Iterative Ensemble Kalman Methods: A Unified Perspective with Some New Variants

TL;DR

This paper unifies various iterative ensemble Kalman methods, introduces new variants based on statistical linearization and continuum limits, and demonstrates their effectiveness in inverse problems, data assimilation, and machine learning.

Contribution

It provides a unified framework for iterative ensemble Kalman methods, identifies key principles, and develops new variants with promising numerical performance.

Findings

New variants show improved performance in Bayesian inverse problems.

Unified perspective clarifies relationships among existing methods.

Numerical experiments demonstrate effectiveness in data assimilation and machine learning.

Abstract

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.