The work presented in this paper aims at developing a novel meshless parameter estimation framework for a system of partial differential equations (PDEs) using artificial neural network (ANN) approximations. The PDE models to be treated consist of linear and nonlinear PDEs, with Dirichlet and Neumann boundary conditions, considering both regular and irregular boundaries. This paper focuses on testing the applicability of neural networks for estimating the process model parameters while simultaneously computing the model predictions of the state variables in the system of PDEs representing the process. The capability of the proposed methodology is demonstrated with five numerical problems, showing that the ANN-based approach is very efficient by providing accurate solutions in reasonable computing times
