Long-term prediction of chaotic systems with machine learning

This paper develops a machine learning scheme to obtain long term predictions on chaotic systems, including high-dimensional, spatiotemporal chaotic systems, by using extremely rare updates

[1]  T. Carroll,et al.  Master Stability Functions for Synchronized Coupled Systems , 1998 .

[2]  Carroll,et al.  Short wavelength bifurcations and size instabilities in coupled oscillator systems. , 1995, Physical review letters.

[3]  Junjie Jiang,et al.  Model-free prediction of spatiotemporal dynamical systems with recurrent neural networks: Role of network spectral radius , 2019, Physical Review Research.

[4]  Xingang Wang,et al.  Network synchronization with periodic coupling. , 2018, Physical review. E.

[5]  Thomas L. Carroll,et al.  Using reservoir computers to distinguish chaotic signals , 2018, Physical Review E.

[6]  Marc Bocquet,et al.  Combining data assimilation and machine learning to emulate a dynamical model from sparse and noisy observations: a case study with the Lorenz 96 model , 2019, J. Comput. Sci..

[7]  B R Hunt,et al.  Local low dimensionality of atmospheric dynamics. , 2001, Physical review letters.

[8]  Marjan Kuchaki Rafsanjani,et al.  Chaotic time series prediction by artificial neural networks , 2016, J. Comput. Methods Sci. Eng..

[9]  Harald Haas,et al.  Harnessing Nonlinearity: Predicting Chaotic Systems and Saving Energy in Wireless Communication , 2004, Science.

[10]  Henry Markram,et al.  Real-Time Computing Without Stable States: A New Framework for Neural Computation Based on Perturbations , 2002, Neural Computation.

[11]  Yoshitaka Saiki,et al.  Machine-learning inference of fluid variables from data using reservoir computing. , 2018, Physical review. E.

[12]  Edward Ott,et al.  Attractor reconstruction by machine learning. , 2018, Chaos.

[13]  T Kapitaniak,et al.  Experimental observation of ragged synchronizability. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  Duong Tuan Anh,et al.  Chaotic Time Series Prediction Using Radial Basis Function Networks , 2018, 2018 4th International Conference on Green Technology and Sustainable Development (GTSD).

[15]  Laurent Larger,et al.  High-Speed Photonic Reservoir Computing Using a Time-Delay-Based Architecture: Million Words per Second Classification , 2017 .

[16]  Bernd Blasius,et al.  Complex dynamics and phase synchronization in spatially extended ecological systems , 1999, Nature.

[17]  Istvan Szunyogh,et al.  A Local Ensemble Kalman Filter for Atmospheric Data Assimilation , 2002 .

[18]  Jaideep Pathak,et al.  Using machine learning to replicate chaotic attractors and calculate Lyapunov exponents from data. , 2017, Chaos.

[19]  Herbert Jaeger,et al.  Echo State Property Linked to an Input: Exploring a Fundamental Characteristic of Recurrent Neural Networks , 2013, Neural Computation.

[20]  David S. Broomhead,et al.  Multivariable Functional Interpolation and Adaptive Networks , 1988, Complex Syst..

[21]  Jaideep Pathak,et al.  Model-Free Prediction of Large Spatiotemporally Chaotic Systems from Data: A Reservoir Computing Approach. , 2018, Physical review letters.

[22]  D. Broomhead,et al.  Radial Basis Functions, Multi-Variable Functional Interpolation and Adaptive Networks , 1988 .

[23]  J. Hindmarsh,et al.  A model of neuronal bursting using three coupled first order differential equations , 1984, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[24]  M. Cross,et al.  Pattern formation outside of equilibrium , 1993 .

[25]  Michael Small,et al.  Synchronization of chaotic systems and their machine-learning models. , 2019, Physical review. E.

[26]  E. Lorenz.  Deterministic nonperiodic flow , 1963 .

[27]  R. Brockett,et al.  Reservoir observers: Model-free inference of unmeasured variables in chaotic systems. , 2017, Chaos.

[28]  Wenting Han,et al.  Prediction of multivariate chaotic time series via radial basis function neural network , 2013, Complex..

[29]  Babak Nadjar Araabi,et al.  Predicting Chaotic Time Series Using Neural and Neurofuzzy Models: A Comparative Study , 2006, Neural Processing Letters.

[30]  Miguel C. Soriano,et al.  Reservoir computing with a single time-delay autonomous Boolean node , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[31]  L Chen,et al.  Synchronization with on-off coupling: Role of time scales in network dynamics. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[32]  O. Rössler.  An equation for continuous chaos , 1976 .

[33]  Przemyslaw Perlikowski,et al.  Ragged synchronizability of coupled oscillators. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[34]  F. Girosi,et al.  Networks for approximation and learning , 1990, Proc. IEEE.

[35]  Istvan Szunyogh,et al.  Assessing a local ensemble Kalman filter : perfect model experiments with the National Centers for Environmental Prediction global model , 2004 .

[36]  I. Aranson,et al.  The world of the complex Ginzburg-Landau equation , 2001, cond-mat/0106115.

[37]  Michelle Girvan,et al.  Hybrid Forecasting of Chaotic Processes: Using Machine Learning in Conjunction with a Knowledge-Based Model , 2018, Chaos.

[38]  Ulrich Parlitz,et al.  Observing spatio-temporal dynamics of excitable media using reservoir computing. , 2018, Chaos.