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. This is joint work with Michele Coghi, Torstein Nilssen and Sebastian Reich.
Nikolas Nüsken is a postdoctoral researcher in the Numerical Analysis group at the University of Potsdam led by Sebastian Reich. His research interests lie at the interface of computational statistics, machine learning, and the mathematics of stochastic dynamics and interacting particle systems.
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