Context : We present a new methodology for the estimation of stellar atmospheric parameters from narrow- and intermediate-band photometry of the Javalambre Photometric Local Universe Survey ( J-PLUS ) , and propose a method for target pre-selection of low-metallicity stars for follow-up spectroscopic studies . Photometric metallicity estimates for stars in the globular cluster M15 are determined using this method . Aims : By development of a neural-network-based photometry pipeline , we aim to produce estimates of effective temperature , T _ { eff } , and metallicity , [ Fe/H ] , for a large subset of stars in the J-PLUS footprint . Methods : The Stellar Photometric Index Network Explorer , SPHINX , is developed to produce estimates of T _ { eff } and [ Fe/H ] , after training on a combination of J-PLUS photometric inputs and synthetic magnitudes computed for medium-resolution ( R \sim 2000 ) spectra of the Sloan Digital Sky Survey . This methodology is applied to J-PLUS photometry of the globular cluster M15 . Results : Effective temperature estimates made with J-PLUS Early Data Release photometry exhibit low scatter , \sigma ( T _ { eff } ) = 91 K , over the temperature range 4500 < T _ { eff } ( K ) < 8500 . For stars from the J-PLUS First Data Release with 4500 < T _ { eff } ( K ) < 6200 , 85 \pm 3 % of stars known to have [ Fe/H ] < -2.0 are recovered by SPHINX . A mean metallicity of [ Fe/H ] = -2.32 \pm 0.01 , with a residual spread of 0.3 dex , is determined for M15 using J-PLUS photometry of 664 likely cluster members . Conclusions : We confirm the performance of SPHINX within the ranges specified , and verify its utility as a stand-alone tool for photometric estimation of effective temperature and metallicity , and for pre-selection of metal-poor spectroscopic targets .