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