Improved estimation of Fokker-Planck equations through optimisation

Details Improved estimation of Fokker-Planck equations through optimisation Improved estimation of Fokker-Planck equations through optimisation

2007-05-09

arxiv.org/abs/0705.1292v1

Physics

Data Analysis, Statistics and Probability

Scientific paper

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.

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