Introducing a training methodology for cellular neural networks solving partial differential equations

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 previous work on CNN, employed fixed parameters or learning methods which need many iterations of an algorithm. There is a lack of 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. Another modification is decrease the learning rate to avoid unwanted oscillations. To evaluate the performance of the training scheme a set of simulations are performed on two-dimensional heat conduction problem. The results obtained by using CNN are compared to those of analytic solutions.