# Storing only rolling mean and variance when solving SDEProblems

**URL:** <https://discourse.julialang.org/t/storing-only-rolling-mean-and-variance-when-solving-sdeproblems/125900>\
**Category:** Modelling & Simulations\
**Tags:** differentialequation, diffeqcallbacks\
**Created:** [February 14, 2025, 11:46am UTC](https://discourse.julialang.org/t/storing-only-rolling-mean-and-variance-when-solving-sdeproblems/125900 "2025-02-14T11:46:16Z")\
**Posts on this page:** 1\
**Showing post:** 5

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**Author:** ![johannesnauta](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/johannesnauta/32/47434_2.png) [@johannesnauta](https://discourse.julialang.org/u/johannesnauta)\
**Post date:** [February 17, 2025, 12:06pm UTC](https://discourse.julialang.org/t/storing-only-rolling-mean-and-variance-when-solving-sdeproblems/125900/5 "2025-02-17T12:06:41Z")

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Thanks for the suggestions, I really need to how `Ref`s 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:

```julia
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…

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