# Using the noise parameters sol.W.W from an SDE solution throws an error when taking gradients
**URL:** https://discourse.julialang.org/t/using-the-noise-parameters-sol-w-w-from-an-sde-solution-throws-an-error-when-taking-gradients/47640
**Category:** Machine Learning
**Tags:** question, diffeq, sde
**Created:** [October 2, 2020, 1:32pm UTC](https://discourse.julialang.org/t/using-the-noise-parameters-sol-w-w-from-an-sde-solution-throws-an-error-when-taking-gradients/47640 "2020-10-02T13:32:31Z")
**Posts on this page:** 4
**Page:** 1
### Author:  [@MikeKlocCZ](https://discourse.julialang.org/u/MikeKlocCZ)
#### Post date: [October 2, 2020, 1:32pm UTC](https://discourse.julialang.org/t/using-the-noise-parameters-sol-w-w-from-an-sde-solution-throws-an-error-when-taking-gradients/47640/1 "2020-10-02T13:32:31Z")
I need to work with individual Wiener increments from an SDE solution in my loss function. Whenever I try to get these values from `sol.W.W` command, the `ERROR: type Nothing has no field W` pops up when computing the gradients. Can it be a bug in DiffEqSensitivity package?
MWE:
```julia
using DifferentialEquations, Flux, DiffEqFlux
using DiffEqSensitivity
function dt!(du, u, p, t)
x, y = u
α, β, δ, γ = p
du[1] = dx = α*x - β*x*y
du[2] = dy = -δ*y + γ*x*y
end
function dW!(du, u, p, t)
du[1] = 0.1u[1]
du[2] = 0.1u[2]
end
u0 = [1.0,1.0]
tspan = (0.0, 10.0)
p = [2.2, 1.0, 2.0, 0.4]
W = WienerProcess(0.0,0.0,0.0)
prob_sde = SDEProblem(dt!, dW!, u0, tspan,p,noise=W)
function some_loss(p) #some loss function
sol=solve(prob_sde, EM(), saveat = 0.1,sensealg = ForwardDiffSensitivity(), dt=0.001)
Wsum=sum(sol.W.W) #problematic part
println("Wsum=",Wsum)
sum(abs2, x-1 for x in Array(sol))
end
ps = Flux.params(p)
@time gs = gradient(ps) do
some_loss(p)
end #ERROR: type Nothing has no field W
```
---
### Author:  [@frankschae](https://discourse.julialang.org/u/frankschae)
#### Post date: [October 6, 2020, 1:18pm UTC](https://discourse.julialang.org/t/using-the-noise-parameters-sol-w-w-from-an-sde-solution-throws-an-error-when-taking-gradients/47640/2 "2020-10-06T13:18:48Z")
I think the problem traces back to `sol.W` being `nothing` in the backward pass. Using `ForwardDiff` instead of `Zygote` to compute the gradients
```julia
@time gs = ForwardDiff.gradient(p) do p
some_loss(p)
end
```
removes the error. If reverse-mode AD is needed, you could use pre-defined noise values and `NoiseGrid` from the `DiffEqNoiseProcess` package
```julia
t = Array(tspan[0]:dt:tspan[1])
Z = randn(length(t))
Z1 = cumsum([0;sqrt(dt)*Z[1:end-1]])
Zygote.ignore() do
NG = NoiseGrid(t,Z1)
end
tmp_prob = remake(prob,p=p,noise=NG)
```
as a possible workaround. @ChrisRackauckas, do you have a better idea for using the noise values in a loss function with `Zygote`?
---
### Author:  [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)
#### Post date: [October 7, 2020, 1:20am UTC](https://discourse.julialang.org/t/using-the-noise-parameters-sol-w-w-from-an-sde-solution-throws-an-error-when-taking-gradients/47640/3 "2020-10-07T01:20:33Z")
So we would need to calculate the derivative w.r.t. the Brownian motion? I think that’s defined by the Malliavan calculus but I don’t think we’ve implemented it in the adjoint expressions. I think @frankschae is right that the best way to do this right now would be to define the `AbstractNoiseProcess` directly as a `NoiseGrid` with the variables from the AD system so that you supply them and AD will differentiate them. That would at least be a way to do it today.
---
### Author:  [@MikeKlocCZ](https://discourse.julialang.org/u/MikeKlocCZ)
#### Post date: [October 7, 2020, 2:13pm UTC](https://discourse.julialang.org/t/using-the-noise-parameters-sol-w-w-from-an-sde-solution-throws-an-error-when-taking-gradients/47640/4 "2020-10-07T14:13:03Z")
Thank you both for comments and suggestions!