References

Barbosa, W. A.; Griffith, A.; Rowlands, G. E.; Govia, L. C.; Ribeill, G. J.; Nguyen, M.-H.; Ohki, T. A. and Gauthier, D. J. (2021). Symmetry-aware reservoir computing. Physical Review E 104.

Chattopadhyay, A.; Hassanzadeh, P. and Subramanian, D. (2020). Data-driven predictions of a multiscale Lorenz 96 chaotic system using machine-learning methods: reservoir computing, artificial neural network, and long short-term memory network. Nonlinear Processes in Geophysics 27, 373–389.

Cho, K.; Van Merriënboer, B.; Gulcehre, C.; Bahdanau, D.; Bougares, F.; Schwenk, H. and Bengio, Y. (2014). Learning phrase representations using RNN encoder-decoder for statistical machine translation, arXiv preprint arXiv:1406.1078.

Dey, R. and Salem, F. M. (Aug 2017). Gate-variants of Gated Recurrent Unit (GRU) neural networks. In: 2017 IEEE 60th International Midwest Symposium on Circuits and Systems (MWSCAS) (IEEE); pp. 1597–1600.

Elsarraj, D.; Qisi, M. A.; Rodan, A.; Obeid, N.; Sharieh, A. and Faris, H. (2019). Demystifying echo state network with deterministic simple topologies. International Journal of Computational Science and Engineering 19, 407–417.

Fu, J.; Li, G.; Tang, J.; Xia, L.; Wang, L. and Duan, S. (2023). A double-cycle echo state network topology for time series prediction. Chaos: An Interdisciplinary Journal of Nonlinear Science 33.

Gallicchio, C. and Micheli, A. (2017). Deep echo state network (deepesn): A brief survey, arXiv preprint arXiv:1712.04323.

Griffith, A.; Pomerance, A. and Gauthier, D. J. (2019). Forecasting chaotic systems with very low connectivity reservoir computers. Chaos: An Interdisciplinary Journal of Nonlinear Science 29.

Hübner, U.; Abraham, N. B. and Weiss, C. O. (1989). Dimensions and entropies of chaotic intensity pulsations in a single-mode far-infrared<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">NH</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>laser. Physical Review A 40, 6354–6365.

Herteux, J. and Räth, C. (2020). Breaking symmetries of the reservoir equations in echo state networks. Chaos: An Interdisciplinary Journal of Nonlinear Science 30.

Lu, Z.; Pathak, J.; Hunt, B.; Girvan, M.; Brockett, R. and Ott, E. (2017). Reservoir observers: Model-free inference of unmeasured variables in chaotic systems. Chaos: An Interdisciplinary Journal of Nonlinear Science 27.

Lukoševičius, M. (2012). A Practical Guide to Applying Echo State Networks. In: Neural Networks: Tricks of the Trade (Springer Berlin Heidelberg); pp. 659–686.

Lun, S.-X.; Yao, X.-S.; Qi, H.-Y. and Hu, H.-F. (2015). A novel model of leaky integrator echo state network for time-series prediction. Neurocomputing 159, 58–66.

Margem, M. and Yilmaz, O. (2017). An experimental study on cellular automata reservoir in pathological sequence learning tasks.

Nichele, S. and Molund, A. (2017). Deep reservoir computing using cellular automata, arXiv preprint arXiv:1703.02806.

Pathak, J.; Lu, Z.; Hunt, B. R.; Girvan, M. and Ott, E. (2017). Using machine learning to replicate chaotic attractors and calculate Lyapunov exponents from data. Chaos: An Interdisciplinary Journal of Nonlinear Science 27.

Pathak, J.; Wikner, A.; Fussell, R.; Chandra, S.; Hunt, B. R.; Girvan, M. and Ott, E. (2018). Hybrid forecasting of chaotic processes: Using machine learning in conjunction with a knowledge-based model. Chaos: An Interdisciplinary Journal of Nonlinear Science 28.

Rodan, A. and Tino, P. (2011). Minimum Complexity Echo State Network. IEEE Transactions on Neural Networks 22, 131–144.

Rodan, A. and Tiňo, P. (2012). Simple Deterministically Constructed Cycle Reservoirs with Regular Jumps. Neural Computation 24, 1822–1852.

Sarli, D. D.; Gallicchio, C. and Micheli, A. (Aug 2020). Gated Echo State Networks: a preliminary study. In: 2020 International Conference on INnovations in Intelligent SysTems and Applications (INISTA) (IEEE); pp. 1–5.

Viehweg, J.; Poll, C. and Mäder, P. (2025). Deterministic Reservoir Computing for Chaotic Time Series Prediction, arXiv preprint arXiv:2501.15615.

Wang, H.; Liu, Y.; Lu, P.; Luo, Y.; Wang, D. and Xu, X. (2022). Echo state network with logistic mapping and bias dropout for time series prediction. Neurocomputing 489, 196–210.

Wang, X.; Jin, Y. and Hao, K. (Jul 2020). A Gated Recurrent Unit based Echo State Network. In: 2020 International Joint Conference on Neural Networks (IJCNN) (IEEE); pp. 1–7.

Xie, M.; Wang, Q. and Yu, S. (2024). Time Series Prediction of ESN Based on Chebyshev Mapping and Strongly Connected Topology. Neural Processing Letters 56.

Yang, C.; Qiao, J.; Han, H. and Wang, L. (2018). Design of polynomial echo state networks for time series prediction. Neurocomputing 290, 148–160.

Yilmaz, O. (2014). Reservoir computing using cellular automata, arXiv preprint arXiv:1410.0162.