  The Echo State Network (ESN) is a class of Recurrent Neural Network with a
large number of hidden-hidden weights (in the so-called reservoir). Canonical
ESN and its variations have recently received significant attention due to
their remarkable success in the modeling of non-linear dynamical systems. The
reservoir is randomly connected with fixed weights that don't change in the
learning process. Only the weights from reservoir to output are trained. Since
the reservoir is fixed during the training procedure, we may wonder if the
computational power of the recurrent structure is fully harnessed. In this
article, we propose a new computational model of the ESN type, that represents
the reservoir weights in the Fourier space and performs a fine-tuning of these
weights applying genetic algorithms in the frequency domain. The main interest
is that this procedure will work in a much smaller space compared to the
classical ESN, thus providing a dimensionality reduction transformation of the
initial method. The proposed technique allows us to exploit the benefits of the
large recurrent structure avoiding the training problems of gradient-based
method. We provide a detailed experimental study that demonstrates the good
performances of our approach with well-known chaotic systems and real-world
data.
