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We combine discrete element method simulations, evolutionary algorithms, and experiments to search for granular packings of variable modulus (VM) particles arranged in a triangular lattice with optimal bulk mechanical properties. 

There is growing interest in engineering uncon- ventional computing devices that leverage the in- trinsic dynamics of physical substrates to perform fast and energy-efficient computations. Granu- lar 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 non- linear dynamics result in nontrivial and some- times 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 mechan- ical computing in special-purpose applications. However, there are currently no general frame- works for the inverse design of large-scale granu- lar materials. Here, we build upon the similarity between the spatiotemporal dynamics of wave propagation in material and the computational dy- namics of Recurrent Neural Networks to develop a gradient-based optimization framework for har- monically 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 pro- vide the opportunity to systematically traverse the parameter space to find materials with the desired functionalities.