Recently, a groundbreaking study emerged from the collaborative efforts of Professor Wang Zhanshan and Professor Cheng Xinbin's teams at the School of Physical Science and Engineering, Tongji University, alongside Associate Professor Wei Zeyong, Professor Shi Yuzhi, Professor Yan Gang, and Professor Qiu Chengwei from the National University of Singapore. They introduced a Hybrid Probabilistic Sampling Network (MPSN) aimed at tackling the 'one-to-many' mapping dilemma inherent in the inverse design of structural colors. This innovative network not only attains a remarkable 99.9% prediction accuracy but also generates multiple viable nanoscale structural solutions. Their significant findings have been featured in Light: Science & Applications, a prestigious international optics journal.

Structural colors, which arise from the scattering and interference of light by nanostructures, offer a vast palette of hues with tremendous promise in applications like high-definition displays and information encryption. Nevertheless, the intricate interplay between color and nanostructure poses a challenge for conventional neural networks, which struggle to reconcile high precision with the generation of multiple solutions. The MPSN framework ingeniously integrates a hybrid density network with a pre-trained forward network in a series connection, creating an end-to-end mapping pathway. It produces candidate structures through multiple sampling processes and selects the sample with the minimal error for backpropagation, thereby substantially boosting training stability and design precision.

In experimental trials involving square ring-column composite structures, the MPSN achieved an impressive 99.9% prediction accuracy on the test set, with a mean absolute error of less than 0.002. Furthermore, the research team successfully fabricated a 16-color swatch and structural color images of the logos from three institutions. The experimental measurements closely aligned with the design objectives, and the color resolution surpassed that of traditional designs.

This study establishes a novel paradigm for the inverse design of nanophotonic devices and holds potential for extension into areas such as waveguide design, plasmonic structures, and zero-refractive-index metamaterials.