The accurate theoretical treatment of nonadiabatic nuclear quantum dynamics requires the accurate description of potential energy surfaces (PESs) and their couplings. While ab initio molecular dynamics approaches provide an attractive solution to this problem, their computational cost continues to limit their applicability. An alternative approach is provided by the construction of analytic coupled PES models. However, the development of such PES models is still an unsolved problem. We present a new, modular diabatization method based on artificial neural networks (ANNs), which is capable of reproducing high-quality ab initio data with excellent accuracy. The diabatic potential matrix is expanded in terms of a set of basic coupling matrices and the expansion coefficients are made geometry-dependent by the output neurons of the ANN. This novel ANN diabatization approach has been applied to the low-lying electronic states of NO3 as a prototypical and notoriously difficult Jahn-Teller system in which the accurate description of the very strong non-adiabatic coupling is of paramount importance.The results show unprecedented agreement with experimental data, and greatly improve previous results. Current efforts focus on extending key ideas of this new, promising method to larger systems without a fixed reference point, with fitting data being generated on the fly by direct dynamics calculations.