Hello,

I am currently working on resolving a poisson equation for both forward and ajdoint problem. Here is my code :

```
from dolfin import *
from dolfin_adjoint import *
import matplotlib.pyplot as plt
import numpy as np
mesh = UnitSquareMesh ( 50 , 50 )
V = FunctionSpace ( mesh , "Lagrange" , 1 )
# Define basis functions and parameters
u = TrialFunction ( V )
v = TestFunction ( V )
f = interpolate(Expression("10*exp(-(pow(x[0] - 0.5, 2) + pow(x[1] - 0.5, 2)) / 0.02)", degree=2), V)
# Define variational problem
a = inner ( grad ( u ) , grad ( v ) ) * dx
L = f * v * dx
bc = DirichletBC (V , 0.0 , "on_boundary" )
# Solve variational problem
u = Function ( V )
solve ( a == L , u , bc )
plt.colorbar (plot(u))
ud = Function(V)
j = inner ( u - ud , u - ud ) * dx
J = assemble(j)
fc = Control(f)
dJdf = compute_gradient (J , fc)
# solution of the adjoint problem
tape = get_working_tape()
solve_block = tape.get_blocks()[1]
adj_u = solve_block.adj_sol.vector()[:]
adj_u_func = Function(V)
adj_u_func.assign(u)
adj_u_func.vector()[:]= adj_u
plot(adj_u_func)
plt.colorbar(plot(adj_u_func))
noise_level = 2
u_noise = Function(V)
u_noise.assign(u)
MAX = u_noise.vector().norm("linf")
noise_rand = noise_level * MAX * np.random.normal(0, 1, len(u_noise.vector().get_local()))
for i in range(len(u_noise.vector())):
u_noise.vector()[i] = u_noise.vector()[i] + noise_rand[i]*u_noise.vector()[i]
plot(u_noise)
plt.colorbar(plot(u_noise))
j = inner ( u_noise - ud , u_noise - ud ) * dx
J = assemble(j)
fc = Control(f)
dJdf = compute_gradient (J , fc)
import numpy as np
# solution of the adjoint problem
tape = get_working_tape()
solve_block = tape.get_blocks()[1]
adj_u = solve_block.adj_sol.vector()[:]
adj_u_func_noise = Function(V)
adj_u_func_noise.assign(u_noise)
adj_u_func_noise.vector()[:]= adj_u
plot(adj_u_func_noise)
plt.colorbar(plot(adj_u_func_noise))
```

Itâ€™s weird that both the adjoint solution with and without noise are the same.

Am I misunderstaing something ?

PS : I think the tape call always get back to the adjoint solution without noise, even though we specify the noisy adjoint solution.