Understanding the future climate is crucial for informed policy decisions on climatechange prevention and mitigation. Earth system models play an important rolein predicting future climate, requiring accurate representation of complex sub-processes that span multiple time scales and spatial scales. One such process thatlinks seasonal and interannual climate variability to cyclical biological events istree phenology in deciduous forests. Phenological dates, such as the start andend of the growing season, are critical for understanding the exchange of carbonand water between the biosphere and the atmosphere. Mechanistic predictionof these dates is challenging. Hybrid modelling, which integrates data-drivenapproaches into complex models, offers a solution. In this work, as a first steptowards this goal, train a deep neural network to predict a phenological index frommeteorological time series. We find that this approach outperforms traditionalprocess-based models. This highlights the potential of data-driven methods toimprove climate predictions. We also analyze which variables and aspects of thetime series influence the predicted onset of the season, in order to gain a betterunderstanding of the advantages and limitations of our model.