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Process-based modelling offers interpretability and physical consistency in many domains of geosciences but struggles to leverage large datasets efficiently. Machine-learning methods, especially deep networks, have strong predictive skills yet are unable to answer specific scientific questions. In this Perspective, we explore differentiable modelling as a pathway to dissolve the perceived barrier between process-based modelling and machine learning in the geosciences and demonstrate its potential with examples from hydrological modelling. ‘Differentiable’ refers to accurately and efficiently calculating gradients with respect to model variables or parameters, enabling the discovery of high-dimensional unknown relationships. Differentiable modelling involves connecting (flexible amounts of) prior physical knowledge to neural networks, pushing the boundary of physics-informed machine learning. It offers better interpretability, generalizability, and extrapolation capabilities than purely data-driven machine learning, achieving a similar level of accuracy while requiring less training data. Additionally, the performance and efficiency of differentiable models scale well with increasing data volumes. Under data-scarce scenarios, differentiable models have outperformed machine-learning models in producing short-term dynamics and decadal-scale trends owing to the imposed physical constraints. Differentiable modelling approaches are primed to enable geoscientists to ask questions, test hypotheses, and discover unrecognized physical relationships. Future work should address computational challenges, reduce uncertainty, and verify the physical significance of outputs. 

Abstract—The emergence of remote sensing technologies cou- pled with local monitoring workstations enables us the un- precedented ability to monitor the environment in large scale. Information mining from multi-channel geo-spatiotemporal data however poses great challenges to many computational sustainability applications. Most existing approaches adopt various dimensionality reduction techniques without fully taking advantage of the spatiotemporal nature of the data. In addition, the lack of labeled training data raises another challenge for modeling such data. In this work, we propose a novel semi-supervised attention-based deep representation model that learns context-aware spatiotemporal representations for prediction tasks. A combination of convolutional neural networks with a hybrid attention mechanism is adopted to extract spatial and temporal variations in the geo-spatiotemporal data. Recognizing the importance of capturing more complete temporal dependencies, we propose the hybrid attention mechanism which integrates a learnable global query into the classic self-attention mechanism. To overcome the data scarcity issue, sampled spatial and temporal context that naturally reside in the largely-available unlabeled geo-spatiotemporal data are exploited to aid meaningful representation learning. We conduct experiments on a large-scale real-world crop yield prediction task. The results show that our methods significantly outperforms existing state-of-the-art yield prediction methods, especially under the stress of training data scarcity.