Rough McKean–Vlasov dynamics for robust ensemble Kalman filtering

TY - JOUR

T1 - Rough McKean–Vlasov dynamics for robust ensemble Kalman filtering

AU - Coghi, Michele

AU - Nilssen, Torstein

AU - Nusken, Nikolas

AU - Reich, Sebastian

PY - 2023/12/13

Y1 - 2023/12/13

N2 - 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.

AB - 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.

M3 - Article

SN - 1050-5164

VL - 33

SP - 5693

EP - 5752

JO - The Annals of Applied Probability

JF - The Annals of Applied Probability

IS - 6B

ER -