References

Bishop, C. H.; Etherton, B. J. and Majumdar, S. J. (2001). Adaptive Sampling with the Ensemble Transform Kalman Filter. Part I: Theoretical Aspects. Mon. Wea. Rev. 129, 420–436. ↩¹ ↩² ↩³

Calvello, E.; Reich, S. and Stuart, A. M. (2025). Ensemble Kalman Methods: A Mean Field Perspective. Acta Numerica 34, 123–291. ↩¹ ↩² ↩³

Chada, N. K.; Chen, Y. and Sanz-Alonso, D. (2021). Iterative Ensemble Kalman Methods: A Unified Perspective with Some New Variants. Found. Data Sci. 3, 331–369. ↩¹ ↩²

Chada, N. K.; Stuart, A. M. and Tong, X. T. (2020). Tikhonov Regularization within Ensemble Kalman Inversion. SIAM J. Numer. Anal. 58, 1263–1294. ↩¹ ↩²

Chen, Y. and Oliver, D. S. (2013). Levenberg–Marquardt forms of the iterative ensemble smoother for efficient history matching and uncertainty quantification. Comput. Geosci. 17, 689–703. ↩¹ ↩²

Cleary, E.; Garbuno-Inigo, A.; Lan, S.; Schneider, T. and Stuart, A. M. (2021). Calibrate, emulate, sample. J. Comp. Phys. 424, 109716. ↩¹

Garbuno-Inigo, A.; Hoffmann, F.; Li, W. and Stuart, A. M. (2020). Interacting Langevin Diffusions: Gradient Structure and Ensemble Kalman Sampler. SIAM J. Appl. Dyn. Sys. 19, 412–441. ↩¹

Garbuno-Inigo, A.; Nüsken, N. and Reich, S. (2020). Affine Invariant Interacting Langevin Dynamics for Bayesian Inference. SIAM J. Appl. Dyn. Sys. 19, 1633–1658. ↩¹ ↩² ↩³

Huang, D. Z.; Huang, J.; Reich, S. and Stuart, A. M. (2022). Efficient derivative-free Bayesian inference for large-scale inverse problems. Inverse Problems 38, 125006. ↩¹ ↩² ↩³

Huang, D. Z.; Schneider, T. and Stuart, A. M. (2022). Iterated Kalman methodology for inverse problems. J. Comp. Phys. 463, 111262. ↩¹ ↩² ↩³ ↩⁴

Iglesias, M. A.; Law, K. J. and Stuart, A. M. (2013). Ensemble Kalman methods for inverse problems. Inverse Problems 29, 045001 (20pp). ↩¹ ↩²

Iglesias, M. A. and Yang, Y. (2021). Adaptive regularisation for ensemble Kalman inversion. Inverse Problems 37, 025008. ↩¹ ↩²

Jazwinski, A. H. (1970). Stochastic Processes and Filtering Theory. Vol. 64 of Mathematics in Science and Engineering (Academic Press, New York). ↩¹

Kovachki, N. B. and Stuart, A. M. (2019). Ensemble Kalman inversion: A derivative-free technique for machine learning tasks. Inverse Problems 35, 095005. ↩¹ ↩²

Lopez-Gomez, I.; Christopoulos, C.; Ervik, H. L.; Dunbar, O. R.; Cohen, Y. and Schneider, T. (2022). Training physics-based machine-learning parameterizations with gradient-free ensemble Kalman methods. J. Adv. Model. Earth Sys. 14, e2022MS003105. ↩¹

Lorenz, E. N. (1996). Predictability—a problem partly solved. In: Proc. Seminar on Predictability, Vol. 1 (ECMWF, Reading, Berkshire, UK); pp. 1–18. Reprinted in T. N. Palmer and R. Hagedorn, eds., Predictability of Weather and Climate, Cambridge UP (2006). ↩¹ ↩²

Schneider, T.; Stuart, A. M. and Wu, J. (2022). Ensemble Kalman inversion for sparse learning of dynamical systems from time-averaged data. J. Comp. Phys. 470, 111559. ↩¹ ↩²

Su, W.; Boyd, S. and Candès, E. J. (2016). A Differential Equation for Modeling Nesterov's Accelerated Gradient Method: Theory and Insights. J. Mach. Learn. Res. 17, 1–43. ↩¹ ↩²

Tong, X. T. and Morzfeld, M. (2023). Localization in Ensemble Kalman inversion. Inverse Problems 39, 064002. ↩¹

Vernon, S.; Bach, E. and Dunbar, O. (2025). Nesterov acceleration for ensemble Kalman inversion and variants. J. Comp. Phys. 535, 114063. ↩¹ ↩²