A Langevinized Ensemble Kalman Filter for Large-Scale Dynamic Learning

Peiyi Zhang, Qifan Song, Faming Liang
2023 Statistica sinica  
The Ensemble Kalman Filter (EnKF) has achieved great successes in data assimilation in atmospheric and oceanic sciences, but it fails in converging to the correct filtering distribution which precludes its use for uncertainty quantification of dynamic systems. We reformulate EnKF under the framework of Langevin dynamics, which leads to a new particle filtering algorithm, the so-called Langevinized EnKF (LEnKF). LEnKF inherits the forecast-analysis procedure from EnKF and the use of mini-batch
more » ... ta from stochastic gradient Langevin dynamics (SGLD). We prove that LEnKF turns out to be a sequential preconditioned SGLD sampler but, like EnKF, with its execution being accelerated by the forecast-analysis procedure and that LEnKF converges to the right filtering distribution in 2-Wasserstein distance as the number of iterations per stage becomes large. We illustrate the performance of LEnKF using a variety of examples. LEnKF is not only scalable with respect to the state dimension and sample size, but also tends to be immune to sample degeneracy for long series dynamic data.
doi:10.5705/ss.202022.0172 fatcat:dla3zdorrrbbdfcmqzkbiabyz4