Out-of-Distribution Domain Exploration by a Multifidelity Deep Learning Model to Estimate Electromagnetic Responses of Metasurfaces

The multifidelity approach is a promising way to efficiently train the neural network which can be used to estimate the electromagnetic (EM) responses of metasurfaces. Empirical formulas or coarse-meshed full-wave simulation (FS) are two widely adopted sources of LF data. However, the accuracy of the empirical formulas is too low to use in some cases and the coarse-meshed FS is still sensitive to computational costs. To mitigate these issues, a new multifidelity neural network (MFNN) and a new source of LF data are proposed to estimate the EM responses. First, the nonlinear coefficient between the low- and high-fidelity (HF) data is modeled by the neural network layers instead of the Gaussian process or polynomials for higher accuracy. Second, the out-of-distribution (OOD) generalization property of the neural network is exploited, and the outputs of neural networks on OOD samples are regarded as low-fidelity (LF) data, which further get rid of the necessity to generate LF data by the FS with coarse-discretized mesh. The results from two metasurface cases demonstrate the enhanced accuracy of the proposed method when a specific amount of HF data is available, and about 30% reduction of required simulation to obtain a specific accuracy requirement. This reveals a brand-new insight that the OOD generalization property of neural networks can be further used in the metasurface scenario to enhance accuracy and efficiency.