A two-stage approach for frequency response modeling and metamaterial rapid design

We introduce a novel two-stage approach for rapid design of massive metamaterials (MTMs), where performances of thousands of microstructures require evaluation. In Stage I, an equivalent circuit model is synthesized via rational function modeling to represent the frequency response of MTMs microstructures. In Stage II, Gaussian process (GP) regression models are unitized to build the relation between the physical setting of the microstructure, including geometric design variables and incident angles of electromagnetic (EM) waves, and the representing parameters of the equivalent circuit model. As a consequence, the mapping from the microstructure physical parameters to the frequency response is easy to achieve and with high accuracy. We offer two metamaterial prototypes to illustrate that the proposed approach allows high efficiency in facilitating the design of massive MTMs. The experimental results demonstrate that our method is no longer limited by the complexity of microstructures and the spatial dispersion, induced by the variation of incident angle. We compare the accuracy of predicted responses against the reference data, and both examples yield average RMSE less than 0.05, which meets the requirements for many MTMs engineering applications.