声学超材料优化设计的机器学习技术
Machine-learning techniques for the optimal design of acoustic metamaterials
摘要：
近年来，越来越多的研究致力于分析周期性声学超材料的传输和色散特性，其特征在于存在局部谐振器。在这种情况下，特别注意已支付的振幅和中心频率的优化内的Floquet-Bloch频谱的声学超材料的手性或反手性微结构的特征的选定的停止和通带。这种研究的新功能的应用，预计在智能可调谐机械滤波器和定向波导的最佳参数设计。本文讨论了低频带隙的振幅最大化，提出了适当的数值技术来解决相关的优化问题。具体而言，径向基函数网络和准蒙特卡罗方法的插值的目标函数的优化问题的可行性和有效性进行了讨论，并提出了它们的数值应用到一个特定的声学超材料与四手性微结构。讨论的动机是理论上的高计算工作量经常需要一个精确的评估所产生的带隙优化问题的目标函数，当迭代算法用于其近似解。通过用应用机器学习技术构造的合适的替代目标函数替换这些函数，可以用较小的计算工作量获得性能良好的次优解。数值结果表明，所提出的方法的有效潜力。目前的研究方向，涉及使用额外的机器学习技术。
英文摘要：
Recently, an increasing research effort has been dedicated to analyse the transmission and dispersion properties of periodic acoustic metamaterials, characterized by the presence of local resonators. Within this context, particular attention has been paid to the optimization of the amplitudes and center frequencies of selected stop and pass bands inside the Floquet-Bloch spectra of the acoustic metamaterials featured by a chiral or antichiral microstructure. Novel functional applications of such research are expected in the optimal parametric design of smart tunable mechanical filters and directional waveguides. The present paper deals with the maximization of the amplitude of low-frequency band gaps, by proposing suitable numerical techniques to solve the associated optimization problems. Specifically, the feasibility and effectiveness of Radial Basis Function networks and Quasi-Monte Carlo methods for the interpolation of the objective functions of such optimization problems are discussed, and their numerical application to a specific acoustic metamaterial with tetrachiral microstructure is presented. The discussion is motivated theoretically by the high computational effort often needed for an exact evaluation of the objective functions arising in band gap optimization problems, when iterative algorithms are used for their approximate solution. By replacing such functions with suitable surrogate objective functions constructed applying machine-learning techniques, well performing suboptimal solutions can be obtained with a smaller computational effort. Numerical results demonstrate the effective potential of the proposed approach. Current directions of research involving the use of additional machine-learning techniques are also presented.
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