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