Nesterov acceleration for ensemble Kalman inversion and variants

Vernon, S., Bach, E. ORCID: https://orcid.org/0000-0002-9725-0203 and Dunbar, O. R. A. (2025) Nesterov acceleration for ensemble Kalman inversion and variants. Journal of Computational Physics, 535. 114063. ISSN 0021-9991 doi: 10.1016/j.jcp.2025.114063

Abstract/Summary

Ensemble Kalman inversion (EKI) is a derivative-free, particle-based optimization method for solving inverse problems. It can be shown that EKI approximates a gradient flow, which allows the application of methods for accelerating gradient descent. Here, we show that Nesterov acceleration is effective in speeding up the reduction of the EKI cost function on a variety of inverse problems. We also implement Nesterov acceleration for two EKI variants, unscented Kalman inversion and ensemble transform Kalman inversion. Our specific implementation takes the form of a particle-level nudge that is demonstrably simple to couple in a black-box fashion with any existing EKI variant algorithms, comes with no additional computational expense, and with no additional tuning hyperparameters. This work shows a pathway for future research to translate advances in gradient-based optimization into advances in gradient-free Kalman optimization.

Item Type	Article
URI	https://reading-pure-test.eprints-hosting.org/id/eprint/122782
Identification Number/DOI	10.1016/j.jcp.2025.114063
Refereed	Yes
Divisions	Central Services Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
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