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Context. The Javalambre Photometric Local Universe Survey (J-PLUS) hasobtained precise photometry in twelve specially designed filters for largenumbers of Galactic stars. Deriving their precise stellar atmosphericparameters and individual elemental abundances is crucial for studies ofGalactic structure, and the assembly history and chemical evolution of ourGalaxy. Aims. Our goal is to estimate not only stellar parameters (effectivetemperature, Teff, surface gravity, log g, and metallicity, [Fe/H]), but also[{\alpha}/Fe] and four elemental abundances ([C/Fe], [N/Fe], [Mg/Fe], and[Ca/Fe]) using data from J-PLUS DR1. Methods. By combining recalibratedphotometric data from J-PLUS DR1, Gaia DR2, and spectroscopic labels fromLAMOST, we design and train a set of cost-sensitive neural networks, the CSNet,to learn the non-linear mapping from stellar colors to their labels. Results.We have achieved precisions of {\delta}Teff {\sim}55K,{\delta}logg{\sim}0.15dex, and {\delta}[Fe/H]{\sim}0.07dex, respectively, overa wide range of temperature, surface gravity, and metallicity. Theuncertainties of the abundance estimates for [{\alpha}/Fe] and the fourindividual elements are in the range 0.04-0.08 dex. We compare our parameterand abundance estimates with those from other spectroscopic catalogs such asAPOGEE and GALAH, and find an overall good agreement. Conclusions. Our resultsdemonstrate the potential of well-designed, high-quality photometric data fordeterminations of stellar parameters as well as individual elementalabundances. Applying the method to J-PLUS DR1, we have obtained theaforementioned parameters for about two million stars, providing an outstandingdata set for chemo-dynamic analyses of the Milky Way. The catalog of theestimated parameters is publicly accessible.

J-PLUS: Stellar Parameters, C, N, Mg, Ca and [{\alpha}/Fe] Abundances for Two Million Stars from DR1