485

IGPM485.pdf 2018 
TITLE 
Kinetic Methods for Inverse Problems

AUTHORS 
Michael Herty, Giuseppe Visconti

ABSTRACT 
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 meanfield 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 FokkerPlancktype 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.

KEYWORDS 
Kinetic Partial Differential Equations, Nonlinear Filtering Methods, Inverse Problems
