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 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 discrete combinatorial problem with 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, 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.