title: Improved estimation of Fokker-Planck equations through optimization.
abstract: An improved method for the description of hierarchical complex systems by means of a Fokker-Planck equation is presented. In particular the limited-memory Broyden-Fletcher-Goldfarb-Shanno algorithm for constraint problems is used to minimize the distance between the numerical solutions of the Fokker-Planck equation and the empirical probability density functions and thus to estimate properly the drift and diffusion term of the Fokker-Planck equation. The optimization routine is applied to a time series of velocity measurements obtained from a turbulent helium gas jet in order to demonstrate the benefits and to quantify the improvements of this optimization routine.
authors.affiliation: Institut for Physics, Carl-von-Ossietzky University Oldenburg, D-26111 Oldenburg, Germany.
authors.forename: A P
authors.initials: AP
authors.lastname: Nawroth
authors.forename: J
authors.initials: J
authors.lastname: Peinke
authors.forename: D
authors.initials: D
authors.lastname: Kleinhans
authors.forename: R
authors.initials: R
authors.lastname: Friedrich