An algorithm for training multi-hidden-layer neural networks is presented. The algorithm system for fast training consists of a pseudoinverse matrix least squares procedure used incrementally to solve a nonlinear neural network, together with a preconditioning algorithm to preset the weights for optimum training. The system was applied to the training of chaotic time series from various standard models and compared to corresponding results published in the literature, for the same models using conventional training methods based on the method of steepest descents. In simulation, the training system was shown to obtain equivalent accuracy in a few minutes on a 80386 level PC, whereas the conventional backpropagation algorithm requires considerably more time on a CRAY supercomputer.
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