  We introduce a novel technique for designing color filter metasurfaces using
a data-driven approach based on deep learning. Our innovative approach employs
inverse design principles to identify highly efficient designs that outperform
all the configurations in the dataset, which consists of 585 distinct
geometries solely. By combining Multi-Valued Artificial Neural Networks and
back-propagation optimization, we overcome the limitations of previous
approaches, such as poor performance due to extrapolation and undesired local
minima. Consequently, we successfully create reliable and highly efficient
configurations for metasurface color filters capable of producing exceptionally
vivid colors that go beyond the sRGB gamut. Furthermore, our deep learning
technique can be extended to design various pixellated metasurface
configurations with different functionalities.
