# Strange results when using seed kwarg in solve function

**URL:** https://discourse.julialang.org/t/strange-results-when-using-seed-kwarg-in-solve-function/99128
**Category:** Modelling & Simulations
**Tags:** package, sde
**Created:** [May 19, 2023, 5:45pm UTC](https://discourse.julialang.org/t/strange-results-when-using-seed-kwarg-in-solve-function/99128 "2023-05-19T17:45:53Z")
**Posts on this page:** 3
**Page:** 1

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### Author: ![stochasticguy](https://avatars.discourse-cdn.com/v4/letter/s/278dde/32.png) [@stochasticguy](https://discourse.julialang.org/u/stochasticguy)
#### Post date: [May 19, 2023, 5:45pm UTC](https://discourse.julialang.org/t/strange-results-when-using-seed-kwarg-in-solve-function/99128/1 "2023-05-19T17:45:53Z")

</div>

Hi everyone,

First of all I wanted to congratulate you all for this amazing community.

I’m having issues with the solution of a Stochastic Differential Equation (SDE) when passing the seed kwarg to the solve method.

When I don’t pass the seed kwarg, the results I get are reasonable. On the other hand, when I pass the seed kwarg, the results are strange (i.e I get results that are either zero or far away from the expected result). I tried out different random number generators and the results are the same in the sense that are far from the expected ones.

I know that this problem is stochastic. Therefore, I don’t expect the results to be the same when I use different seeds, rngs, etc. But I’m surprised to see how off they are.

Below there’s an example.

```julia

using DifferentialEquations, Parameters, RandomNumbers, Statistics

X0 = 90.0
K = 80.0
r = 0.0
σ = 0.2
p = (m = r, s = σ)

function f(u, p, t)
    @unpack m = p
    m * u
end

function g(u, p, t)
    @unpack s = p
    s * u
end

# Instantiate random number generators
mtw_rng = MersenneTwisters.MT19937()
pcg_rng = PCG.PCGStateOneseq()
pil_rng = Random123.Philox4x()
xor_rng = Xorshifts.Xoroshiro128Plus()

# Create noise processes with the previously created random number generators
W_mtw = WienerProcess(0.0, 1.0, 1.0; rng=mtw_rng)
W_pcg = WienerProcess(0.0, 1.0, 1.0; rng=pcg_rng)
W_pil = WienerProcess(0.0, 1.0, 1.0; rng=pil_rng)
W_xor = WienerProcess(0.0, 1.0, 1.0; rng=xor_rng)

# Create sde problems
sde = SDEProblem{false}(f, g, X0, (0.0, 1.0), p)
sde_mtw = SDEProblem{false}(f, g, X0, (0.0, 1.0), p; noise=W_mtw)
sde_pcg = SDEProblem{false}(f, g, X0, (0.0, 1.0), p; noise=W_pcg)
sde_pil = SDEProblem{false}(f, g, X0, (0.0, 1.0), p; noise=W_pil)
sde_xor = SDEProblem{false}(f, g, X0, (0.0, 1.0), p; noise=W_xor)

function relu(X, p)
    @unpack K, τ = p
    return max(X(τ) - K, 0.0)
end

# Create Ensemble problems using Relu function as output
ens = EnsembleProblem(sde, output_func = (sol, i) -> (relu(sol, (K = K, τ = 1.0)), false))
ens_mtw = EnsembleProblem(sde_mtw, output_func = (sol, i) -> (relu(sol, (K = K, τ = 1.0)), false))
ens_pcg = EnsembleProblem(sde_pcg, output_func = (sol, i) -> (relu(sol, (K = K, τ = 1.0)), false))
ens_pil = EnsembleProblem(sde_pil, output_func = (sol, i) -> (relu(sol, (K = K, τ = 1.0)), false))
ens_xor = EnsembleProblem(sde_xor, output_func = (sol, i) -> (relu(sol, (K = K, τ = 1.0)), false))

# Set seed and number of trajectories
seed = 1234
n = 100_000

# When seed kwarg is passed to the solve method the results are way off 
mean(solve(ens; trajectories=n).u) # The value for this is: 12.96215350985002
mean(solve(ens; trajectories=n, seed=seed).u) # The value for this is: 0.0
mean(solve(ens_mtw; trajectories=n, seed=seed).u) # The value for this is: 0.0
mean(solve(ens_pcg; trajectories=n, seed=seed).u) # The value for this is: 0.0
mean(solve(ens_xor; trajectories=n, seed=seed).u) # The value for this is: 7.115400747775788

# When seed kwarg is NOT passed to the solve method the results are close to the expected
mean(solve(ens; trajectories=n).u) # The value for this is: 12.861788416616768
mean(solve(ens_mtw; trajectories=n).u) # The value for this is: 12.932072289191881
mean(solve(ens_pcg; trajectories=n).u) # The value for this is: 12.879136140283649
mean(solve(ens_xor; trajectories=n).u) # The value for this is: 12.831574338732501

```

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<div class="post-metadata">

### Author: ![ChrisRackauckas](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chrisrackauckas/32/77_2.png) [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)
#### Post date: [May 19, 2023, 5:53pm UTC](https://discourse.julialang.org/t/strange-results-when-using-seed-kwarg-in-solve-function/99128/2 "2023-05-19T17:53:15Z")

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You’re setting the seed for the whole ensemble, so they are all using the same stochastic process. Keyword arguments on a solve of an ensemble process are used for each of the solves. You want to use a different seed for each solve, so you’d want to set the seed in the `prob_func`.

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<div class="post-metadata">

### Author: ![stochasticguy](https://avatars.discourse-cdn.com/v4/letter/s/278dde/32.png) [@stochasticguy](https://discourse.julialang.org/u/stochasticguy)
#### Post date: [May 20, 2023, 12:58pm UTC](https://discourse.julialang.org/t/strange-results-when-using-seed-kwarg-in-solve-function/99128/3 "2023-05-20T12:58:13Z")

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Makes complete sense. Thank you, Chris!