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RR Lyrae stars are useful chemical tracers thanks to the empiricalrelationship between their heavy-element abundance and the shape of their lightcurves. However, the consistent and accurate calibration of this relationacross multiple photometric wavebands has been lacking. We have devised a newmethod for the metallicity estimation of fundamental-mode RR Lyrae stars in theGaia optical $G$ and near-infrared VISTA $K_s$ wavebands by deep learning.First, an existing metallicity prediction method is applied to largephotometric data sets, which are then used to train long short-term memoryrecurrent neural networks for the regression of the [Fe/H] to the light curvesin other wavebands. This approach allows an unbiased transfer of our accurate,spectroscopically calibrated $I$-band formula to additional bands at theexpense of minimal additional noise. We achieve a low mean absolute error of$0.1$ dex and high $R^2$ regression performance of $0.84$ and $0.93$ for the$K_s$ and $G$ bands, respectively, measured by cross-validation. The resultingpredictive models are deployed on the Gaia DR2 and VVV inner-bulge RR Lyraecatalogs. We estimate mean metallicities of $-1.35$ dex for the inner bulge and$-1.7$ for the halo, which are significantly less than values obtained byearlier photometric prediction methods. Using our results, we establish apublic catalog of photometric metallicities of over 60,000 Galactic RR Lyraestars, and provide an all-sky map of the resulting RR Lyrae metallicitydistribution. The software code used for training and deploying our recurrentneural networks is made publicly available in the open-source domain.

Photometric [Fe/H] of RRab stars in the $G$ and $K_s$ bands by deep learning