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.

翻译：人们对利用物理基板的内在动力学来构建高速且节能的非传统计算设备兴趣日益浓厚。颗粒超材料正是这样一种基板，它已成为构建基于波的信息处理设备的有前景平台，有望集成传感、驱动和计算功能。其高维非线性动力学导致非平凡且有时反直觉的波响应，这些响应可通过单个颗粒的材料属性、几何形状和构型进行调控。这种高度可调的丰富动力学可被用于专用应用中的机械计算。然而，目前缺乏用于大规模颗粒材料逆向设计的通用框架。在此，我们基于材料中波传播的时空动力学与递归神经网络计算动力学之间的相似性，开发了一种用于谐波驱动颗粒晶体的基于梯度的优化框架。我们展示了如何利用该框架设计基本逻辑门，其中机械振动以预定频率携带信息。我们将我们的设计方法与经典的无梯度方法进行比较，发现我们的方法能以更少的计算工作量发现性能更优的构型。我们的研究结果表明，基于梯度的优化方法能极大扩展超材料的设计空间，并为系统遍历参数空间以寻找具有所需功能的材料提供了机会。