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Abstract:
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Integro-difference equation (IDE) models capture complex spatio-temporal dependencies by modeling the conditional dependence between the spatial field at a future time point and the field at the present time point through an integral operator. Typically, operator linearity and temporal invariance are assumed, yielding a model that is only valid and interpretable over short time horizons. Here, we tackle this issue by using a deep convolution neural network (CNN) in a hierarchical statistical IDE framework, where the CNN identifies process dynamics from the process' past behaviour. Once the CNN is fitted, probabilistic forecasting can be done extremely quickly online using an ensemble Kalman filter with no requirement for repeated parameter estimation. We show that the proposed model is able to provide forecasts that are accurate and well calibrated. A key advantage is that the CNN provides a global prior model for the dynamics that is realistic and interpretable. We demonstrate its versatility by successfully producing 10-minute nowcasts of weather radar reflectivities in Sydney using the same model that was trained on daily sea-surface temperature data in the North Atlantic Ocean.
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