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Data assimilation is concerned with sequentially estimating a temporally-evolving state. This task, which arises in a wide range of scientific and engineering applications, is particularly challenging when the state is high-dimensional and the state-space dynamics are unknown. This paper introduces a machine learning framework for learning dynamical systems in data assimilation. Our auto-differentiable ensemble Kalman filters (AD-EnKFs) blend ensemble Kalman filters for state recovery with machine learning tools for learning the dynamics. In doing so, AD-EnKFs leverage the ability of ensemble Kalman filters to scale to high-dimensional states and the power of automatic differentiation to train high-dimensional surrogate models for the dynamics. Numerical results using the Lorenz-96 model show that AD-EnKFs outperform existing methods that use expectation-maximization or particle filters to merge data assimilation and machine learning. In addition, AD-EnKFs are easy to implement and require minimal tuning.
Variational Inference (VI) combined with Bayesian nonlinear filtering produces the state-of-the-art results for latent trajectory inference. A body of recent works focused on Sequential Monte Carlo (SMC) and its expansion, e.g., Forward Filtering Bac
Kalman filters are routinely used for many data fusion applications including navigation, tracking, and simultaneous localization and mapping problems. However, significant time and effort is frequently required to tune various Kalman filter model pa
Kalman Filters are one of the most influential models of time-varying phenomena. They admit an intuitive probabilistic interpretation, have a simple functional form, and enjoy widespread adoption in a variety of disciplines. Motivated by recent varia
A new type of ensemble Kalman filter is developed, which is based on replacing the sample covariance in the analysis step by its diagonal in a spectral basis. It is proved that this technique improves the aproximation of the covariance when the covar
Various methods have been proposed for the nonlinear filtering problem, including the extended Kalman filter (EKF), iterated extended Kalman filter (IEKF), unscented Kalman filter (UKF) and iterated unscented Kalman filter (IUKF). In this paper two n