Automated model discovery for skin: Discovering the best model, data, and experiment

Abstract

Choosing the best constitutive model and the right set of model parameters is at the heart of continuum mechanics. For decades, the gold standard in constitutive modeling has been to first select a model and then fit its parameters to data. However, the success of this approach dependends hugely on user experience and personal preference. Here we propose a new method that simultaneously and fully autonomously discovers the best model and parameters to explain experimental data. Mathematically, model discovery translates into a complex non-convex optimization problem. We solve this problem by formulating it as a neural network, and leverage the success, robustness, and stability of the optimization tools developed in deep learning. Yet, instead of using a classical off-the-shelf neural network, we design our own family of Constitutive Artificial Neural Networks with activation functions that feature popular constitutive models and parameters that have a clear physical interpretation. Our new network inherently satisfies general kinematic, thermodynamic, and physical constraints and trains robustly, even with sparse data. We illustrate its potential for biaxial extension experiments on skin and demonstrate that the majority of network weights train to zero, while the small subset of non-zero weights defines the discovered model. Unlike classical network weights, these weights are physically interpretable and translate naturally into engineering parameters and microstructural features such as stiffnesses and fiber orientations. Our results suggest that Constitutive Artificial Neural Networks enable a fully automated model, parameter, and experiment discovery and could induce a paradigm shift in constitutive modeling, from manual to automated model selection and parameterization. Our source code, data, and examples are available at https://github.com/LivingMatterLab/CANN.