Large yield airbursts generate powerful outdoor blast waves. Over long propagation distances, the blast is significantly altered by the topographical relief. Usually, the terrain effects are quantified by running accurate but expensive hydrodynamics or CFD codes. We present an alternative approach based on artificial neural networks, which is applicable wherever the blast–relief interaction can be approximated by an axisymmetric configuration. A database of overpressures associated with a very large sample of the French topography is constructed by running a high-fidelity hydrodynamics code. The proposed neural networks then learn the relationship between the relief geometry and the ground overpressures. The predictive ability of the networks is assessed extensively over a test database for several error metrics. \({97}{\%}\) of the peak overpressure predictions can be considered accurate for most practical purposes, and the pressure impulse predictions are even more accurate. Finally, specific artificial neural networks able to estimate the model uncertainties are presented and their performances are discussed.