Ensemble Controlled-Flow Filtering for Implicit Data Assimilation

EnCF is an ensemble filter that performs implicit data assimilation by defining the analysis law as an energy tilt of the forecast distribution, realized through a stochastic controlled flow with observation-dependent control learned by adjoint matching. For simulator-defined observations, EnCF-LF learns a surrogate conditional energy from samples. The authors prove ideal exactness and establish non-accumulation of local errors under filter stability. Numerical results show EnCF and EnCF-LF outperform Kalman-type filters on non-Gaussian, many-to-one, multimodal, and implicit observation models.