Relative entropy minimizing noisy non-linear neural network to   approximate stochastic processes
  A method is provided for designing and training noise-driven recurrent neural networks as models of stochastic processes. The method unifies and generalizes two known separate modeling approaches, Echo State Networks (ESN) and Linear Inverse Modeling (LIM), under the common principle of relative entropy minimization. The power of the new method is demonstrated on a stochastic approximation of the El Nino phenomenon studied in climate research. 
Mathieu N. Galtier and Camille Marini and Gilles Wainrib and Herbert   Jaeger
nlin.AO