A Python Framework for Fast Modelling and Simulation of Cellular Nonlinear Networks and other Finite-difference Time-domain Systems

Abstract

This paper introduces and evaluates a freely available cellular nonlinear network simulator optimized for the effective use of GPUs, to achieve fast modelling and simulations. Its relevance is demonstrated for several applications in nonlinear complex dynamical systems, such as slow-growth phenomena as well as for various image processing applications such as edge detection. The simulator is designed as a Jupyter notebook written in Python and functionally tested and optimized to run on the freely available cloud platform Google Collaboratory. Although the simulator, in its actual form, is designed to model the FitzHugh Nagumo Reaction-Diffusion cellular nonlinear network, it can be easily adapted for any other type of finite-difference time-domain model. Four implementation versions are considered, namely using the PyCUDA, NUMBA respectively CUPY libraries (all three supporting GPU computations) as well as a NUMPY-based implementation to be used when GPU is not available. The specificities and performances for each of the four implementations are analyzed concluding that the PyCUDA implementation ensures a very good performance being capable to run up to 14000 Mega cells per seconds (each cell referring to the basic nonlinear dynamic system composing the cellular nonlinear network).