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Recently, extracting data-driven governing laws of dynamical systems through deep learning frameworks has gained a lot of attention in various fields.
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John P. Nolan, · 2001
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Wojbor A. Woyczyński, · 2001
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“Modeling financial data with stable distributions,”
John P. Nolan, · 2003
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Statistical tools for finance and insurance
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“Video foreground detection based on symmetric alpha-stable mixture models,”
Harish Bhaskar, Lyudmila S. Mihaylova, and Alin Achim, · 2010
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“Parameter estimation of alpha-stable distributions based on mcmc,”
Yanling Hao, Zhiming Shan, Feng Shen, and Dongze Lv, · 2011
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“Introduction to second kind statistics: Application of log-moments and log-cumulants to the analysis of radar image distributions,”
Jean-Marie Nicolas and Stian Normann Anfinsen, · 2011
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“Lévy flights in evolutionary ecology,”
Benjamin Jourdain, Sylvie Méléard, and Wojbor A. Woyczynski, · 2012
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“Multivariate elliptically contoured stable distributions: theory and estimation,”
John P. Nolan, · 2013
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“Approximate gaussian process inference for the drift function in stochastic differential equations,”
Andreas Ruttor, Philipp Batz, and Manfred Opper, · 2013
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“Generative adversarial nets,”
Ian J. Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron C. Courville, and Yoshua Bengio, · 2014
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“Auto-encoding variational bayes,”
Diederik P. Kingma and Max Welling, · 2014
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An introduction to stochastic dynamics
Jinqiao Duan, · 2015
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“Discovering governing equations from data by sparse identification of nonlinear dynamical systems,”
Steven L. Brunton, Joshua L. Proctor, and J. Nathan Kutz, · 2016
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“Deep residual learning for image recognition,”
“Data-driven approximation of the koopman generator: Model reduction, system identification, and control,”
Stefan Klus, Feliks Nuske, Sebastian Peitz, Jan-Hendrik Niemann, Cecilia Clementi, and Christof Schutte, · 2020
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“Discovering transition phenomena from data of stochastic dynamical systems with lévy noise,”
Yubin Lu and Jinqiao Duan, · 2020
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“Most probable dynamics of stochastic dynamical systems with exponentially light jump fluctuations,”
Yang Li, Jinqiao Duan, Xianbin Liu, and Yanxia Zhang, · 2020
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“Scalable gradients for stochastic differential equations,”
Xuechen Li, Ting-Kam Leonard Wong, Ricky T. Q. Chen, and David Kristjanson Duvenaud, · 2020
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“The tipping times in an arctic sea ice system under influence of extreme events,”
Fang Yang, Yayun Zheng, Jinqiao Duan, Ling Fu, and Stephen Wiggins, · 2020
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Kaiming He, X. Zhang, Shaoqing Ren, and Jian Sun, · 2016
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“Characteristic function based parameter estimation of skewed alpha-stable distribution: An analytical approach,”
Mohammadreza Hassannejad Bibalan, Hamidreza Amindavar, and Maryam Amirmazlaghani, · 2017
Cited alongside, same era.
“Lévy noise-induced escape in an excitable system,”
Rui Cai, Xiaoli Chen, Jinqiao Duan, Jürgen Kurths, and Xiaofang Li, · 2017
Cited alongside, same era.
“Nonparametric estimation of stochastic differential equations with sparse gaussian processes,”
Constantino A. García, Abraham Otero, Paulo Félix, Jesús María Rodríguez Presedo, and David G. Márquez, · 2017
Cited alongside, same era.
“Neural ordinary differential equations,”
Ricky T. Q. Chen, Yulia Rubanova, Jesse Bettencourt, and David Kristjanson Duvenaud, · 2018
Cited alongside, same era.
“Black-box variational inference for stochastic differential equations,”
Tom Ryder, Andrew Golightly, Andrew Stephen McGough, and Dennis Prangle, · 2018
Cited alongside, same era.
“Neural jump stochastic differential equations,”
Junteng Jia and Austin R. Benson, · 2019
Cited alongside, same era.
“Solving inverse stochastic problems from discrete particle observations using the fokker-planck equation and physics-informed neural networks,”
Xiaoli Chen, Liu Yang, Jinqiao Duan, and George Em Karniadakis, · 2021
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“Learning stochastic dynamical systems with neural networks mimicking the euler-maruyama scheme,”
Noura Dridi, Lucas Drumetz, and Ronan Fablet, · 2021
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Felix Dietrich, Alexei Makeev, George Kevrekidis, Nikolaos Evangelou, Tom S. Bertalan, Sebastian Reich, and Ioannis G. Kevrekidis, · 2021
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“A data-driven approach for discovering stochastic dynamical systems with non-gaussian lévy noise,”
Yang Li and Jinqiao Duan, · 2021
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“Extracting stochastic governing laws by nonlocal kramers-moyal formulas,”
Yubin Lu, Yang Li, and Jinqiao Duan, · 2021
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Alexander Norcliffe, Cristian Bodnar, Ben Day, Jacob Moss, and Pietro Liò, · 2021
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“Parameter Estimation of Cauchy Distribution,”
Bingzhang Wang, · 2021
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“Solving inverse problems in stochastic models using deep neural networks and adversarial training,”
Kailai Xu and Eric F Darve, · 2021
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“Extracting governing laws from sample path data of non-gaussian stochastic dynamical systems,”
Yang Li and Jinqiao Duan, · 2022
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“Extracting stochastic dynamical systems with alpha-stable Lévy noise from data,”
Yang Li, Yubin Lu, Shengyuan Xu, and Jinqiao Duan, · 2022
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