Improved estimation of Fokker-Planck equations through optimisation

TL;DR

This paper introduces an enhanced optimization method using L-BFGS-B to more accurately estimate the drift and diffusion terms in Fokker-Planck equations, demonstrated on turbulent helium gas jet data.

Contribution

It presents a novel application of L-BFGS-B optimization to improve Fokker-Planck equation parameter estimation from empirical data.

Findings

Improved fit between numerical solutions and empirical PDFs.

Enhanced accuracy in drift and diffusion term estimation.

Demonstrated effectiveness on turbulent flow data.

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.