☆ 4.7 Article

An end-to-end deep learning approach for extracting stochastic dynamical systems with a-stable Levy noise

CHAOS (2022)

相关参考文献

注意：仅列出部分参考文献，下载原文获取全部文献信息。

Article Physics, Mathematical

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

Yang Li et al.

Summary: Advances in data science are enabling us to analyze and understand the complex dynamics of systems with experimental and observational data. This study presents a data-driven method to infer the governing laws of stochastic dynamical systems with non-Gaussian asymmetric Levy processes and Gaussian Brownian motion from available data.

JOURNAL OF STATISTICAL PHYSICS (2022)

添加到收藏夹

Article Mechanics

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

Yang Li et al.

Summary: This study proposes a data-driven method for extracting stochastic dynamical systems with alpha-stable Levy noise from sample path data. By estimating the Levy jump measure and noise intensity through computing the mean and variance of the amplitude of sample path increments, the drift coefficient can be approximated. Numerical experiments on one- and two-dimensional prototypical examples demonstrate the accuracy and effectiveness of the method, which will serve as a scientific tool for discovering stochastic governing laws of complex phenomena and understanding dynamical behaviors under non-Gaussian fluctuations.

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT (2022)

添加到收藏夹

Article Multidisciplinary Sciences

Extracting stochastic governing laws by non-local Kramers-Moyal formulae

Yubin Lu et al.

Summary: This paper proposes a data-driven approach to extract stochastic governing laws with both Gaussian and non-Gaussian fluctuations. By using the normalizing flows technology and the non-local Kramers-Moyal formulae, the Levy jump measure, drift coefficient, and diffusion coefficient can be estimated. The approach is validated through examples of decoupled and coupled systems.

PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES (2022)

添加到收藏夹

Article Engineering, Multidisciplinary

Solving inverse problems in stochastic models using deep neural networks and adversarial training

Kailai Xu et al.

Summary: Inverse problems associated with stochastic models, where the unknown quantities are distributions, often face limitations with traditional methods that require closed-form density functions or a large number of simulations. A new method is proposed in this study which utilizes neural networks to approximate the unknown distribution and compute statistical discrepancies. Numerical experiments demonstrate the effectiveness of the proposed method in estimating model parameters and learning complex unknown distributions.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2021)

添加到收藏夹

Article Mathematics, Applied

A data-driven approach for discovering stochastic dynamical systems with non-Gaussian Levy noise

Yang Li et al.

Summary: In this study, a new data-driven approach is developed to extract stochastic dynamical systems with non-Gaussian and Gaussian noise, by computing drift, diffusion coefficient and jump measure using a numerical algorithm. The efficacy and accuracy of this method is demonstrated through application to systems in one, two, and three dimensions.

PHYSICA D-NONLINEAR PHENOMENA (2021)

添加到收藏夹

Article Mathematics, Applied

SOLVING INVERSE STOCHASTIC PROBLEMS FROM DISCRETE PARTICLE OBSERVATIONS USING THE FOKKER-PLANCK EQUATION AND PHYSICS-INFORMED NEURAL NETWORKS

Xiaoli Chen et al.

Summary: Researchers developed a new framework based on physics-informed neural networks, connecting stochastic samples with the FP equation using Kullback-Leibler divergence to infer multidimensional PDF at all times, solving inverse problems with only sparse data available.

SIAM JOURNAL ON SCIENTIFIC COMPUTING (2021)

添加到收藏夹

Article Mathematics, Applied

Data-driven approximation of the Koopman generator: Model reduction, system identification, and control

Stefan Klus et al.

PHYSICA D-NONLINEAR PHENOMENA (2020)

添加到收藏夹

Article Mathematics, Applied

Most probable dynamics of stochastic dynamical systems with exponentially light jump fluctuations

Yang Li et al.

CHAOS (2020)

添加到收藏夹

Article Mathematics, Applied

The tipping times in an Arctic sea ice system under influence of extreme events

Fang Yang et al.

CHAOS (2020)

添加到收藏夹

Article Mathematics, Applied

Discovering transition phenomena from data of stochastic dynamical systems with Levy noise

Yubin Lu et al.

CHAOS (2020)

添加到收藏夹

Article Mathematics, Applied

Detecting the maximum likelihood transition path from data of stochastic dynamical systems

Min Dai et al.

CHAOS (2020)

添加到收藏夹

Article Physics, Multidisciplinary

Variational Inference for Stochastic Differential Equations

Manfred Opper

ANNALEN DER PHYSIK (2019)

添加到收藏夹

Article Mechanics

Levy noise-induced escape in an excitable system

Rui Cai et al.

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT (2017)

添加到收藏夹

Article Engineering, Electrical & Electronic

Characteristic function based parameter estimation of skewed alpha-stable distribution: An analytical approach

Mohammadreza Hassannejad Bibalan et al.

SIGNAL PROCESSING (2017)

添加到收藏夹

Article Physics, Fluids & Plasmas

Nonparametric estimation of stochastic differential equations with sparse Gaussian processes

Constantino A. Garcia et al.

PHYSICAL REVIEW E (2017)

添加到收藏夹

Article Multidisciplinary Sciences

Discovering governing equations from data by sparse identification of nonlinear dynamical systems

Steven L. Brunton et al.

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA (2016)

添加到收藏夹

Article Statistics & Probability

Multivariate elliptically contoured stable distributions: theory and estimation

John P. Nolan

COMPUTATIONAL STATISTICS (2013)

添加到收藏夹

Article Biology

L,vy flights in evolutionary ecology

Benjamin Jourdain et al.

JOURNAL OF MATHEMATICAL BIOLOGY (2012)

添加到收藏夹

Article Engineering, Electrical & Electronic

Video Foreground Detection Based on Symmetric Alpha-Stable Mixture Models

Harish Bhaskar et al.

IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY (2010)

添加到收藏夹

© Peeref 2019-2024. All rights reserved.