Improved estimation of Fokker-Planck equations through optimization.
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.
Nawroth
A P
AP
Institut for Physics, Carl-von-Ossietzky University Oldenburg, D-26111 Oldenburg, Germany.
Peinke
J
J
Kleinhans
D
D
Friedrich
R
R