Neural network identification of uncertain 2D partial differential equations

There are many examples in science and engineering which are reduced to a set of partial differential equations (PDE's) through a process of mathematical modeling. Nevertheless there exist many sources of uncertainties around the aforementioned mathematical representation. It is well known that neural networks can approximate a large set of continuous functions defined on a compact set to an arbitrary accuracy. In this paper a strategy based on DNN for the non parametric identification of a mathematical model described by a class of two dimensional (2D) partial differential equations is proposed. The adaptive laws for weights ensure the "practical stability" of the DNN trajectories to the parabolic 2D-PDE states. To verify the qualitative behavior of the suggested methodology, here a non parametric modeling problem for a distributed parameter plant is analyzed.