mlsanityData to 14 Oct 2026

Extracting stochastic dynamical systems with α-stable L'evy noise from data

arXiv 2109.14881 ↗First posted 30 Sep 2021stat.ML cs.LG math.PRcited by 8

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Abstract (arXiv)

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) L'evy noise are relatively few so far. In this work, we propose a data-driven method to extract stochastic dynamical systems with α-stable L'evy noise from short burst data based on the properties of α-stable distributions. More specifically, we first estimate the L'evy 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.

Key facts. Cited by 8 papers in the map (data through 14 Oct 2026). Builds on 14 of its 47 references that are in the map. First posted on arXiv 30 Sep 2021.

Builds on

14 of 47 references.

References · 14

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2 more
  1. 2021Extracting Governing Laws from Sample Path Data of Non-Gaussian Stochastic Dynamical Systemscited by 7
  2. 2021Extracting Stochastic Governing Laws by Nonlocal Kramers-Moyal Formulascited by 6

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 3; 2023: 0; 2024: 3; 2025: 1; 2026: 1.

8 papers.

  1. 2022Nonparametric learning of kernels in nonlocal operatorscited by 10
  2. 2022An end-to-end deep learning approach for extracting stochastic dynamical systems with α-stable L'evy noisecited by 7
  3. 2024Modeling Unknown Stochastic Dynamical System Subject to External Excitationcited by 7
  4. 2022Drift Identification for L'evy alpha-Stable Stochastic Systemscited by 1
  5. 2024Weak Collocation Regression for Inferring Stochastic Dynamics with L'evy Noisecited by 1
  6. 2024An evolutionary approach for discovering non-Gaussian stochastic dynamical systems based on nonlocal Kramers-Moyal formulascited by 1
  7. 2025A Robust Model-Based Approach for Continuous-Time Policy Evaluation with Unknown L'evy Process Dynamicscited by 0
  8. 2026Variational Inference for L'evy Process-Driven SDEs via Neural Tiltingcited by 0