Spatial Jump Simulations

Our introduction to spatial lattice simulations has already described how to simulate LatticeReactionSystems using ODEs. Jump simulations of LatticeReactionSystem are carried out using an almost identical approach. However, just like for non-spatial models, we must first create a DiscreteProblem, which is then used as input to our JumpProblem. Furthermore, a spatial jump aggregator (like NSM) can be used. Spatial jump simulations in Catalyst are built on top of JumpProcesses.jl's spatial jump simulators, more details on which can be found here.

Below we perform a spatial jump simulation of a simple birth-death process. Note that we use our LatticeReactionSystem as input to both our DiscreteProblem and JumpProblem, and that we provide the spatial NSM jump aggregator to JumpProblem.

using Catalyst, JumpProcesses
bd_model = @reaction_network begin
    (p,d), 0 <--> X
end
diffusion_rx = @transport_reaction D X
lattice = CartesianGrid((10,10))
lrs = LatticeReactionSystem(bd_model, [diffusion_rx], lattice)

u0 = [:X => 0]
tspan = (0.0, 200.0)
ps = [:p => 10.0, :d => 1.0, :D => 0.1]
dprob = DiscreteProblem(lrs, u0, tspan, ps)
jprob = JumpProblem(lrs, dprob, NSM())
sol = solve(jprob, SSAStepper())

We can now access the values of sol using the interfaces described here, and plot it using the functions described here.

Currently, the only available spatial jump aggregators are NSM and DirectCRDirect, with DirectCRDirect expected to perform better for large networks.