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Probabilistic spatiotemporal forecasting comprising acquiring a time series of observed states from a real-world system, each observed state corresponding to a respective time-step in the time series and including a set of data observations of the real-world system for the respective time-step. For each of a plurality of the time steps in the time series of observed states, a hidden state is generated for the time-step based on an observed state for a prior time-step and an approximated posterior distribution generated for a hidden state for the prior time-step. The use of an approximated posterior distribution can enable improved forecasting in complex, high dimensional settings.