Reservoir computing with error correction: Long-term behaviors of stochastic dynamical systems

Fang, Cheng; Lu, Yubin; Gao, Ting; Duan, Jinqiao

doi:10.1016/j.physd.2023.133919

Title: Reservoir computing with error correction: Long-term behaviors of stochastic dynamical systems

Journal Article · 01 December 2023 · Physica. D, Nonlinear Phenomena

DOI: https://doi.org/10.1016/j.physd.2023.133919 · OSTI ID:2007096

Fang, Cheng;

; Gao, Ting; Duan, Jinqiao

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Sponsoring Organization:: USDOE

Grant/Contract Number:: USA DE-SC00222766

OSTI ID:: 2007096

Journal Information:: Physica. D, Nonlinear Phenomena, Journal Name: Physica. D, Nonlinear Phenomena Vol. 456 Journal Issue: C; ISSN 0167-2789

Publisher:: ElsevierCopyright Statement

Country of Publication:: Netherlands

Language:: English

References (48)

Tipping points in open systems: bifurcation, noise-induced and rate-dependent examples in the climate system Ashwin, Peter; Wieczorek, Sebastian; Vitolo, Renato Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 370, Issue 1962 https://doi.org/10.1098/rsta.2011.0306	journal	March 2012
Discovering transition phenomena from data of stochastic dynamical systems with Lévy noise Lu, Yubin; Duan, Jinqiao Chaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 30, Issue 9 https://doi.org/10.1063/5.0004450	journal	September 2020
Learning unseen coexisting attractors Gauthier, Daniel J.; Fischer, Ingo; Röhm, André Chaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 32, Issue 11 https://doi.org/10.1063/5.0116784	journal	November 2022
Stochastic approach for assessing the predictability of chaotic time series using reservoir computing Khovanov, I. A. Chaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 31, Issue 8 https://doi.org/10.1063/5.0058439	journal	August 2021
A Delayed Action Oscillator for ENSO Suarez, Max J.; Schopf, Paul S. Journal of the Atmospheric Sciences, Vol. 45, Issue 21 https://doi.org/10.1175/1520-0469(1988)045<3283:ADAOFE>2.0.CO;2	journal	November 1988
Normalizing Flows: An Introduction and Review of Current Methods Kobyzev, Ivan; Prince, Simon; Brubaker, Marcus IEEE Transactions on Pattern Analysis and Machine Intelligence https://doi.org/10.1109/TPAMI.2020.2992934	journal	January 2020
Fading memory and the problem of approximating nonlinear operators with Volterra series Boyd, S.; Chua, L. IEEE Transactions on Circuits and Systems, Vol. 32, Issue 11 https://doi.org/10.1109/TCS.1985.1085649	journal	November 1985
Maximal stochastic transport in the Lorenz equations Agarwal, Sahil; Wettlaufer, J. S. Physics Letters A, Vol. 380, Issue 1-2 https://doi.org/10.1016/j.physleta.2015.09.046	journal	January 2016
Detecting stochastic governing laws with observation on stationary distributions Chen, Xiaoli; Wang, Hui; Duan, Jinqiao Physica D: Nonlinear Phenomena, Vol. 448 https://doi.org/10.1016/j.physd.2023.133691	journal	June 2023
Learning effective stochastic differential equations from microscopic simulations: Linking stochastic numerics to deep learning Dietrich, Felix; Makeev, Alexei; Kevrekidis, George Chaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 33, Issue 2 https://doi.org/10.1063/5.0113632	journal	February 2023
Using machine learning to anticipate tipping points and extrapolate to post-tipping dynamics of non-stationary dynamical systems Patel, Dhruvit; Ott, Edward Chaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 33, Issue 2 https://doi.org/10.1063/5.0131787	journal	February 2023
Recent advances in physical reservoir computing: A review Tanaka, Gouhei; Yamane, Toshiyuki; Héroux, Jean Benoit Neural Networks, Vol. 115 https://doi.org/10.1016/j.neunet.2019.03.005	journal	July 2019
Model-Free Prediction of Large Spatiotemporally Chaotic Systems from Data: A Reservoir Computing Approach Pathak, Jaideep; Hunt, Brian; Girvan, Michelle Physical Review Letters, Vol. 120, Issue 2 https://doi.org/10.1103/PhysRevLett.120.024102	journal	January 2018
Reservoir Computing Universality With Stochastic Inputs Gonon, Lukas; Ortega, Juan-Pablo IEEE Transactions on Neural Networks and Learning Systems, Vol. 31, Issue 1 https://doi.org/10.1109/TNNLS.2019.2899649	journal	January 2020
Forecasting chaotic systems with very low connectivity reservoir computers Griffith, Aaron; Pomerance, Andrew; Gauthier, Daniel J. Chaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 29, Issue 12 https://doi.org/10.1063/1.5120710	journal	December 2019
Sparse learning of stochastic dynamical equations Boninsegna, Lorenzo; Nüske, Feliks; Clementi, Cecilia The Journal of Chemical Physics, Vol. 148, Issue 24 https://doi.org/10.1063/1.5018409	journal	June 2018
Stochastic weather and climate models Palmer, T. N. Nature Reviews Physics, Vol. 1, Issue 7 https://doi.org/10.1038/s42254-019-0062-2	journal	May 2019
Harnessing Nonlinearity: Predicting Chaotic Systems and Saving Energy in Wireless Communication Jaeger, H. Science, Vol. 304, Issue 5667 https://doi.org/10.1126/science.1091277	journal	April 2004
Predicting critical transitions in multiscale dynamical systems using reservoir computing Lim, Soon Hoe; Theo Giorgini, Ludovico; Moon, Woosok Chaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 30, Issue 12 https://doi.org/10.1063/5.0023764	journal	December 2020
Extracting stochastic governing laws by non-local Kramers–Moyal formulae Lu, Yubin; Li, Yang; Duan, Jinqiao Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 380, Issue 2229 https://doi.org/10.1098/rsta.2021.0195	journal	June 2022
Using machine learning to replicate chaotic attractors and calculate Lyapunov exponents from data Pathak, Jaideep; Lu, Zhixin; Hunt, Brian R. Chaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 27, Issue 12 https://doi.org/10.1063/1.5010300	journal	December 2017
An end-to-end deep learning approach for extracting stochastic dynamical systems withα-stable Lévy noise Fang, Cheng; Lu, Yubin; Gao, Ting Chaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 32, Issue 6 https://doi.org/10.1063/5.0089832	journal	June 2022
A framework for machine learning of model error in dynamical systems Levine, Matthew; Stuart, Andrew Communications of the American Mathematical Society, Vol. 2, Issue 7 https://doi.org/10.1090/cams/10	journal	October 2022
T RANSITION P ATH S AMPLING : Throwing Ropes Over Rough Mountain Passes, in the Dark Bolhuis, Peter G.; Chandler, David; Dellago, Christoph Annual Review of Physical Chemistry, Vol. 53, Issue 1 https://doi.org/10.1146/annurev.physchem.53.082301.113146	journal	October 2002
Classification of hyperchaotic, chaotic, and regular signals using single nonlinear node delay-based reservoir computers Wenkack Liedji, Dagobert; Talla Mbé, Jimmi Hervé; Kenne, Godpromesse Chaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 32, Issue 12 https://doi.org/10.1063/5.0124204	journal	December 2022
Optimization and applications of echo state networks with leaky- integrator neurons Jaeger, Herbert; Lukoševičius, Mantas; Popovici, Dan Neural Networks, Vol. 20, Issue 3 https://doi.org/10.1016/j.neunet.2007.04.016	journal	April 2007
Fading memory echo state networks are universal Gonon, Lukas; Ortega, Juan-Pablo Neural Networks, Vol. 138 https://doi.org/10.1016/j.neunet.2021.01.025	journal	June 2021
Model-free prediction of multistability using echo state network Roy, Mousumi; Mandal, Swarnendu; Hens, Chittaranjan Chaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 32, Issue 10 https://doi.org/10.1063/5.0119963	journal	October 2022
Time evolution of probability density in stochastic dynamical systems with time delays: The governing equation and its numerical solution Sun, Xu; Yang, Fang Chaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 32, Issue 12 https://doi.org/10.1063/5.0125949	journal	December 2022
A New Approach to Linear Filtering and Prediction Problems Kalman, R. E. Journal of Basic Engineering, Vol. 82, Issue 1 https://doi.org/10.1115/1.3662552	journal	March 1960
Deterministic Nonperiodic Flow Lorenz, Edward N. Journal of the Atmospheric Sciences, Vol. 20, Issue 2 https://doi.org/10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2	journal	March 1963
Minimum Complexity Echo State Network Rodan, A.; Tino, P. IEEE Transactions on Neural Networks, Vol. 22, Issue 1 https://doi.org/10.1109/TNN.2010.2089641	journal	January 2011
Re-visiting the echo state property Yildiz, Izzet B.; Jaeger, Herbert; Kiebel, Stefan J. Neural Networks, Vol. 35 https://doi.org/10.1016/j.neunet.2012.07.005	journal	November 2012
A practical method for calculating largest Lyapunov exponents from small data sets Rosenstein, Michael T.; Collins, James J.; De Luca, Carlo J. Physica D: Nonlinear Phenomena, Vol. 65, Issue 1-2 https://doi.org/10.1016/0167-2789(93)90009-P	journal	May 1993
Real-Time Computing Without Stable States: A New Framework for Neural Computation Based on Perturbations Maass, Wolfgang; Natschläger, Thomas; Markram, Henry Neural Computation, Vol. 14, Issue 11 https://doi.org/10.1162/089976602760407955	journal	November 2002
Solving Inverse Stochastic Problems from Discrete Particle Observations Using the Fokker--Planck Equation and Physics-Informed Neural Networks Chen, Xiaoli; Yang, Liu; Duan, Jinqiao SIAM Journal on Scientific Computing, Vol. 43, Issue 3 https://doi.org/10.1137/20M1360153	journal	January 2021
Deep reservoir computing: A critical experimental analysis Gallicchio, Claudio; Micheli, Alessio; Pedrelli, Luca Neurocomputing, Vol. 268 https://doi.org/10.1016/j.neucom.2016.12.089	journal	December 2017
Low-power-consumption physical reservoir computing model based on overdamped bistable stochastic resonance system Liao, Zhiqiang; Wang, Zeyu; Yamahara, Hiroyasu Neurocomputing, Vol. 468 https://doi.org/10.1016/j.neucom.2021.09.074	journal	January 2022
Next generation reservoir computing Gauthier, Daniel J.; Bollt, Erik; Griffith, Aaron Nature Communications, Vol. 12, Issue 1 https://doi.org/10.1038/s41467-021-25801-2	journal	September 2021
Learning the temporal evolution of multivariate densities via normalizing flows Lu, Yubin; Maulik, Romit; Gao, Ting Chaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 32, Issue 3 https://doi.org/10.1063/5.0065093	journal	March 2022
Using machine learning to predict statistical properties of non-stationary dynamical processes: System climate,regime transitions, and the effect of stochasticity Patel, Dhruvit; Canaday, Daniel; Girvan, Michelle Chaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 31, Issue 3 https://doi.org/10.1063/5.0042598	journal	March 2021
On the Mathematics of RNA Velocity I: Theoretical Analysis Li, Tiejun CSIAM Transactions on Applied Mathematics, Vol. 2, Issue 1 https://doi.org/10.4208/csiam-am.SO-2020-0001	journal	June 2021
Machine learning for prediction with missing dynamics Harlim, John; Jiang, Shixiao W.; Liang, Senwei Journal of Computational Physics, Vol. 428 https://doi.org/10.1016/j.jcp.2020.109922	journal	March 2021
Data-driven approximation of the Koopman generator: Model reduction, system identification, and control Klus, Stefan; Nüske, Feliks; Peitz, Sebastian Physica D: Nonlinear Phenomena, Vol. 406 https://doi.org/10.1016/j.physd.2020.132416	journal	May 2020
Learning stochastic dynamics with statistics-informed neural network Zhu, Yuanran; Tang, Yu-Hang; Kim, Changho Journal of Computational Physics, Vol. 474 https://doi.org/10.1016/j.jcp.2022.111819	journal	February 2023
Supervised learning from noisy observations: Combining machine-learning techniques with data assimilation Gottwald, Georg A.; Reich, Sebastian Physica D: Nonlinear Phenomena, Vol. 423 https://doi.org/10.1016/j.physd.2021.132911	journal	September 2021
Transition path sampling and the calculation of rate constants Dellago, Christoph; Bolhuis, Peter G.; Csajka, Félix S. The Journal of Chemical Physics, Vol. 108, Issue 5 https://doi.org/10.1063/1.475562	journal	February 1998
Topological analysis and synthesis of chaotic time series Mindlin, Gabriel M.; Gilmore, R. Physica D: Nonlinear Phenomena, Vol. 58, Issue 1-4 https://doi.org/10.1016/0167-2789(92)90111-Y	journal	September 1992

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