The fast and accurate estimation of planetary mass-loss rates is critical for planet population and evolution modelling. We use machine learning (ML) for fast interpolation across an existing large grid of hydrodynamic upper atmosphere models, providing mass-loss rates for any planet inside the grid boundaries with superior accuracy compared to previously published interpolation schemes. We consider an already available grid comprising about 11000 hydrodynamic upper atmosphere models for training and generate an additional grid of about 250 models for testing purposes. We develop the ML interpolation scheme (dubbed "atmospheric Mass Loss INquiry frameworK"; MLink) using a Dense Neural Network, further comparing the results with what was obtained employing classical approaches (e.g. linear interpolation and radial basis function-based regression). Finally, we study the impact of the different interpolation schemes on the evolution of a small sample of carefully selected synthetic planets. MLink provides high-quality interpolation across the entire parameter space by significantly reducing both the number of points with large interpolation errors and the maximum interpolation error compared to previously available schemes. For most cases, evolutionary tracks computed employing MLink and classical schemes lead to comparable planetary parameters at Gyr-timescales. However, particularly for planets close to the top edge of the radius gap, the difference between the predicted planetary radii at a given age of tracks obtained employing MLink and classical interpolation schemes can exceed the typical observational uncertainties. Machine learning can be successfully used to estimate atmospheric mass-loss rates from model grids paving the way to explore future larger and more complex grids of models computed accounting for more physical processes.