Gradient-based Design of Computational Granular Crystals

TL;DR

This paper introduces a gradient-based optimization framework for designing granular crystals that can perform mechanical computing, enabling systematic exploration of material configurations for desired wave-based functionalities.

Contribution

It develops a novel gradient-based inverse design method for large-scale granular metamaterials, outperforming traditional gradient-free approaches in efficiency and effectiveness.

Findings

Gradient-based optimization discovers higher-performing configurations.

The method reduces computational effort compared to gradient-free methods.

Designed structures can implement basic logic gates using mechanical vibrations.

Abstract

There is growing interest in engineering unconventional computing devices that leverage the intrinsic dynamics of physical substrates to perform fast and energy-efficient computations. Granular metamaterials are one such substrate that has emerged as a promising platform for building wave-based information processing devices with the potential to integrate sensing, actuation, and computation. Their high-dimensional and nonlinear dynamics result in nontrivial and sometimes counter-intuitive wave responses that can be shaped by the material properties, geometry, and configuration of individual grains. Such highly tunable rich dynamics can be utilized for mechanical computing in special-purpose applications. However, there are currently no general frameworks for the inverse design of large-scale granular materials. Here, we build upon the similarity between the spatiotemporal dynamics of wave propagation in material and the computational dynamics of Recurrent Neural Networks to develop a gradient-based optimization framework for harmonically driven granular crystals. We showcase how our framework can be utilized to design basic logic gates where mechanical vibrations carry the information at predetermined frequencies. We compare our design methodology with classic gradient-free methods and find that our approach discovers higher-performing configurations with less computational effort. Our findings show that a gradient-based optimization method can greatly expand the design space of metamaterials and provide the opportunity to systematically traverse the parameter space to find materials with the desired functionalities.