time-integrated functional depending on constant-in-time control

[Stephan Kramer]

In the attached example (based on test_firedrake/identity/test_identity) I have a functional with a time integral that explicitly depends on the control, a function s. Because s doesn't actually get touched during the forward model this seems to confuse dolfin-adjoint with the following error:

LibadjointErrorInvalidInputs: Error in adj_iteration_count: No iteration found for supplied variable w_2:1:0:Forward

This can be worked around by adding a spurious projection to itself of s every time step (commented out in the example test). The same issue seems to be present in firedrake-adjoint and dolfin-adjoint.

[Miguel Salazar]

The following code works for me:

from dolfin import *
from dolfin_adjoint import *

mesh = UnitIntervalMesh(mpi_comm_world(), 2)

W = FunctionSpace(mesh, "CG", 1)
rho_const = interpolate(Constant(5.0), W, annotate=False)
rho = interpolate(rho_const, W, name="Control")

##################### BRIEF EXPLANATION #############################
# It seems that we need the state_1 and state_2 to make it work
#

g_const = interpolate(Constant(5.0), W)
g = interpolate(g_const, W, name="Control2")


u = Function(W, name="State")
u1 = Function(W, name="State_1")
u0 = Function(W, name="State_0")

u_ = TrialFunction(W)
v = TestFunction(W)

F = rho*u_*v * dx - Constant(1)*g*v*dx
adj_start_timestep(0.0)

solve(lhs(F) == rhs(F), u)
u0.assign(u1, annotate=True)
u1.assign(u, annotate=True)
rho.assign(rho_const, annotate=True)

adj_inc_timestep(time=100.0, finished=False)

solve(lhs(F) == rhs(F), u)
u0.assign(u1, annotate=True)
u1.assign(u, annotate=True)
rho.assign(rho_const, annotate=True)

adj_inc_timestep(time=200.0, finished=True)

adj_html("forward.html", "forward")
adj_html("adjoint.html", "adjoint")

success = replay_dolfin(tol=0.0, stop=True)
print success
J = Functional((rho*0.5 * inner(u1, u1) * dx)*dt)

# Reduced functional with single control
m = FunctionControl(rho)

Jhat = ReducedFunctional(J, m)
Jhat.derivative()
Jhat(rho)
Jhat.hessian(rho)

direction = interpolate(Constant(1), W)
assert Jhat.taylor_test(rho, test_hessian=False, perturbation_direction=direction) > 1.9

I had to include the functions u0 and u1 to pass the taylor test. I am not entirely sure why. I also wonder what's the cost of doing the assign for the control variable. Now you need to save also the design variable even though it is a constant.