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While traditional biophysical models can be used for season-long predictions, they lack the precision required for site-specific management. Deep learning methods are a compelling alternative, but can produce biologically unrealistic predictions and require large-scale data. We propose a \\emph{hybrid modeling} approach that uses a neural network to parameterize a differentiable biophysical model and leverages multi-task learning for efficient data sharing across crop cultivars in data limited settings. By predicting the \\emph{parameters} of the biophysical model, our approach improves the prediction accuracy while preserving biological realism. 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We propose a \\emph{hybrid modeling} approach that uses a neural network to parameterize a differentiable biophysical model and leverages multi-task learning for efficient data sharing across crop cultivars in data limited settings. By predicting the \\emph{parameters} of the biophysical model, our approach improves the prediction accuracy while preserving biological realism. 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