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Gene regulatory networks allow us to study and understand genes' roles in biological processes. Among others, regulatory networks help to identify pathway initiator genes and therefore potential drug targets. In this paper, we discuss mining temporal microarray data for regulatory network information. For this study we have used simulated data in order to be able to verify our results. The data set was generated using a simulation model similar to the model proposed by Wahde and Hertz (2001). For data mining, we have used order estimation criteria, in conjunction with artificial neural networks. This approach allows us to incorporate a priori biological knowledge, and thereby reduces dimensionality. This in turn produces more determined and accurate models of regulatory networks. Our experiments show that this approach produces more determined and more accurate models of the regulatory network. This was especially true in cases where the number of genes is much greater than the number of time points at which gene expression is measured.