image: Figure 1| Diagram of the MPSN architecture. a, MPSN consists of a mixture density network mapping from color to material distribution and a pretrained network mapping from material parameters to color. b, MDN outputs the mixture Gaussian distribution of the structure, sampling this distribution several times can yield many different structures. Then all structures are input into the pre-trained network to predict the colors. c, Details of the evaluation step. The smallest MSE between sampling colors and real colors is selected for the network training.
Credit: Yuzhi Shi et al.
Structural colors, produced by light interaction with nanostructures, offer advantages in resolution and durability over conventional pigments. However, inverse design—finding structures that produce target colors—is challenging due to the one-to-many relationship between color and geometry. Existing neural network methods struggle with accuracy or diversity in solution output.
In a new paper published in Light: Science & Applications, a team of scientists led by Professors Xinbin Cheng, Gang Yan, Yuzhi Shi and Zeyong Wei from Tongji University, China and Professor Cheng-Wei Qiu from National University of Singapore, Singapore, and co-workers have developed the MPSN to overcomes these limitations. MPSN combines a mixture density network with a pre-trained forward network to sample and evaluate multiple structural solutions, selecting the best match for a given color.
The system was tested on a square ring-pillar metasurface, achieving a prediction accuracy of 99.9% and a mean absolute error below 0.002. It also demonstrated wide gamut coverage, reaching over 100% of the sRGB color space. Experimental validation included the fabrication of a 16-color palette and institutional logos, confirming high fidelity between design and measurement. These scientists summarize the key innovations of this work.
“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.”
“We develop a network architecture that inherently incorporates non-uniqueness characteristics, capable of generating multiple structural-parameter sets for a single design objective while maintaining the training stability to be unaffected by the solution degeneracy.”
“This work benchmarks 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 approach is applicable beyond color design, including metamaterials and waveguide optimization, and is compatible with physics-informed neural networks for reduced data dependency. The method paves the way for high-performance optical devices in augmented reality, encryption, and biomedical imaging.
Journal
Light Science & Applications
Article Title
Ultraprecision, high-capacity, and wide-gamut structural colors enabled by a mixture probability sampling network