Hey! I want to integrate a system of 40+ differential equations each with independent additive white noise. With the current implementation I’m trying this is using way too much memory and is too slow. A minimal example of this is:

```
using StochasticDiffEq, DiffEqNoiseProcess, OrdinaryDiffEq
function system!(du, u, p, t)
du .= 0
end
function noise!(du, u, p, t)
noise = p[1]
du .= noise
end
function test_memory_usage()
N = 40
noise = 0.1
ps = [noise]
u0s = ones(Float64, N)
tend = 50000.0
ttrans = 0.0
noise_seed = 1
alg = EM()
dt = 0.01
Δt = 10.0
#1. For reference, integrate without noise
prob_ode = ODEProblem(system!, u0s, (0.0, tend), ps)
sol_ode = @time solve(prob_ode, Euler(); dt, saveat=ttrans:Δt:tend)
#2. with the Wiener Process it's way too slow
W = WienerProcess(0.0, zeros(length(u0s)))
prob_independent_noise = SDEProblem(system!, noise!, u0s, (0.0, tend), ps, noise=W)
sol_inde = @time solve(prob_independent_noise, alg; dt, saveat=ttrans:Δt:tend, seed=noise_seed);
#3. in place doesn't help
W = WienerProcess!(0.0, zeros(length(u0s)))
prob_independent_noise_inplace = SDEProblem(system!, noise!, u0s, (0.0, tend), ps, noise=W)
sol_inde_in = @time solve(prob_independent_noise_inplace, alg; dt, saveat=ttrans:Δt:tend, seed=noise_seed);
#4. without the Wiener Processes it's way faster, but not the same result.
prob_independent_noise_2 = SDEProblem(system!, noise!, u0s, (0.0, tend), ps)
sol_inde_2 = @time solve(prob_independent_noise_2, alg; dt, saveat=ttrans:Δt:tend, seed=noise_seed);
#5. Single process, with dependent noise is also fast.
W = WienerProcess(0.0, 0.0)
prob_dependent_noise = SDEProblem(system!, noise!, u0s, (0.0, tend), ps, noise=W)
sol_de = @time solve(prob_dependent_noise, alg; dt, saveat=ttrans:Δt:tend, seed=noise_seed)
nothing
end
```

The results I got are:

```
1.925835 seconds (2.47 M allocations: 136.644 MiB, 69.99% compilation time)
15.889349 seconds (42.77 M allocations: 13.568 GiB, 35.68% gc time, 17.75% compilation time)
7.392910 seconds (13.65 M allocations: 4.117 GiB, 29.45% gc time, 21.90% compilation time)
2.718504 seconds (2.95 M allocations: 143.125 MiB, 47.44% compilation time)
2.235974 seconds (3.59 M allocations: 396.477 MiB, 61.13% compilation time)
```

I also don’t understand why case 4 does not lead to the same result as case 1.

Could someone please help me here? I’m guessing I’m messing something up, but have no clue what.

Thanks a lot!