Analogic cellular PDE machines

This paper gives an overview on analogic cellular array architectures that can also be used to approximate partial differential equations (PDEs). Cellular arrays are massively parallel computing structures composed of cells placed on a regular grid. These cells interact locally an th e array can have both local and global dynamics. The software of this architecture is an analogic algorithm that builds on analog and logical spatio-temporal instructions of the underlying hardware, that is a locally connected cellular nonlinear network (CNN). Within this framework two classes of PDEs, motivated also by image processing methodologies will be discussed: (i) reaction-diffusion (local) types and (ii) contrast modification (global) types. It will be shown that based on cellular diffusion and wave-computing formulations these classes can be approximated on existing CNN Universal Machine (CNN-UM) chips. Thus, the last generation of stored program topographic array microprocessors with integrated sensing and computing could also be viewed as the first prototypes of analogic cellular PDE machines implemented on silicon.