  Numerous processes across both the physical and biological sciences are
driven by diffusion. Partial differential equations (PDEs) are a popular tool
for modelling such phenomena deterministically, but it is often necessary to
use stochastic models to accurately capture the behaviour of a system,
especially when the number of diffusing particles is low. The stochastic models
we consider in this paper are `compartment-based': the domain is discretized
into compartments, and particles can jump between these compartments.
Volume-excluding effects (crowding) can be incorporated by blocking movement
with some probability.
  Recent work has established the connection between fine-grained models and
coarse-grained models incorporating volume exclusion, but only for uniform
lattices. In this paper we consider non-uniform, hybrid lattices that
incorporate both fine- and coarse-grained regions, and present two different
approaches to describing the interface of the regions. We test both techniques
in a range of scenarios to establish their accuracy, benchmarking against
fine-grained models, and show that the hybrid models developed in this paper
can be significantly faster to simulate than the fine-grained models in certain
situations, and are at least as fast otherwise.
