Iterative ensemble Kalman methods: A unified perspective with some new variants

<p style='text-indent:20px;'>This paper provides a unified perspective of iterative ensemble Kalman methods, family derivative-free algorithms for parameter reconstruction and other related tasks. We identify, compare develop three subfamilies methods that differ in the objective they seek to minimize derivative-based optimization scheme approximate through ensemble. Our work emphasizes two principles derivation analysis methods: statistical linearization continuum limits. Following these guiding principles, we introduce new show promising numerical performance Bayesian inverse problems, data assimilation machine learning tasks.</p>