Fundamentals of Artificial Neural Networks
Fundamentals of Artificial Neural Networks
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We propose a new neural network residual minimization training method for the reconstruction of nonlinear dynamical systems empirically from observational data. In this method, an unknown dynamical system is expressed as a set of first order ordinary differential equations. The object function consists of squared deviations of the observations from the computed values and squared residuals of the differential equations at evaluation points. An algorithm for the training of the network system over wider assimilation window is employed. The performance of the method is examined over the prediction period by applying it to the chaotic Lorenz system. The results are compared with those computed by auto regression and conventional neural network methods and a considerable improvement in prediction skill is obtained. Its application to data from real climate system is in progress.