Subrahmanya, Amit N.Popov, Andrey A.Sandu, Adrian2022-02-272022-02-272021-11-27http://hdl.handle.net/10919/108891Particle flow filters that aim to smoothly transform particles from samples from a prior distribution to samples from a posterior are a major topic of active research. In this work we introduce a generalized framework which we call the the Variational Fokker-Planck method for filtering and smoothing in data assimilation that encompasses previous methods such as the mapping particle filter and the particle flow filter. By making use of the properties of the optimal Ito process that solves the underlying Fokker-Planck equation we can explicitly include heuristics methods such as rejuvenation and regularization that fit into this framework. We also extend our framework to higher dimensions using localization and covariance shrinkage, and provide a robust implicit-explicit method for solving the stochastic initial value problem describing the Ito process. The effectiveness of the variational Fokker-Planck method is demonstrated on three test problems, namely the Lorenz '63, Lorenz '96 and the quasi-geostrophic equations.application/pdfenIn Copyrightmath.OCcs.CEcs.NAmath.NA65C05, 93E11, 62F15, 86A22Article2022-02-27Sandu, Adrian [0000-0002-5380-0103]