<p>Our subject is a new Catalogue of radar-based heavy Rainfall Events (CatRaRE) over Germany, and how it relates to the concurrent atmospheric circulation. We classify daily atmospheric ERA5 fields of convective indices according to CatRaRE, using an array of conventional statistical and more recent machine learning (ML) algorithms, and apply them to corresponding fields of simulated present and future atmospheres from the CORDEX project. Due to the stochastic nature of ML optimization there is some spread in the results. The ALL-CNN network performs best on average, with several learning runs exceeding an Equitable Threat Score (ETS) of <em>0.52</em>; the single best result was from ResNet with <em>ETS</em> = <em>0.54</em>. The best performing classical scheme was a Random Forest with <em>ETS</em> = <em>0.51</em>. Regardless of the method, increasing trends are predicted for the probability of CatRaRE-type events, from ERA5 as well as from the CORDEX fields.</p>