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arXiv · 0705.1292

Improved estimation of Fokker-Planck equations through optimisation

A. P. Nawroth·J. Peinke·D. Kleinhans·R. Friedrich
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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.

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A. P. Nawroth, J. Peinke, D. Kleinhans, R. Friedrich. 2007-05-09. Improved estimation of Fokker-Planck equations through optimisation. https://doi.org/10.1103/physreve.76.056102

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