Kinetic Methods for Inverse Problems

Michael Herty, Giuseppe Visconti

Published 2018-11-23Version 1

The Ensemble Kalman Filter method can be used as an iterative numerical scheme for parameter identification or nonlinear filtering problems. We study the limit of infinitely large ensemble size and derive the corresponding mean-field limit of the ensemble method. The kinetic equation allows in simple cases to analyze stability of the solution to inverse problems as mean of the distribution of the ensembles. Further, we present a slight but stable modification of the method which leads to a Fokker-Planck-type kinetic equation. The kinetic methods proposed here are able to solve the problem with a reduced computational complexity in the limit of a large ensemble size. We illustrate the properties and the ability of the kinetic model to provide solution to inverse problems by using examples from the literature.