Accurate prediction of grape phenology is essential for timely vineyard management decisions, such as scheduling irrigation and fertilization, to maximize crop yield and quality. While traditional biophysical models calibrated on historical field data can be used for season-long predictions, they lack the precision required for fine-grained vineyard management. Deep learning methods are a compelling alternative but their performance is hindered by sparse phenology datasets, particularly at the cultivar level. We propose a hybrid modeling approach that combines multi-task learning with a recurrent neural network to parameterize a differentiable biophysical model. By using multi-task learning to predict the parameters of the biophysical model, our approach enables shared learning across cultivars while preserving biological structure, thereby improving the robustness and accuracy of predictions. Empirical evaluation using real-world and synthetic datasets demonstrates that our method significantly outperforms both conventional biophysical models and baseline deep learning approaches in predicting phenological stages, as well as other crop state variables such as cold-hardiness and wheat yield.