This paper presents the state identification study of 3D partial differential equations (PDEs) using the differential neural networks\n(DNNs) approximation. There are so many physical situations in applied mathematics and engineering that can be described by\nPDEs; these models possess the disadvantage of having many sources of uncertainties around their mathematical representation.\nMoreover, to find the exact solutions of those uncertain PDEs is not a trivial task especially if the PDE is described in two or more\ndimensions. Given the continuous nature and the temporal evolution of these systems, differential neural networks are an attractive\noption as nonparametric identifiers capable of estimating a 3D distributed model. The adaptive laws for weights ensure the\nââ?¬Å?practical stabilityââ?¬Â of the DNN trajectories to the parabolic three-dimensional (3D) PDE states. To verify the qualitative behavior\nof the suggested methodology, here a nonparametric modeling problem for a distributed parameter plant is analyzed.
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