A method to coarse-grain multi-agent stochastic systems with regions of multistability

Hybrid multiscale modelling has emerged as a useful framework for modelling complex biological phenomena. However, when accounting for stochasticity in the internal dynamics of agents, these models frequently become computationally expensive. Traditional techniques to reduce the computational intensity of such models can lead to a reduction in the richness of the dynamics observed, compared to the original system. Here we use large deviation theory to decrease the computational cost of a spatially-extended multi-agent stochastic system with a region of multi-stability by coarse-graining it to a continuous time Markov chain on the state space of stable steady states of the original system. Our technique preserves the original description of the stable steady states of the system and accounts for noise-induced transitions between them. We apply the method to a bistable system modelling phenotype specification of cells driven by a lateral inhibition mechanism. For this system, we demonstrate how the method may be used to explore different pattern configurations and unveil robust patterns emerging on longer timescales. We then compare the full stochastic, coarse-grained and mean-field descriptions via pattern quantification metrics and in terms of the numerical cost of each method. Our results show that the coarse-grained system exhibits the lowest computational cost while preserving the rich dynamics of the stochastic system. The method has the potential to reduce the computational complexity of hybrid multiscale models, making them more tractable for analysis, simulation and hypothesis testing.