Evaluating strong measurement noise in data series with simulated annealing method

TL;DR

This paper introduces a simulated annealing-based method to accurately reconstruct stochastic processes from time series data affected by strong measurement noise, improving upon previous algorithms.

Contribution

The paper presents a novel reconstruction method using simulated annealing to handle strong measurement noise in stochastic time series, enhancing accuracy and reliability.

Findings

Simulated annealing outperforms Levenberg-Marquardt in reconstruction quality.

The method effectively reconstructs drift and diffusion functions under high noise conditions.

Reconstruction process is rapid and reliable with the proposed approach.

Abstract

Many stochastic time series can be described by a Langevin equation composed of a deterministic and a stochastic dynamical part. Such a stochastic process can be reconstructed by means of a recently introduced nonparametric method, thus increasing the predictability, i.e. knowledge of the macroscopic drift and the microscopic diffusion functions. If the measurement of a stochastic process is affected by additional strong measurement noise, the reconstruction process cannot be applied. Here, we present a method for the reconstruction of stochastic processes in the presence of strong measurement noise, based on a suitably parametrized ansatz. At the core of the process is the minimization of the functional distance between terms containing the conditional moments taken from measurement data, and the corresponding ansatz functions. It is shown that a minimization of the distance by means of a simulated annealing procedure yields better results than a previously used Levenberg-Marquardt algorithm, which permits a rapid and reliable reconstruction of the stochastic process.