Abstract
A long-held tenet in computer science asserts that the training of deep learning is analogous to an alchemical furnace, and its "black box" signature brings forth inexplicability. For electromagnetic metasurfaces, the related intelligent applications also get stuck into such a dilemma. Although the past 5 years have witnessed a proliferation of deep learning-based works across complex photonic scenarios, they neglect the already existing but untapped physical laws. Here, the intrinsic correlation between the real and imaginary parts of the spectra are revealed using Kramers-Kronig relations, which is then mimicked by bidirectional information flow in neural network space. Such consideration harnesses the missing spectral connection to extract crucial features effectively. The bidirectional recurrent neural network is benchmarked in metasurface inverse design and compare it with a fully-connected neural network, unidirectional recurrent neural network, and attention-based transformer. Beyond the improved accuracy, the study examines the intermediate information products and physically explains why different network structures yield different performances. The work offers explicable perspectives to utilize physical information in the deep learning field and facilitates many data-intensive research endeavors.