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We consider the problem of data-assisted forecasting of chaotic dynamicalsystems when the available data is in the form of noisy partial measurements ofthe past and present state of the dynamical system. Recently there have beenseveral promising data-driven approaches to forecasting of chaotic dynamicalsystems using machine learning. Particularly promising among these are hybridapproaches that combine machine learning with a knowledge-based model, where amachine-learning technique is used to correct the imperfections in theknowledge-based model. Such imperfections may be due to incompleteunderstanding and/or limited resolution of the physical processes in theunderlying dynamical system, e.g., the atmosphere or the ocean. Previouslyproposed data-driven forecasting approaches tend to require, for training,measurements of all the variables that are intended to be forecast. We describea way to relax this assumption by combining data assimilation with machinelearning. We demonstrate this technique using the Ensemble Transform KalmanFilter (ETKF) to assimilate synthetic data for the 3-variable Lorenz system andfor the Kuramoto-Sivashinsky system, simulating model error in each case by amisspecified parameter value. We show that by using partial measurements of thestate of the dynamical system, we can train a machine learning model to improvepredictions made by an imperfect knowledge-based model.

Using Data Assimilation to Train a Hybrid Forecast System that Combines Machine-Learning and Knowledge-Based Components