We consider the Ensemble Kalman Inversion which has been recently introduced as an efficient, gradient-free optimisation method to estimate unknown parameters in an inverse setting. In the case of large data sets, the Ensemble Kalman Inversion becomes computationally infeasible as the data misfit needs to be evaluated for each particle in each iteration. Here, randomised algorithms like stochastic gradient descent have been demonstrated to successfully overcome this issue by using only a random subset of the data in each iteration, so-called subsampling techniques. Based on a recent analysis of a continuous-time representation of stochastic gradient methods, we propose, analyse, and apply subsampling-techniques within Ensemble Kalman Inversion. Indeed, we propose two different subsampling techniques: either every particle observes the same data subset (single subsampling) or every particle observes a different data subset (batch subsampling).

翻译：我们考虑近年来引入的集成卡尔曼反演方法，这是一种高效且无梯度的优化方法，用于在反问题框架中估计未知参数。在处理大规模数据集时，由于每次迭代中每个粒子均需计算数据不匹配项，集成卡尔曼反演在计算上变得不可行。随机梯度下降等随机化算法通过每次迭代仅使用数据的随机子集（即子采样技术）成功解决了这一问题。基于近期对随机梯度方法连续时间表示的分析，我们提出、分析并应用了集成卡尔曼反演中的子采样技术。具体而言，我们提出了两种不同的子采样方法：要么所有粒子观测同一数据子集（单子采样），要么每个粒子观测不同的数据子集（批量子采样）。