Automated Metamaterial Design with Computer Model Emulation and Bayesian Optimization

Abstract:

We present an automated computation system for large scale design of metamaterials (MTMs). A computer model emulation (CME) technique is used to generate a forward mapping from the MTM particle’s geometric dimension to the corresponding electromagnetic (EM) response. Then the design problem translates to be a reverse engineering process which aims to find optimal values of the geometric dimensions for the MTM particles. The core of the CME process is a statistical functional regression module using a Gaussian Process mixture (GPM) model. The reverse engineering process is implemented with a Bayesian optimization technique. Experimental results demonstrate that the proposed approach can facilitate rapid design of MTMs.

• Periodical: Applied Mechanics and Materials (Volume 575)
• Pages: 201-205
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.575.201
• Online since: June 2014
• Authors: Bin Liu*, Chun Lin Ji
• Keywords: Automated Metamaterial Design, Bayesian Technique, Computer Model Emulation

References

[1] G. V. Eleftheriades and K. G. Balmain, Negative-refraction Metamaterials: Fundamental Principles and Applications. Wiley-IEEE Press, (2005).

DOI: 10.1002/0471744751

[2] R. Marques, Metamaterials with Negative Parameter: Theory, Design, and Microwave Applications. Wiley-IEEE Press, (2005).

[3] T. J. Cui, D. Smith and R. Liu, Metamaterials: Theory, Design and Applications. Springer, (2009).

[4] F. Bilotti, A. Toscano and L. Vegni, Design of spiral and multiple split-ring resonators for the realization of miniaturized metamaterial samples, IEEE Trans. Antennas Propag., vol. 55, pp.2258-2267, (2007).

DOI: 10.1109/tap.2007.901950

[5] F. Bilotti, A. Toscano, L. Vegni, K. Aydin, K.B. Alici and E. Ozbay, Equivalent-circuit models for the design of metamaterials based on artificial magnetic inclusions, IEEE Trans. Micro. Theory Tech., vol. 55, pp.2865-2873, (2007).

DOI: 10.1109/tmtt.2007.909611

[6] H. Chen, L. Ran, J. Huangfu, T.M. Grzegorczyk and J.A. Kong, Equivalent circuit model for left-handed metamaterials, J. Appl. Phys., vol. 100, p.024915, (2006).

DOI: 10.1063/1.2219986

[7] I. Gil, J. Bonache, J. Garcia-Garcia and F. Martin, Tunable metamaterial transmission lines based on varactor-loaded split-ring resonators, IEEE Trans. Micro. Theory Tech., vol. 54 , pp.2665-2674, (2006).

DOI: 10.1109/tmtt.2006.872949

[8] G. Kiziltas, J.L. Volakis and N. Kikuchi, Metamaterial design via the density method, IEEE AP-S Symposium, vol. 1, pp.748-751, (2002).

DOI: 10.1109/aps.2002.1016451

[9] Y. Ge and K.P. Esselle, GA/FDTD technique for the design and optimisation of periodic meta-materials, IET Micro. Antennas Propag., vol. 1, p.158–164, (2007).

DOI: 10.1049/iet-map:20050313

[10] P.Y. Chen, C.H. Chen, H. Wang, J.H. Tsai and W.X. Ni, Synthesis design of artificial magnetic metamaterials using a genetic algorithm, Opt. Express, vol. 16, pp.12806-12818, (2008).

DOI: 10.1364/oe.16.012806

[11] O. Sigmund, Systematic Design of Metamaterials by Topology Optimization, Springer, Netherlands, (2008).

[12] N. Tsuyoshi, Metamaterials and automotive applications: topology optimization of electro-magnetic materials, R&D Rev. Toyota CRDL41, pp.9-15, (2006).

[13] I. Yoshinori, N. Tsuyoshi, T. Yasuhide and H. Koichi, Metamaterials and automotive applications: design of optical devices based on topology optimization, R&D Rev. Toyota CRDL 41, pp.26-31, (2006).

[14] C. E. Rasmussen and Z. Ghahramani, Infinite mixtures of Gaussian process experts, Advances in Neural Information Processing Systems, vol. 2, p.881–888, (2002).

[15] E. Meeds and S. Osindero, An alternative infinite mixture of Gaussian process experts, Advances in Neural Information Processing Systems, vol. 18, p.883–890, (2006).

[16] C. Yuan and C. Neubauer, Variational mixture of Gaussian process experts, Advances in Neural Information Processing Systems, vol. 21, p.1897–1904, (2009).

[17] B. Liu and C. Ji, Bayesian Nonparametric Modeling for Rapid Design of Meta-material Micro-structures, submitted to IET Micro. Antennas Propag.

[18] B. Liu and C. Ji, A general algorithm scheme mixing computational intelligence with Bayesian simulation, Proc. of the 6th International Conf. on advanced computational intelligence, pp.1-6, (2013).

DOI: 10.1109/icaci.2013.6748464

[19] R. Liu, T. J. Cui, D. Huang, B. Zhao and D. Smith, Description and explanation of electromagnetic behaviors in artificial metamaterials based on effective medium theory, Physical Review E, vol. 76, no. 2, p.026606, (2007).

DOI: 10.1103/physreve.76.026606

[20] A. Semichaevsky and A. Akyurtlu, Homogenization of metamaterial-loaded substrates and superstrates for antennas, Progress In Electromagnetics Research, vol. 71, p.129–147, (2007).

DOI: 10.2528/pier07021001

[21] N. B. Kundtz, D. R. Smith, and J. B. Pendry, Electromagnetic design with transformation optics, Proc. IEEE, vol. 99, no. 10, p.1622–1633, (2011).

DOI: 10.1109/jproc.2010.2089664