Use of CNN processors for ultra-fast solution ODE’s and PDE‘s: A renaissance of the analog computer

Abstract:
Setting analog cellular computers based on cellular neural networks systems (CNNs) to change the way analog signals are processed is a revolutionary idea and a proof as well of the high importance devoted to the analog simulation methods. This paper provides basics of the methods based on the CNNs paradigm that can be exploited for analog simulation of very complex systems which are modelled by ODEs and/or PDEs (an implementation on chip using CNN technology is possible even in FPGA). A proof of concept of the simulation approach developed in this paper is validated by solving some complex ODEs and/or PDEs models and by comparing the results obtained with those available in the literature (benchmarking). The computation based CNNs paradigm is advantageous as it provides accurate and ultra-fast solutions of very complex ODEs and PDEs.