# Predicting the Mechanical Properties of Biopolymer Gels Using Neural Networks Trained on Discrete Fiber Network Data

arXiv: https://arxiv.org/abs/2101.11712 · HTML: https://mlsanity.com/paper/2101.11712/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 77 references that are in the map.
- First posted on arXiv 23 Jan 2021.

## Builds on (most cited first, 7 of 7)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima](https://mlsanity.com/paper/1609.04836/) (2016)
- [Geometric deep learning for computational mechanics Part I: Anisotropic Hyperelasticity](https://mlsanity.com/paper/2001.04292/) (2020)
- [Performance Metrics (Error Measures) in Machine Learning Regression, Forecasting and Prognostics: Properties and Typology](https://mlsanity.com/paper/1809.03006/) (2018)
- [Tensor Basis Gaussian Process Models of Hyperelastic Materials](https://mlsanity.com/paper/1912.10872/) (2019)
- [Exploring the potential of transfer learning for metamodels of heterogeneous material deformation](https://mlsanity.com/paper/2010.16260/) (2020)
- [Backpropagation generalized for output derivatives](https://mlsanity.com/paper/1712.04185/) (2017)

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

- [Data-driven Tissue Mechanics with Polyconvex Neural Ordinary Differential Equations](https://mlsanity.com/paper/2110.03774/) (2021)
- [Deep Learning in Deterministic Computational Mechanics](https://mlsanity.com/paper/2309.15421/) (2023)
- [Data-driven anisotropic finite viscoelasticity using neural ordinary differential equations](https://mlsanity.com/paper/2302.03598/) (2023)
- [Generative Hyperelasticity with Physics-Informed Probabilistic Diffusion Fields](https://mlsanity.com/paper/2310.03745/) (2023)
- [Learning Mechanically Driven Emergent Behavior with Message Passing Neural Networks](https://mlsanity.com/paper/2202.01380/) (2022)
- [Exploring hyperelastic material model discovery for human brain cortex: multivariate analysis vs. artificial neural network approaches](https://mlsanity.com/paper/2310.10762/) (2023)

## Abstract (arXiv)

Biopolymer gels, such as those made out of fibrin or collagen, are widely used in tissue engineering applications and biomedical research. Moreover, fibrin naturally assembles into gels in vivo during wound healing and thrombus formation. Macroscale biopolymer gel mechanics are dictated by the microscale fiber network. Hence, accurate description of biopolymer gels can be achieved using representative volume elements (RVE) that explicitly model the discrete fiber networks of the microscale. These RVE models, however, cannot be efficiently used to model the macroscale due to the challenges and computational demands of multiscale coupling. Here, we propose the use of an artificial, fully connected neural network (FCNN) to efficiently capture the behavior of the RVE models. The FCNN was trained on 1100 fiber networks subjected to 121 biaxial deformations. The stress data from the RVE, together with the total energy and the condition of incompressibility of the surrounding matrix, were used to determine the derivatives of an unknown strain energy function with respect to the deformation invariants. During training, the loss function was modified to ensure convexity of the strain energy function and symmetry of its Hessian. A general FCNN model was coded into a user material subroutine (UMAT) in the software Abaqus. In this work, the FCNN trained on the discrete fiber network data was used in finite element simulations of fibrin gels using our UMAT. We anticipate that this work will enable further integration of machine learning tools with computational mechanics. It will also improve computational modeling of biological materials characterized by a multiscale structure.