Improved estimation of Fokker-Planck equations through optimisation
Data Analysis, Statistics and Probability
2013-05-29 v1
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 (L-BFGS-B) 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 optimisation 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 new optimisation routine.
Cite
@article{arxiv.0705.1292,
title = {Improved estimation of Fokker-Planck equations through optimisation},
author = {A. P. Nawroth and J. Peinke and D. Kleinhans and R. Friedrich},
journal= {arXiv preprint arXiv:0705.1292},
year = {2013}
}