Current methods for atmosphere and ocean prediction propagate gridded state variables, or ensembles thereof, forward in time. Powerful as these methods are, they do not handle outliers well and cannot simultaneously entertain divergent hypotheses about system state. We report on some experiments with a two-level framework that is designed to circumvent these problems. The framework consists of two pieces. First, there are the exact grid-level (nonlinear) dynamical equations. We have used a shallow-water ocean simulation based on the MICOM approach. The second piece is a coarse-level, learned representation of the dynamics of emergent features in the gridded simulation. The coarse features and their dynamics are learned from realizations of the gridded simulation. The coarse dynamics then provide a computationally-efficient way to explore the very large state space of the gridded system. For example, to compute relative probabilities of two highly divergent end states of the system, we can use the learned dynamics to develop a path from the present state to each end state, and a Markov chain Monte Carlo adaptation to fine-tune the coarse dynamics to conform with the original dynamical equations.
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