Maximal Likely Phase Lines for a Reduced Ice Growth Model

Tsiairis, Athanasios; Wei, Pingyuan; Chao, Ying; Duan, Jinqiao

doi:10.48550/arxiv.1912.00471

Cited by 3 publications

(3 citation statements)

References 22 publications

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“…Subsequently, Zheng et al [38] developed a probabilistic framework to investigate the maximum likelihood climate change for an energy balance system under the combined influence of greenhouse effect and α-stable Lévy motions. Additionally, there are also some researchers using the Lévy motion to characterize the random fluctuations emerged in neural systems [28], gene networks [6], epidemic model [21], and the Earth systems [2,20,33,34,37].…”

Section: Mathematics Subject Classification (2020) Msc 60g51 • Msc 60...mentioning

confidence: 99%

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

Li,

Lu,

et al. 2021

Preprint

Self Cite

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With the rapid increase of valuable observational, experimental and simulated data for complex systems, much efforts have been devoted to identifying governing laws underlying the evolution of these systems. Despite the wide applications of non-Gaussian fluctuations in numerous physical phenomena, the data-driven approaches to extract stochastic dynamical systems with (non-Gaussian) Lévy noise are relatively few so far. In this work, we propose a data-driven method to extract stochastic dynamical systems with α-stable Lévy noise from short burst data based on the properties of α-stable distributions. More specifically, we first estimate the Lévy jump measure and noise intensity via computing mean and variance of the amplitude of the increment of the sample paths. Then we approximate the drift coefficient by combining nonlocal Kramers-Moyal formulas with normalizing flows. Numerical experiments on one-and two-dimensional prototypical examples illustrate the accuracy and effectiveness of our method. This approach will become an effective scientific tool in discovering stochastic governing laws of complex phenomena and understanding dynamical behaviors under non-Gaussian fluctuations.

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Section: Mathematics Subject Classification (2020) Msc 60g51 • Msc 60...mentioning

confidence: 99%

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

Li,

Lu,

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…Subsequently, Zheng et al [41] developed a probabilistic framework to investigate the maximum likelihood climate change for an energy balance system under the combined influence of greenhouse effect and α-stable Lévy motions. Additionally, there are also some researchers using the Lévy motion to characterize the random fluctuations emerged in neural systems [31], gene networks [6], epidemic model [23], and the earth systems [2,22,36,37,40].…”

Section: Introductionmentioning

confidence: 99%

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

Li¹,

Lu²,

Xu³

et al. 2022

J. Stat. Mech.

View full text Add to dashboard Cite

With the rapid increase of valuable observational, experimental and simulated data for complex systems, much efforts have been devoted to identifying governing laws underlying the evolution of these systems. Despite the wide applications of non-Gaussian fluctuations in numerous physical phenomena, the data-driven approaches to extract stochastic dynamical systems with (non-Gaussian) Lévy noise are relatively few so far. In this work, we propose a data-driven method to extract stochastic dynamical systems with α-stable Lévy noise from sample path data based on the properties of α-stable distributions. More specifically, we first estimate the Lévy jump measure and noise intensity via computing mean and variance of the amplitude of the increment of the sample paths. Then we approximate the drift coefficient by combining nonlocal Kramers–Moyal formulas with normalizing flows. Numerical experiments on one- and two-dimensional prototypical examples including simulated and real world measurement data illustrate the accuracy and effectiveness of our method. This approach will become an effective scientific tool in discovering stochastic governing laws of complex phenomena and understanding dynamical behaviors under non-Gaussian fluctuations.

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“…According to the Greenland ice core measurement data, Ditlevsen [18] found that the temperature in that climate system could be modeled as stochastic differential equations with α-stable Lévy motion. Other researchers also used the non-Gaussian Lévy motion to characterize the random fluctuations emerged in neural systems [42], gene networks [8], and the Earth systems [3,58,60,55,53].…”

Section: Introductionmentioning

confidence: 99%

Extracting Stochastic Governing Laws by Nonlocal Kramers-Moyal Formulas

Lu¹,

Li²,

Duan

2021

Preprint

Self Cite

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With the rapid development of computational techniques and scientific tools, great progress of data-driven analysis has been made to extract governing laws of dynamical systems from data. Despite the wide occurrences of non-Gaussian fluctuations, the effective data-driven methods to identify stochastic differential equations with non-Gaussian Lévy noise are relatively few so far. In this work, we propose a data-driven approach to extract stochastic governing laws with both (Gaussian) Brownian motion and (non-Gaussian) Lévy motion, from short bursts of simulation data. Specifically, we use the normalizing flows technology to estimate the transition probability density function (solution of nonlocal Fokker-Planck equation) from data, and then substitute it into the recently proposed nonlocal Kramers-Moyal formulas to approximate Lévy jump measure, drift coefficient and diffusion coefficient. We demonstrate that this approach can learn the stochastic differential equation with Lévy motion. We present examples with one-and two-dimensional, decoupled and coupled systems to illustrate our method. This approach will become an effective tool for discovering stochastic governing laws and understanding complex dynamical behaviors.

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Maximal Likely Phase Lines for a Reduced Ice Growth Model

Cited by 3 publications

References 22 publications

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

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

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

Extracting Stochastic Governing Laws by Nonlocal Kramers-Moyal Formulas

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