Open AccessIterative ensemble Kalman methods: A unified perspective with some new variants
Author(s) -
Neil K. Chada,
Yuming Chen,
Daniel Sanz-Alonso
Publication year - 2021
Publication title -
foundations of data science
Language(s) - English
Resource type - Journals
ISSN - 2639-8001
DOI - 10.3934/fods.2021011
Subject(s) - computer science , linearization , kalman filter , perspective (graphical) , bayesian probability , algorithm , ensemble learning , artificial intelligence , bayesian optimization , iterative learning control , iterative method , machine learning , mathematical optimization , mathematics , nonlinear system , control (management) , physics , quantum mechanics
This paper provides a unified perspective of iterative ensemble Kalman methods, a family of derivative-free algorithms for parameter reconstruction and other related tasks. We identify, compare and develop three subfamilies of ensemble methods that differ in the objective they seek to minimize and the derivative-based optimization scheme they approximate through the ensemble. Our work emphasizes two principles for the derivation and analysis of iterative ensemble Kalman methods: statistical linearization and continuum limits. Following these guiding principles, we introduce new iterative ensemble Kalman methods that show promising numerical performance in Bayesian inverse problems, data assimilation and machine learning tasks.