We present an ultrafast neural network model, QLKNN, which predicts core tokamak transport heat and particle fluxes. QLKNN is a surrogate model based on a database of 3 × 108 flux calculations of the quasilinear gyrokinetic transport model, QuaLiKiz. The database covers a wide range of realistic tokamak core parameters. Physical features such as the existence of a critical gradient for the onset of turbulent transport were integrated into the neural network training methodology. We have coupled QLKNN to the tokamak modeling framework JINTRAC and rapid control-oriented tokamak transport solver RAPTOR. The coupled frameworks are demonstrated and validated through application to three JET shots covering a representative spread of H-mode operating space, predicting the turbulent transport of energy and particles in the plasma core. JINTRAC–QLKNN and RAPTOR–QLKNN are able to accurately reproduce JINTRAC–QuaLiKiz Ti,e and ne profiles, but 3–5 orders of magnitude faster. Simulations which take hours are reduced down to only a few tens of seconds. The discrepancy in the final source-driven predicted profiles between QLKNN and QuaLiKiz is on the order of 1%–15%. Also the dynamic behavior was well captured by QLKNN, with differences of only 4%–10% compared to JINTRAC–QuaLiKiz observed at mid-radius, for a study of density buildup following the L–H transition. Deployment of neural network surrogate models in multi-physics integrated tokamak modeling is a promising route toward enabling accurate and fast tokamak scenario optimization, uncertainty quantification, and control applications.