Long-term prediction of chaotic systems with machine learning

H Fan, J Jiang, C Zhang, X Wang, YC Lai - Physical Review Research, 2020 - APS
Reservoir computing systems, a class of recurrent neural networks, have recently been
exploited for model-free, data-based prediction of the state evolution of a variety of chaotic …

Synchronization of chaotic systems and their machine-learning models

T Weng, H Yang, C Gu, J Zhang, M Small - Physical Review E, 2019 - APS
Recent advances have demonstrated the effectiveness of a machine-learning approach
known as “reservoir computing” for model-free prediction of chaotic systems. We find that a …

[HTML][HTML] Predicting phase and sensing phase coherence in chaotic systems with machine learning

C Zhang, J Jiang, SX Qu, YC Lai - Chaos: An Interdisciplinary Journal …, 2020 - pubs.aip.org
Recent interest in exploiting machine learning for model-free prediction of chaotic systems
focused on the time evolution of the dynamical variables of the system as a whole, which …

A systematic exploration of reservoir computing for forecasting complex spatiotemporal dynamics

JA Platt, SG Penny, TA Smith, TC Chen, HDI Abarbanel - Neural Networks, 2022 - Elsevier
A reservoir computer (RC) is a type of recurrent neural network architecture with
demonstrated success in the prediction of spatiotemporally chaotic dynamical systems. A …

Model-free prediction of large spatiotemporally chaotic systems from data: A reservoir computing approach

J Pathak, B Hunt, M Girvan, Z Lu, E Ott - Physical review letters, 2018 - APS
We demonstrate the effectiveness of using machine learning for model-free prediction of
spatiotemporally chaotic systems of arbitrarily large spatial extent and attractor dimension …

[HTML][HTML] Hybrid forecasting of chaotic processes: Using machine learning in conjunction with a knowledge-based model

J Pathak, A Wikner, R Fussell, S Chandra… - … Journal of Nonlinear …, 2018 - pubs.aip.org
A model-based approach to forecasting chaotic dynamical systems utilizes knowledge of the
mechanistic processes governing the dynamics to build an approximate mathematical …

Backpropagation algorithms and reservoir computing in recurrent neural networks for the forecasting of complex spatiotemporal dynamics

PR Vlachas, J Pathak, BR Hunt, TP Sapsis, M Girvan… - Neural Networks, 2020 - Elsevier
We examine the efficiency of Recurrent Neural Networks in forecasting the spatiotemporal
dynamics of high dimensional and reduced order complex systems using Reservoir …

[HTML][HTML] Emerging opportunities and challenges for the future of reservoir computing

M Yan, C Huang, P Bienstman, P Tino, W Lin… - Nature …, 2024 - nature.com
Reservoir computing originates in the early 2000s, the core idea being to utilize dynamical
systems as reservoirs (nonlinear generalizations of standard bases) to adaptively learn …

Robust optimization and validation of echo state networks for learning chaotic dynamics

A Racca, L Magri - Neural Networks, 2021 - Elsevier
An approach to the time-accurate prediction of chaotic solutions is by learning temporal
patterns from data. Echo State Networks (ESNs), which are a class of Reservoir Computing …

[HTML][HTML] Forecasting chaotic systems with very low connectivity reservoir computers

A Griffith, A Pomerance, DJ Gauthier - Chaos: An Interdisciplinary …, 2019 - pubs.aip.org
We explore the hyperparameter space of reservoir computers used for forecasting of the
chaotic Lorenz'63 attractor with Bayesian optimization. We use a new measure of reservoir …