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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.
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R. González-García, R. Rico-Martínez, and I. Kevrekidis · 1998
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Observation of α \alpha -stable noise induced millennial climate changes from an ice-core record
P. D. Ditlevsen · 1999
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Multivariate stable densities and distribution functions: general and elliptical case
J. P. Nolan · 2005
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Stochastic resonance in continuous and spiking neural models with lévy noise
A. Patel and B. Kosko · 2008
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Lévy Processes and Stochastic Calculus, second ed
D. Applebaum · 2009
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Feller processes: The next generation in modeling. brownian motion, lévy processes and beyond
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Density estimation by dual ascent of the log-likelihood
E. G. Tabak and E. Vanden-Eijnden · 2010
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Tipping points in open systems: Bifurcation, noise-induced and rate-dependent examples in the climate system
P. Ashwin, S. Wieczorek, R. Vitolo, and P. Cox · 2012
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Multivariate elliptically contoured stable distributions: theory and estimation
J. P. Nolan · 2013
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Approximate gaussian process inference for the drift of stochastic differential equations
A. Ruttor, P. Batz, and M. Opper · 2013
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Sparse dynamics for partial differential equations
H. Schaeffer, R. Caflisch, C. D. Hauck, and S. Osher · 2013
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An Introduction to Stochastic Dynamics
J. Duan · 2015
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A data-driven approximation of the koopman operator: Extending dynamic mode decomposition
M. O. Williams, I. G. Kevrekidis, and C. Rowley · 2015
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Discovering governing equations from data by sparse identification of nonlinear dynamical systems
S. L. Brunton, J. Proctor, and J. Kutz · 2016
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Lévy noise-induced escape in an excitable system
R. Cai, X. Chen, J. Duan, J. Kurths, and X. Li · 2017
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Density estimation using real nvp
L. Dinh, J. Sohl-Dickstein, and S. Bengio · 2017
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Nonparametric estimation of stochastic differential equations with sparse gaussian processes
C. A. García, P. Félix, J. Presedo, and D. G. Márquez · 2017
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Sparse learning of stochastic dynamical equations
L. Boninsegna, F. Nüske, and C. Clementi · 2018
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Neural ordinary differential equations
Scalable gradients for stochastic differential equations
X. Li, R. T. Q. Chen, T.-K. L. Wong, and D. Duvenaud · 2020
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Most probable dynamics of stochastic dynamical systems with exponentially light jump fluctuations
Y. Li, J. Duan, X. Liu, and Y. Zhang · 2020
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Discovering transition phenomena from data of stochastic dynamical systems with lévy noise
Y. Lu and J. Duan · 2020
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Maximal likely phase lines for a reduced ice growth model
A. Tsiairis, P. Wei, Y. Chao, and J. Duan · 2020
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The tipping times in an arctic sea ice system under influence of extreme events
F. Yang, Y. Zheng, J. Duan, L. Fu, and S. Wiggins · 2020
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R. T. Q. Chen, Y. Rubanova, J. Bettencourt, and D. Duvenaud · 2018
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Analysis of a delayed vaccinated sir epidemic model with temporary immunity and lévy jumps
Q. Liu, D. Jiang, T. Hayat, and B. Ahmad · 2018
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C. Durkan, A. Bekasov, I. Murray, and G. Papamakarios · 2019
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Normalizing flows for probabilistic modeling and inference
G. Papamakarios, E. Nalisnick, D. J. Rezende, S. Mohamed, and B. Lakshminarayanan · 2019
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Data-driven identification of parametric partial differential equations
S. Rudy, A. Alla, S. L. Brunton, and J. N. Kutz · 2019
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Transitions between metastable states in a simplified model for the thermohaline circulation under random fluctuations
D. Tesfay, P. Wei, Y. Zheng, J. Duan, and J. Kurths · 2019
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Neural stochastic differential equations: Deep latent gaussian models in the diffusion limit
B. Tzen and M. Raginsky · 2019
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The maximum likelihood climate change for global warming under the influence of greenhouse effect and lévy noise
Y. Zheng, F. Yang, J. Duan, X. Sun, L. Fu, and J. Kurths · 2020
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Solving inverse stochastic problems from discrete particle observations using the fokker–planck equation and physics-informed neural networks
X. Chen, L. Yang, J. Duan, and G. E. Karniadakis · 2021
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A data-driven approach for discovering stochastic dynamical systems with non-gaussian lévy noise
Y. Li and J. Duan · 2021
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Extracting governing laws from sample path data of non-gaussian stochastic dynamical systems
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Extracting stochastic governing laws by nonlocal kramers-moyal formulas
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Learning the temporal evolution of multivariate densities via normalizing flows
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