Ultraprecision, high-capacity, and wide-gamut structural colors enabled by a mixture probability sampling network.

The advancement of nanophotonic devices is significantly dependent on achieving high-precision inverse design capabilities, which are critical for identifying optimal structural configurations that enable enhanced and multifunctional performances. The process of inverse design confronts a one-to-many relationship due to the complex mapping between optical performance and structure. Though several approaches, including tandem networks, mixture density networks (MDN), and conditional generative adversarial networks, have shown promising outcomes, they still face accuracy limitations when confronted with structures with higher degrees of freedom. Here, we propose a sampling-enhanced MDN called a mixture probability sampling network (MPSN), that outputs mixture Gaussian distributions (MGDs) of structural parameters through an end-to-end framework. The results of multiple samples drawn from the MGDs are fed into a pre-trained network, and the sample that minimizes the error relative to the real data is selected for network training. We benchmark the high performance in nanophotonics through the structural color design, achieving a high precision of up to 99.9% and a mean absolute error of less than 0.002. This work paves the way for resolving intricate inverse design problems in nanophotonics.