Extracting Governing Laws from Sample Path Data of Non-Gaussian Stochastic Dynamical Systems

Abstract

Advances in data science are leading to new progresses in the analysis and understanding of complex dynamics for systems with experimental and observational data. With numerous physical phenomena exhibiting bursting, flights, hopping, and intermittent features, stochastic differential equations with non-Gaussian Lévy noise are suitable to model these systems. Thus it is desirable and essential to infer such equations from available data to reasonably predict dynamical behaviors. In this work, we consider a data-driven method to extract stochastic dynamical systems with non-Gaussian asymmetric (rather than the symmetric) Lévy process, as well as Gaussian Brownian motion. We establish a theoretical framework and design a numerical algorithm to compute the asymmetric Lévy jump measure, drift and diffusion (i.e., nonlocal Kramers-Moyal formulas), hence obtaining the stochastic governing law, from noisy data. Numerical experiments on several prototypical examples confirm the efficacy and accuracy of this method. This method will become an effective tool in discovering the governing laws from available data sets and in understanding the mechanisms underlying complex random phenomena.

arXiv commentarXiv admin note: substantial text overlap with arXiv:2005.03769

References in corpus (19)

• Discovering governing equations from data: Sparse identification of nonlinear dynamical systems
• A Data-Driven Approximation of the Koopman Operator: Extending Dynamic Mode Decomposition
• Data-driven approximation of the Koopman generator: Model reduction, system identification, and control
• Sparse learning of stochastic dynamic equations
• Sparse Dynamics for Partial Differential Equations
• Anomalous transport effects on switching currents of graphene-based Josephson junctions
• Effects of Lévy noise on the dynamics of sine-Gordon solitons in long Josephson junctions
• Josephson-based threshold detector for Lévy distributed fluctuations
• The problem of analytical calculation of barrier crossing characteristics for Levy flights
• A Data-Driven Approach for Discovering Stochastic Dynamical Systems with Non-Gaussian Levy Noise
• Voltage drop across Josephson junctions for Lévy noise detection
• Forecasting in the light of Big Data
• Detecting the maximum likelihood transition path from data of stochastic dynamic systems
• Discovering transition phenomena from data of stochastic dynamical systems with Lévy noise
• Feller Processes: The Next Generation in Modeling. Brownian Motion, Lévy Processes and Beyond
• The Role of Data in Model Building and Prediction: A Survey Through Examples
• Discovering mean residence time and escape probability from data of stochastic dynamical systems
• Most Probable Dynamics of Stochastic Dynamical Systems with Exponentially Light Jump Fluctuations
• Extracting Non-Gaussian Governing Laws from Data on Mean Exit Time

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