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Neural Modeling of Non-Linear Processes: Relevance of the Takens-Mane Theorem

In this paper, we test a constructive methodology for shaping neural networks models of non-linear dynamic systems. The method is supported by results and prescriptions related to the Takens-Mañé theorem, and is based on the measurement of the first minimum of the mutual information of the output signal, and in the application of the method of global false nearest neighbors to determine the embedding dimension. We present a numerical experiment to assess this constructive approach to the identification of a non-linear dynamic system and the application to the design of a neural network to forecasting a time series generated by an accelerometer coupled to a 150 MW steam turbine.