Extreme sparsification of physics-augmented neural networks for interpretable model discovery in mechanics
This work addresses the need for interpretable data-driven constitutive models in mechanics, which is incremental as it builds on existing physics-augmented neural networks by adding sparsification for interpretability.
The authors tackled the problem of interpretability in neural network-based constitutive models by proposing a method that uses smoothed L0-regularization to sparsify physics-augmented neural networks, enabling the discovery of interpretable models without pre-specified functional forms, and demonstrated its reliability on synthetic and experimental data for various mechanical models.
Data-driven constitutive modeling with neural networks has received increased interest in recent years due to its ability to easily incorporate physical and mechanistic constraints and to overcome the challenging and time-consuming task of formulating phenomenological constitutive laws that can accurately capture the observed material response. However, even though neural network-based constitutive laws have been shown to generalize proficiently, the generated representations are not easily interpretable due to their high number of trainable parameters. Sparse regression approaches exist that allow to obtaining interpretable expressions, but the user is tasked with creating a library of model forms which by construction limits their expressiveness to the functional forms provided in the libraries. In this work, we propose to train regularized physics-augmented neural network-based constitutive models utilizing a smoothed version of $L^{0}$-regularization. This aims to maintain the trustworthiness inherited by the physical constraints, but also enables interpretability which has not been possible thus far on any type of machine learning-based constitutive model where model forms were not assumed a-priory but were actually discovered. During the training process, the network simultaneously fits the training data and penalizes the number of active parameters, while also ensuring constitutive constraints such as thermodynamic consistency. We show that the method can reliably obtain interpretable and trustworthy constitutive models for compressible and incompressible hyperelasticity, yield functions, and hardening models for elastoplasticity, for synthetic and experimental data.