Neural identification of 3D Distributed Parameter Systems

Differential Neural Networks (DNN) state identification of 3D Distributed Parameters Systems is studied in this paper. A lot of examples in science and engineering of systems described mathematically by partial differential equations (PDE's), posses the disadvantage of having many sources of uncertainties around their mathematical representation. Moreover to find the exact solutions of those PDE's is not a trivial task especially if the PDE is described in two or more dimensions. It is well known that neural networks can approximate a large set of continuous functions defined on a compact set to an arbitrary accuracy. A strategy based on DNN for the non parametric identification of a mathematical model described by a class of three dimensional (3D) PDE is proposed. The adaptive laws for weights ensure the "practical stability" of the DNN trajectories to the parabolic 3D-PDE states. To verify the qualitative behavior of the suggested methodology, here a non parametric modeling problem for a distributed parameter plant is analyzed.