Abstract
Echo state network (ESN) is a new paradigm for using recurrent neural networks (RNNs) with a simpler training method, where an RNN is generated randomly and only a readout is trained. ESN method has quickly become popular in modeling for nonlinear dynamic systems. However, the classical training method for ESNs can not ensure the dynamics asymptotic stability any more if the trained ESNs run in a closed-loop self-generative mode. The reason is analyzed at first. We then consider the ESN training problem as an optimization problem with a nonlinear constraint, and take a particle swarm optimization (PSO) algorithm solve it. In the simulation experiments, the ESNs are trained as “figure-eight” trajectory generators. The results show that the proposed PSO-based training method can effectively ensure the dynamics asymptotic stability as well as the precision of generating trajectories of the trained ESNs.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Jaeger, H., Haass, H.: Harnessing nonlinearity: predicting chaotic systems and saving energy in wireless communication. Science 304, 78–80 (2004)
Haykin, S.: Neural networks – a comprehensive foundation. Prentice-Hall, NJ (1999)
Lukoševičius, M., Jaeger, H.: Reservoir computing approaches to recurrent neural network training. Computer Science Review (in press) doi:10.1016/j.cosrev.2009.03.005
Jaeger, H.: The echo state approach to analyzing and training recurrent neural networks. GMD Report 148, German National Research Center for Information Technology (2001)
Jaeger, H.: Tutorial on training recurrent neural networks, covering BPTT, RTRL, EKF and the “echo state network” approach. Tech. Rep. No. 159, Bremen: German National Research Center for Information Technology (2002)
Jaeger, H.: Echo state network. Scholarpedia 2, 2330 (2007)
Oden, J.T.: Applied Functional Analysis. Prentice-Hall, NJ (1979)
Jaeger, H., Lukoševičius, M., Popovici, D., Siewert, U.: Optimization and applications of echo state networks with leaky-integrator neurons. Neural Networks 20, 335–352 (2007)
Clerc, M.: Particle Swarm Optimization. Wiley-ISTE (2006)
Maass, W., Natschläger, T., Markram, H.: Real-time computing without stable states: A new framework for neural computation based on perturbations. Neural Computation 14, 2531–2560 (2002)
Eberhart, R.C., Shi, Y.: Comparing inertia weights and constriction factors in particle swarm optimization. In: Proceedings of the 2000 Congress on Evolutionary Computation, vol. 1, pp. 84–88 (2000)
Clerc, M.: The Swarm and the Queen: Towards a Deterministic and Adaptive Particle Swarm Optimization. In: Proc. 1999 ICEC, Washington, DC, pp. 1951–1957 (1999)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Song, Q., Feng, Z., Wang, Y. (2009). Stable Training Method for Echo State Networks Running in Closed-Loop Based on Particle Swarm Optimization Algorithm. In: Leung, C.S., Lee, M., Chan, J.H. (eds) Neural Information Processing. ICONIP 2009. Lecture Notes in Computer Science, vol 5864. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10684-2_28
Download citation
DOI: https://doi.org/10.1007/978-3-642-10684-2_28
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-10682-8
Online ISBN: 978-3-642-10684-2
eBook Packages: Computer ScienceComputer Science (R0)