Machine-Learning Techniques for the Optimal Design of Acoustic Metamaterials

Andrea Bacigalupo (), Giorgio Gnecco (), Marco Lepidi () and Luigi Gambarotta ()
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Andrea Bacigalupo: IMT School for Advanced Studies
Giorgio Gnecco: IMT School for Advanced Studies
Marco Lepidi: University of Genoa
Luigi Gambarotta: University of Genoa

Journal of Optimization Theory and Applications, 2020, vol. 187, issue 3, No 3, 630-653

Abstract: Abstract Recently, an increasing research effort has been dedicated to analyze 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.

Keywords: Nonlinear programming; Surrogate optimization; Radial basis function networks; Lattice materials; Dispersion properties; 41A05; 90C26; 90C90 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10957-019-01614-8

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