Best-in-class modeling: A novel strategy to discover constitutive models for soft matter systems

Abstract

The ability to automatically discover interpretable mathematical models from data could forever change how we model soft matter systems. For convex discovery problems with a unique global minimum, model discovery is well-established. It uses a classical top-down approach that first calculates a dense parameter vector, and then sparsifies the vector by gradually removing terms. For non-convex discovery problems with multiple local minima, this strategy is infeasible since the initial parameter vector is generally non-unique. Here we propose a novel bottom-up approach that starts with a sparse single-term vector, and then densifies the vector by systematically adding terms. Along the way, we discover models of gradually increasing complexity, a strategy that we call best-in-class modeling. To identify and select successful candidate terms, we reverse-engineer a library of sixteen functional building blocks that integrate a century of knowledge in material modeling with recent trends in machine learning and artificial intelligence. Yet, instead of solving the NP hard discrete combinatorial problem with $2^{16}=\text{65,536}$ possible combinations of terms, best-in-class modeling starts with the best one-term model and iteratively repeats adding terms, until the objective function meets a user-defined convergence criterion. Strikingly, for most practical purposes, we achieve good convergence with only one or two terms. We illustrate the best-in-class one- and two-term models for a variety of soft matter systems including rubber, brain, artificial meat, skin, and arteries. Our discovered models display distinct and unexpected features for each family of materials, and suggest that best-in-class modeling is an efficient, robust, and easy-to-use strategy to discover the mechanical signatures of traditional and unconventional soft materials. We anticipate that our technology will generalize naturally to other classes of natural and man made soft matter with applications in artificial organs, stretchable electronics, soft robotics, and artificial meat.