Scale-splitting error in complex automata models for reaction-diffusion systems

Complex Automata (CxA) have been recently proposed as a paradigm for the simulation of multiscale systems. A CxA model is constructed decomposing a multiscale process into single scale sub-models, each simulated using a Cellular Automata algorithm, interacting across the scales via appropriate coupling templates. Focusing on a reactiondiffusion system, we introduce a mathematical framework for CxA modeling. We aim at the identification of error sources in the modeling stages, investigating in particular how the errors depend upon scale separation. Theoretical error estimates will be presented and numerically validated on a simple benchmark, based on a periodic reaction-diffusion problem solved via multistep lattice Boltzmann method.