Emulated digital CNN‐UM solution of partial differential equations

Abstract

AbstractWe present here new cellular neural/non‐linear networks (CNN)‐based emulated digital architectures specifically designed for the solution of different partial differential equations (PDE). The array structure and local connectivity of the CNN paradigm make it a natural framework to describe the behaviour of locally interconnected dynamical systems. Solution of the PDE is carried out by a spatio‐temporal dynamics, which can be computed in real‐time on analogue CNN‐UM chips, but the accuracy of the solution is low. Additionally, solution of PDEs on a CNN‐UM architecture often requires a multi‐layer structure and non‐linear templates which is partially or not supported on the current analogue VLSI CNN‐UM chips. To overcome these obstacles while preserving high computing performance a configurable emulated digital CNN‐UM can be used where the main parameters (accuracy, template size and number of layers) are configurable. Additionally, the symmetry of the finite difference operators makes it possible to specialize the emulated digital CNN‐UM architecture to solve a specific type of PDE, which results in higher performance. Emulated digital CNN‐UM processors use fixed‐point numbers to carry out computations, and by decreasing the precision the speed of the computations can be improved. Hence, a simple algorithm is introduced to determine the optimal fixed‐point precision and maximize computing performance. Copyright © 2006 John Wiley & Sons, Ltd.