/) (2021)
- [Data-driven Modeling of the Mechanical Behavior of Anisotropic Soft Biological Tissue](https://mlsanity.com/paper/2107.05388/) (2021)
- [Model Selection for High Dimensional Quadratic Regression via Regularization](https://mlsanity.com/paper/1501.00049/) (2014)
- [The multiphysics of prion-like diseases: progression and atrophy](https://mlsanity.com/paper/1804.01958/) (2018)
- [Predicting the Mechanical Properties of Biopolymer Gels Using Neural Networks Trained on Discrete Fiber Network Data](https://mlsanity.com/paper/2101.11712/) (2021)

## Built on by (most cited first, 1 of 1)

- [Discovering uncertainty: Gaussian constitutive neural networks with correlated weights](https://mlsanity.com/paper/2503.12679/) (2025)

## Abstract (arXiv)

Traditional computational methods, such as the finite element analysis, have provided valuable insights into uncovering the underlying mechanisms of brain physical behaviors. However, precise predictions of brain physics require effective constitutive models to represent the intricate mechanical properties of brain tissue. In this study, we aimed to identify the most favorable constitutive material model for human brain tissue. To achieve this, we applied artificial neural network and multiple regression methods to a generalization of widely accepted classic models, and compared the results obtained from these two approaches. To evaluate the applicability and efficacy of the model, all setups were kept consistent across both methods, except for the approach to prevent potential overfitting. Our results demonstrate that artificial neural networks are capable of automatically identifying accurate constitutive models from given admissible estimators. Nonetheless, the five-term and two-term neural network models trained under single-mode and multi-mode loading scenarios, were found to be suboptimal and could be further simplified into two-term and single-term, respectively, with higher accuracy using multiple regression. Our findings highlight the importance of hyperparameters for the artificial neural network and emphasize the necessity for detailed cross-validations of regularization parameters to ensure optimal selection at a global level in the development of material constitutive models. This study validates the applicability and accuracy of artificial neural network to automatically discover constitutive material models with proper regularization as well as the benefits in model simplification without compromising accuracy for traditional multivariable regression.