Storing only rolling mean and variance when solving SDEProblems

Specific Domains Modelling & Simulations
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5

Thanks for the suggestions, I really need to how Refs work, as I am not yet familiar with them. In the meantime, I also have managed to find an implementation that relies on a FunctionCallingCallback that simply updates a value in an array. The relevant code is as follows:

function functioncallback(saved_value)
        du = zeros(Float64, S)
        #~ Define Welford's algorithm for rolling mean and variance
        #!note: need to be properly weighted by the current time
        function f(u, t, integrator)
            #~ Compute differences and update mean and sum of squared differences
            du .= u .- saved_value[:,1]
            saved_value[:,1] .= saved_value[:,1] .+ du .* (dt / (t - tstart))
            saved_value[:,2] .= saved_value[:,2] .+ du .* (u .- saved_value[:,1]) .* dt
            return nothing
        end
        #!note: start at tstart=dt to avoid Δt=0
        funcat = (tstart+dt):dt:prob.tspan[end]
        return FunctionCallingCallback(f, funcat=funcat)
    end

This seems to allocate the same amount regardless of dt, which is exactly the behavior that I would expect. It also appears to be thread-safe, but I am not sure whether it actually is…