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Data assimilation techniques, such as ensemble Kalman filtering, have beenshown to be a highly effective and efficient way to combine noisy data with amathematical model to track and forecast dynamical systems. However, whendealing with high-dimensional data, in many situations one does not have amodel, so data assimilation techniques cannot be applied. In this paper, we usedynamic mode decomposition to generate a low-dimensional, linear model of adynamical system directly from high-dimensional data, which is defined bytemporal and spatial modes, that we can then use with data assimilationtechniques such as the ensemble Kalman filter. We show how the dynamic modedecomposition can be combined with the ensemble Kalman filter (which we callthe DMDEnKF) to iteratively update the current state and temporal modes as newdata becomes available. We demonstrate that this approach is able to track timevarying dynamical systems in synthetic examples, and experiment with the use oftime-delay embeddings. We then apply the DMDEnKF to real world seasonalinfluenza-like illness data from the USA Centers for Disease Control andPrevention, and find that for short term forecasting, the DMDEnKF is comparableto the best mechanistic models in the ILINet competition.

Combining Dynamic Mode Decomposition with Ensemble Kalman Filtering for Tracking and Forecasting