Localized ensemble Kalman inversion

Abstract Ensemble Kalman inversion (EKI) is an adaption of the ensemble filter (EnKF) for numerical solution inverse problems. Both EKI and EnKF suffer from ‘subspace property’, i.e. solutions are linear combinations initial ensembles. The subspace property implies that size should be larger than problem dimension to ensure EKI’s convergence correct solution. This scaling impractical prevents use in high-dimensional ‘Localization’ has been used many years break a way localized can solve problems with modest size, independently number unknowns. Here, we study localization demonstrate how (LEKI) size. Our analysis mathematically rigorous applies continuous time limit EKI. Specifically, prove intended collapse guarantees less unknowns, which sets this work apart current state-of-the-art. We illustrate our theory experiments where some mathematical assumptions may only approximately valid.