Manipulating the dispersive characteristics of vibrational waves is beneficial for many applications, e.g., high-precision instruments. architected hierarchical phononic materials have sparked promise tunability of elastodynamic waves and vibrations over multiple frequency ranges. In this article, hierarchical unit-cells are obtained, where features at each length scale result in a band gap within a targeted frequency range. Our novel approach, the “hierarchical unit-cell template method,” is an interpretable machine-learning approach that uncovers global unit-cell shape/topology patterns corresponding to predefined band-gap objectives. A scale-separation effect is observed where the coarse-scale band-gap objective is mostly unaffected by the fine-scale features despite the closeness of their length scales, thus enabling an efficient hierarchical algorithm. Moreover, the hierarchical patterns revealed are not predefined or self-similar hierarchies as common in current hierarchical phononic materials. Thus, our approach offers a flexible and efficient method for the exploration of new regions in the hierarchical design space, extracting minimal effective patterns for inverse design in applications targeting multiple frequency ranges.

中文翻译：

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一种使用可解释机器学习的声子材料多尺度设计方法


纵振动波的色散特性对许多应用都有好处，例如高精度仪器。构建的分层声子材料在多个频率范围内激发了弹性动力波和振动的可调谐性。在本文中，获得了分层晶胞，其中每个长度尺度的特征都会导致目标频率范围内的带隙。我们的新方法，“分层晶胞模板法”，是一种可解释的机器学习方法，可揭示与预定义的带隙目标相对应的全局晶胞形状/拓扑模式。观察到尺度分离效应，其中粗尺度带隙物镜几乎不受精细尺度特征的影响，尽管它们的长度尺度很接近，从而实现了高效的分层算法。此外，所揭示的分层模式并不是当前分层声子材料中常见的预定义或自相似层次结构。因此，我们的方法为探索分层设计空间中的新区域提供了一种灵活有效的方法，在针对多个频率范围的应用中为逆向设计提取最小有效模式。