  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.
