Designing nonlinear perturbative metamaterials that compute

Designing metamaterials that compute is challenging; the space of possible geometries is very large, and the relation between structure and function is complex. Perturbative metamaterials, consisting of weakly interacting unit cells, can be efficiently designed by combining simple geometric building blocks. However, perturbative metamaterials are conventionally defined in terms of linear wave physics, which prevents their use in information-processing applications that require nonlinearity. Here, we introduce a nonlinear formulation for perturbative metamaterials that allows us to identify material geometries that perform target computations. The design is enabled by a nonlinear, localized map connecting metamaterial deformations to a discrete tight-binding model that encodes the computation. We demonstrate the generality of this approach by designing three information-processing metamaterials based on three different computing paradigms: an Ising machine that solves combinatorial optimization problems through energy minimization, a mechanical racetrack device for in-memory computing, and a speech classification metamaterial based on analog neuromorphic computing. Elastic metamaterials provide opportunities for implementing computation tasks, yet generality provides a major challenge with respect to the design of metamaterial geometry. Here, the authors introduce a two-step metamaterial design strategy embedding first the computation functionality in a tight-binding model and subsequently tailoring a metamaterial geometry.