Repository: Freie Universität Berlin, Math Department

Rough McKean-Vlasov dynamics for robust ensemble Kalman filtering

Coghi, Michele and Nilssen, Torstein and Nüsken, Nikolas (2021) Rough McKean-Vlasov dynamics for robust ensemble Kalman filtering. arXive . pp. 1-41. (Submitted)

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Motivated by the challenge of incorporating data into misspecified and multiscale dynamical models, we study a McKean-Vlasov equation that contains the data stream as a common driving rough path. This setting allows us to prove well-posedness as well as continuity with respect to the driver in an appropriate rough-path topology. The latter property is key in our subsequent development of a robust data assimilation methodology: We establish propagation of chaos for the associated interacting particle system, which in turn is suggestive of a numerical scheme that can be viewed as an extension of the ensemble Kalman filter to a rough-path framework. Finally, we discuss a data-driven method based on subsampling to construct suitable rough path lifts and demonstrate the robustness of our scheme in a number of numerical experiments related to parameter estimation problems in multiscale contexts.

Item Type:Article
Subjects:Mathematical and Computer Sciences > Mathematics > Applied Mathematics
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics
ID Code:2584
Deposited By: Monika Drueck
Deposited On:27 Aug 2021 12:28
Last Modified:30 Aug 2021 12:56

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