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With the rapid development of computational techniques and scientific tools, great progress of data-driven analysis has been made to extract governing laws of dynamical systems from data.
Identification of distributed parameter systems: A neural net based approach
R. González-García, R. Rico-Martínez, and I. Kevrekidis · 1998
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A Practical Guide to Heavy Tails: Statistical Techniques and Applications
R. Adler and R. Feldman and M. Taqqu · 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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Lévy Processes: Theory and Applications
O. E. Barndorff-Nielsen and T. Mikosch and S. I. Resnick (Eds.) · 2001
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Financial Modelling with Jump Processes
R. Cont and P. Tankov · 2003
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Coarse-grained kinetic computations for rare events: Application to micelle formation
D. I. Kopelevich, A. Z. Panagiotopoulos, and I. G. Kevrekidis · 2005
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Generator estimation of markov jump processes
P. Metzner, E. Dittmer, T. Jahnke, and C. Schütte · 2007
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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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Dynamic mode decomposition of numerical and experimental data
P. J. Schmid · 2008
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STOCHASTIC MODELING OF WATER VAPOR IN THE CLIMATE SYSTEM
B. Chen · 2009
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Lévy Processes and Stochastic Calculus, second ed
D. Applebaum · 2009
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Seasonal variability of the subpolar gyres in the southern ocean: a numerical investigation based on transfer operators
M. Dellnitz, G. Froyland, C. Horenkamp, K. Padberg-Gehle, and A. S. Gupta · 2009
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Almost-invariant sets and invariant manifolds - connecting probabilistic and geometric descriptions of coherent structures in flows
G. Froyland and K. Padberg · 2009
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Feller processes: The next generation in modeling. brownian motion, lévy processes and beyond
B. Böttcher · 2010
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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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Model reduction for agent-based social simulation: Coarse-graining a civil violence model
Y. Zou, V. A. Fonoberov, M. Fonoberova, I. Mezic, and I. G. Kevrekidis · 2012
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Estimating long-term behavior of flows without trajectory integration: the infinitesimal generator approach
G. Froyland, O. Junge, and P. Koltai · 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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Fluctuations of Lévy Processes with Applications: Introductory Lectures
A. E. Kyprianou · 2014
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An Introduction to Stochastic Dynamics
J. Duan · 2015
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Equation-free model reduction in agent-based computations: Coarse-grained bifurcation and variable-free rare event analysis
P. Liu, C. I. Siettos, C. W. Gear, and I. Kevrekidis · 2015
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Equation-free model reduction in agent-based computations: Coarse-grained bifurcation and variable-free rare event analysis
L. Ping, C. I. Siettos, C. W. Gear, and I. G. Kevrekidis · 2015
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An early warning indicator for atmospheric blocking events using transfer operators
A. Tantet, F. R. van der Burgt, and H. A. Dijkstra · 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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Normalizing flows for probabilistic modeling and inference
G. Papamakarios, E. Nalisnick, D. J. Rezende, S. Mohamed, and B. Lakshminarayanan · 2019
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Operator fitting for parameter estimation of stochastic differential equations
A. N. Riseth and J. Taylor-King · 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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Galerkin approximation of dynamical quantities using trajectory data
E. H. Thiede, D. Giannakis, A. R. Dinner, and J. Weare · 2019
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Neural stochastic differential equations: Deep latent gaussian models in the diffusion limit
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On the numerical approximation of the perron- frobenius and koopman operator
S. Klus, P. Koltai, and C. Schütte · 2016
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Variational inference with normalizing flows
D. J. Rezende and S. Mohamed · 2016
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Understanding the geometry of transport: Diffusion maps for lagrangian trajectory data unravel coherent sets
R. Banisch and P. Koltai · 2017
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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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Improved variational inference with inverse autoregressive flow
D. P. Kingma, T. Salimans, R. Jozefowicz, I. S. X. Chen, and M. Welling · 2017
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B. Tzen and M. Raginsky · 2019
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X. Chen, L. Yang, J. Duan, and G. E. Karniadakis · 2020
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Detecting the maximum likelihood transition path from data of stochastic dynamical systems
M. Dai, T. Gao, Y. Lu, Y. Zheng, and J. Duan · 2020
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Data-driven approximation of the koopman generator: Model reduction, system identification, and control
S. Klus, F. Nüske, S. Peitz, J. H. Niemann, C. Clementi, and C. Schütte · 2020
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Coarse-scale pdes from fine-scale observations via machine learning
S. Lee, M. Kooshkbaghi, K. Spiliotis, C. I. Siettos, and I. G. Kevrekidis · 2020
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Scalable gradients for stochastic differential equations
X. Li, R. T. Q. Chen, T.-K. L. Wong, and D. Duvenaud · 2020
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Data-driven model reduction for stochastic burgers equations
F. Lu · 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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Time-series learning of latent-space dynamics for reduced-order model closure
R. Maulik, A. Mohan, B. Lusch, S. Madireddy, P. Balaprakash, and D. Livescu · 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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L. Yang, C. Daskalakis, and G. E. Karniadakis · 2020
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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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F. Dietrich, A. Makeev, G. Kevrekidis, N. Evangelou, T. Bertalan, S. Reich, and I. G. Kevrekidis · 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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Learning the temporal evolution of multivariate densities via normalizing flows
Y. Lu, R. Maulik, T. Gao, F. Dietrich, I. G. Kevrekidis, and J. Duan · 2021
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