标题： 迭代集合卡尔曼方法：一种统一的视角与一些新变体 显示英文标题

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

摘要： 本文提供了迭代集合卡尔曼方法的统一视角，这是一类用于参数重建和其他相关任务的无导数算法。 我们识别、比较并开发了三种集合方法的子族，它们在所寻求最小化的目标以及通过集合近似基于导数的优化方案方面有所不同。 我们的工作强调了推导和分析迭代集合卡尔曼方法的两个原则：统计线性化和连续极限。 遵循这些指导原则，我们引入了新的迭代集合卡尔曼方法，在贝叶斯反问题、数据同化和机器学习任务中表现出有前景的数值性能。 显示英文摘要

摘要： 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.