This paper presents an online learning scheme to train a Cellular Neural Network (CNN) which can be used to model multidimensional systems whose dynamics are governed by Partial Differential Equations (PDE). Most of the existing works in the literature employ fixed parameters which in turn implies an exact knowledge about the underlying PDE and/or its parameters. Moreover, there is a lack of a fast, online and robust training method in the field of cellular neural networks. The learning method presented in this paper is a modified online backpropagation (BP) algorithm. The modification is concerned with adding a damping term which enhances the robustness of the training scheme. The other modification is the formulation of computation of the gradients in a stable fashion. To evaluate the performance of the training scheme, a set of simulations are performed on two-dimensional mechanical vibration problem. The results obtained by using CNN are compared to those obtained by Finite Element Method (FEM).