Title: Guidelines for choosing hyperparameters of echo state networks for system identification: two case studies

Authors: Thiago de Almeida Ushikoshi; Luis Antonio Aguirre

Addresses: Programa de Pós-Graduação em Engenharia Elétrica, Universidade Federal de Minas Gerais, Av. Antonio Carlos 6627, 31270-901, Belo Horizonte, MG, Brazil ' Departamento de Engenharia Eletrônica, Universidade Federal de Minas Gerais, Av. Antonio Carlos 6627, 31270-901, Belo Horizonte, MG, Brazil

Abstract: Echo state networks (ESN) can be used to model dynamical systems in the context of reservoir computing using standard regression algorithms, which is one of their main advantages. However, there are some hyperparameters that need to be carefully chosen and there is no general recommendation on how to perform this important step. After setting the ESN paradigm for system identification, this paper describes the choice of hyperparameters in the context of two case studies: one using experimental data of a pilot heater and the other using the Duffing-Ueda oscillator with chaotic dynamics. The main findings are: 1) ESNs can reproduce the chaotic regime of the Duffing-Ueda oscillator for a specific region on the hyperparameter space; 2) some hyperparameters may not be critical from a statistical perspective but can still drastically affect the dynamical regime; 3) the ESN initialisation is not critical when the hyperparameters are adequately chosen.

Keywords: reservoir computing; echo state networks; ESN; guidelines for echo state networks; hyperparameters of echo state networks; nonlinear models; system identification; dynamical system identification; modelling; chaotic oscillators.

DOI: 10.1504/IJMIC.2023.129483

International Journal of Modelling, Identification and Control, 2023 Vol.42 No.2, pp.105 - 115

Received: 26 Mar 2022
Accepted: 26 Mar 2022
Published online: 10 Mar 2023 *

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