Biological processes, including those involved in cancer, are often characterised by decision-making systems when cells adjust their behaviour in response to external stimuli. When accounting for stochasticity in the internal dynamics of cells, theoretical models of these processes 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.

We use the large deviation theory to decrease the computational cost of a spatially extended multi-agent stochastic system with a region of multistability by coarse-graining it to a continuous-time Markov chain on the state space of stable steady states of the original system. Our coarse-graining technique preserves the original description of the stable steady states of the system and accounts for noise-induced transitions between them.

We illustrate the method with 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. Our results show that the coarse-graining technique allows us to substantially reduce the computational cost of simulations while preserving the rich dynamics of the stochastic system.