Extracting stochastic dynamical systems with α-stable Lévy noise from data

Li, Yang; Lu, Yubin; Xu, Shengyuan; Duan, Jinqiao

doi:10.1088/1742-5468/ac4e87

Cited by 9 publications

(2 citation statements)

References 37 publications

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“…Also, speed and direction appear to very sensitively depend on the characteristics of the noise. Li and Duan devised an entirely innovative data-driven method to investigate the governing laws [32,33] as well as a framework to extract the most probable path based on the Onsager-Machlup theory [34]. However, for transition events in gene expression, there exists little data-driven work to extract the crucial dynamical indicators.…”

Section: Introductionmentioning

confidence: 99%

Data-driven approximation for extracting the transition dynamics of a genetic regulatory network with non-Gaussian Lévy noise

Lu¹,

Li²,

Liu³

2023

J. Stat. Mech.

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In the study of biological systems, several methods based on statistical physics or machine learning have been developed for inference or prediction in the presence of complicated nonlinear interactions and random noise perturbations. However, there have been few studies dealing with the stochastic non-Gaussian perturbation case, which is more natural and universal than Gaussian white noise. In this manuscript, for a two-dimensional biological model (the MeKS network) perturbed by non-Gaussian stable Lévy noise, we use a data-driven approach with theoretical probabilistic foundation to extract the rare transition dynamics representing gene expression. This involves theories of non-local Kramers–Moyal formulas and the non-local Fokker–Planck equation, as well as the corresponding numerical algorithms, aimed at extracting the maximum likelihood transition path. The feasibility and accuracy of the method are checked. Furthermore, several dynamical behaviors and indicators are investigated. In detail, the investigation shows a bistable transition probability state of the ComK protein concentration and bifurcations in the learned transition paths from vegetative state to competence state. Analysis of the tipping time illustrates the difficulty of the gene expression. This method will serve as an example in the study of stochastic systems with non-Gaussian perturbations from biological data, and provides some insights into the extraction of other dynamical indicators, such as the mean first exit time and the first escape probability with respect to their own biological interpretations.

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Section: Introductionmentioning

confidence: 99%

Data-driven approximation for extracting the transition dynamics of a genetic regulatory network with non-Gaussian Lévy noise

Lu¹,

Li²,

Liu³

2023

J. Stat. Mech.

Self Cite

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“…Together with the Kramers-Moyal formulas and SINDy, governing laws under different Lévy noise were extracted from the observed data of stochastic dynamics equations. [36][37][38] Among these meth-ods, SINDy has been widely applied in discovering governing equations from massive datasets. The method combines the least-squares and compressed-sensing to solve the sparse coefficients of the equations, so that the approximate governing equations can be obtained.…”

Section: Introductionmentioning

confidence: 99%

Sparse identification method of extracting hybrid energy harvesting system from observed data

Sun¹,

Zeng²,

Yang³

2022

Chinese Phys. B

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Hybrid energy harvesters under external excitation have complex dynamical behavior and the superiority of promoting energy harvesting efficiency. Sometimes, it is difficult to model the governing equations of the hybrid energy harvesting system precisely, especially under external excitation. Accompanied with machine learning, data-driven methods play an important role in discovering the governing equations from massive datasets. Recently, there are many studies of data-driven models done in aspect of ordinary differential equations and stochastic differential equations (SDEs). However, few studies are to discover the governing equations for hybrid energy harvesting system under harmonic excitation and Gaussian white noise (GWN). Thus, in this paper, a data-driven approach, with least square and sparse constraint, is devised to discover governing equations of the systems from observed data. Firstly, the algorithm processing and pseudo code are given. Then, the effectiveness and accuracy of the method are verified by taking two examples with harmonic excitation and GWN, respectively. For harmonic excitation, all coefficients of the system can be simultaneously learned. For GWN, we approximate the drift term and diffusion term by using Kramers-Moyal formulas, and separately learn the coefficients of the drift term and diffusion term. Cross-Validation (CV) and Mean-square error (MSE) are utilized to obtain the optimal number of iterations. Finally, the comparisons between true values and learned values are depicted to demonstrate that the approach is well utilized to obtain the governing equations for hybrid energy harvester under harmonic excitation and GWN.

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