Ensemble Kalman methods

Sloppy filters for over-ambitious models



A random-sampling variant/generalisation of the Kalman-Bucy filter, much like particle filters, but with a few tweaks that make it more tenable in very high dimensional state spaces. A popular data assimilation method for spatiotemporal models.

Ensemble Kalman filters make it somewhat easier to wring estimates out of data.

Tutorial introductions

Katzfuss, Stroud, and Wikle (2016); Mandel (2009); Roth et al. (2017); Fearnhead and KΓΌnsch (2018). Wikle and Berliner (2007) puts in in a broader data assimilation context.

System identification in

G. Evensen (2009); Malartic, Farchi, and Bocquet (2021); Moradkhani et al. (2005)

Rigorous theory of

Bishop and Del Moral (2020); Del Moral, Kurtzmann, and Tugaut (2017); Garbuno-Inigo et al. (2020); Kelly, Law, and Stuart (2014); Le Gland, Monbet, and Tran (2009); Taghvaei and Mehta (2019).

Iterative ensemble smoothers

Chada, Chen, and Sanz-Alonso (2021); Luo et al. (2015); White (2018); Zhang et al. (2018).

Relation to particle filters

Close. See particle filters.

References

Bishop, Adrian N., and Pierre Del Moral. 2020. β€œOn the Mathematical Theory of Ensemble (Linear-Gaussian) Kalman-Bucy Filtering.” arXiv:2006.08843 [Math, Stat], June.
Chada, Neil K., Yuming Chen, and Daniel Sanz-Alonso. 2021. β€œIterative Ensemble Kalman Methods: A Unified Perspective with Some New Variants.” Foundations of Data Science 3 (3): 331.
Chen, Yuming, Daniel Sanz-Alonso, and Rebecca Willett. 2021. β€œAuto-Differentiable Ensemble Kalman Filters.” arXiv:2107.07687 [Cs, Stat], July.
Del Moral, P., A. Kurtzmann, and J. Tugaut. 2017. β€œOn the Stability and the Uniform Propagation of Chaos of a Class of Extended Ensemble Kalman–Bucy Filters.” SIAM Journal on Control and Optimization 55 (1): 119–55.
Evensen, G. 2009. β€œThe Ensemble Kalman Filter for Combined State and Parameter Estimation.” IEEE Control Systems 29 (3): 83–104.
Evensen, Geir. 2003. β€œThe Ensemble Kalman Filter: Theoretical Formulation and Practical Implementation.” Ocean Dynamics 53 (4): 343–67.
β€”β€”β€”. 2004. β€œSampling Strategies and Square Root Analysis Schemes for the EnKF.” Ocean Dynamics 54 (6): 539–60.
β€”β€”β€”. 2009. Data Assimilation - The Ensemble Kalman Filter. Berlin; Heidelberg: Springer.
Fearnhead, Paul, and Hans R. KΓΌnsch. 2018. β€œParticle Filters and Data Assimilation.” Annual Review of Statistics and Its Application 5 (1): 421–49.
Finn, Tobias Sebastian, Gernot Geppert, and Felix Ament. 2021. β€œEnsemble-Based Data Assimilation of Atmospheric Boundary Layerobservations Improves the Soil Moisture Analysis.” Preprint. Catchment hydrology/Modelling approaches.
Garbuno-Inigo, Alfredo, Franca Hoffmann, Wuchen Li, and Andrew M. Stuart. 2020. β€œInteracting Langevin Diffusions: Gradient Structure and Ensemble Kalman Sampler.” SIAM Journal on Applied Dynamical Systems 19 (1): 412–41.
Haber, Eldad, Felix Lucka, and Lars Ruthotto. 2018. β€œNever Look Back - A Modified EnKF Method and Its Application to the Training of Neural Networks Without Back Propagation.” arXiv:1805.08034 [Cs, Math], May.
Hou, Elizabeth, Earl Lawrence, and Alfred O. Hero. 2016. β€œPenalized Ensemble Kalman Filters for High Dimensional Non-Linear Systems.” arXiv:1610.00195 [Physics, Stat], October.
Katzfuss, Matthias, Jonathan R. Stroud, and Christopher K. Wikle. 2016. β€œUnderstanding the Ensemble Kalman Filter.” The American Statistician 70 (4): 350–57.
Kelly, D. T. B., K. J. H. Law, and A. M. Stuart. 2014. β€œWell-Posedness and Accuracy of the Ensemble Kalman Filter in Discrete and Continuous Time.” Nonlinearity 27 (10): 2579.
Kuzin, Danil, Le Yang, Olga Isupova, and Lyudmila Mihaylova. 2018. β€œEnsemble Kalman Filtering for Online Gaussian Process Regression and Learning.” 2018 21st International Conference on Information Fusion (FUSION), July, 39–46.
Law, Kody J. H., Hamidou Tembine, and Raul Tempone. 2016. β€œDeterministic Mean-Field Ensemble Kalman Filtering.” SIAM Journal on Scientific Computing 38 (3).
Le Gland, FranΓ§ois, Valerie Monbet, and Vu-Duc Tran. 2009. β€œLarge Sample Asymptotics for the Ensemble Kalman Filter,” 25.
Lei, Jing, Peter Bickel, and Chris Snyder. 2009. β€œComparison of Ensemble Kalman Filters Under Non-Gaussianity.” Monthly Weather Review 138 (4): 1293–1306.
Luo, Xiaodong, Andreas S. Stordal, Rolf J. Lorentzen, and Geir NΓ¦vdal. 2015. β€œIterative Ensemble Smoother as an Approximate Solution to a Regularized Minimum-Average-Cost Problem: Theory and Applications.” SPE Journal 20 (05): 962–82.
Malartic, Quentin, Alban Farchi, and Marc Bocquet. 2021. β€œState, Global and Local Parameter Estimation Using Local Ensemble Kalman Filters: Applications to Online Machine Learning of Chaotic Dynamics.” arXiv:2107.11253 [Nlin, Physics:physics, Stat], July.
Mandel, Jan. 2009. β€œA Brief Tutorial on the Ensemble Kalman Filter.” arXiv:0901.3725 [Physics], January.
Moradkhani, Hamid, Soroosh Sorooshian, Hoshin V. Gupta, and Paul R. Houser. 2005. β€œDual State–Parameter Estimation of Hydrological Models Using Ensemble Kalman Filter.” Advances in Water Resources 28 (2): 135–47.
Roth, Michael, Gustaf Hendeby, Carsten Fritsche, and Fredrik Gustafsson. 2017. β€œThe Ensemble Kalman Filter: A Signal Processing Perspective.” EURASIP Journal on Advances in Signal Processing 2017 (1): 56.
Taghvaei, Amirhossein, and Prashant G. Mehta. 2019. β€œAn Optimal Transport Formulation of the Ensemble Kalman Filter,” October.
White, Jeremy T. 2018. β€œA Model-Independent Iterative Ensemble Smoother for Efficient History-Matching and Uncertainty Quantification in Very High Dimensions.” Environmental Modelling & Software 109 (November): 191–201.
Wikle, Christopher K., and L. Mark Berliner. 2007. β€œA Bayesian Tutorial for Data Assimilation.” Physica D: Nonlinear Phenomena, Data Assimilation, 230 (1): 1–16.
Zhang, Jiangjiang, Guang Lin, Weixuan Li, Laosheng Wu, and Lingzao Zeng. 2018. β€œAn Iterative Local Updating Ensemble Smoother for Estimation and Uncertainty Assessment of Hydrologic Model Parameters With Multimodal Distributions.” Water Resources Research 54 (3): 1716–33.

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