def gradient(m):
"""
Compute the gradient of the QoI with respect to the input parameters.
"""
dJdm = adolc.fos_reverse(tape_tag, 1.0)
op.dJdm_progress.append(vecnorm(dJdm, order=np.Inf))
return dJdm
def gradient__save(m):
"""
Apply the chain rule to both tapes
"""
dJdm = gradient(m)
g = vecnorm(dJdm, order=np.Inf)
msg = "functional {:15.8e} gradient {:15.8e}"
print(msg.format(op._J, g))
op.control_trajectory.append(m)
op.functional_trajectory.append(op._J)
op.gradient_trajectory.append(dJdm)
np.save(fname.format('ctrl'), op.control_trajectory)
np.save(fname.format('func'), op.functional_trajectory)
np.save(fname.format('grad'), op.gradient_trajectory)
return dJdm
def derivative_cb_post(j, dj, m):
"""
Callback for saving progress data to file during discrete adjoint inversion.
"""
control = [mi.dat.data[0] for mi in m]
djdm = [dji.dat.data[0] for dji in dj]
msg = "functional {:15.8e} gradient {:15.8e}"
print_output(msg.format(j, vecnorm(djdm, order=np.Inf)))
# Save progress to NumPy arrays on-the-fly
control_values_opt.append(control)
func_values_opt.append(j)
gradient_values_opt.append(djdm)
np.save(fname.format('ctrl'), np.array(control_values_opt))
np.save(fname.format('func'), np.array(func_values_opt))
np.save(fname.format('grad'), np.array(gradient_values_opt))
def gradient(m):
"""
Gradient of reduced functional for continuous adjoint inversion.
"""
J = reduced_functional(m) if len(
swp.checkpoint) == 0 else swp.quantity_of_interest()
swp.solve_adjoint(checkpointing_mode=chk)
g = np.array([
assemble(inner(bf, swp.adj_solution) * dx)
for bf in op.basis_functions
]) # TODO: No minus sign?
if use_regularisation:
g += op.regularisation_term_gradient
msg = " functional = {:15.8e} gradient = {:15.8e}"
print_output(msg.format(J, vecnorm(g, order=np.Inf)))
return g
axis.grid(True, which='major', color='lightgrey')
axes.set_xlabel("Mesh element count")
axes.set_ylabel("Square timeseries error QoI")
savefig('converged_J', plot_dir, extensions=plot.extensions)
# Plot progress of gradient
print_output("Plotting progress of gradient norm...")
fig, axes = plt.subplots(figsize=(8, 6))
for level in range(levels):
fname = os.path.join(
op.di, 'optimisation_progress_{:s}' + '_{:d}.npy'.format(level))
gradient_values_opt = np.load(fname.format('grad', level))
label = '{:d} elements'.format(op.num_cells[level])
its = range(1, len(gradient_values_opt) + 1)
axes.loglog(its,
[vecnorm(djdm, order=np.Inf) for djdm in gradient_values_opt],
label=label)
axes.set_xticks([1, 10, 100])
# axes.set_yticks([2e3, 7e3])
for axis in (axes.xaxis, axes.yaxis):
axis.grid(True, which='minor', color='lightgrey')
axis.grid(True, which='major', color='lightgrey')
axes.set_xlabel("Iteration")
axes.set_ylabel(r"$\ell_\infty$-norm of gradient")
axes.legend(loc='best', fontsize=fontsize_legend)
savefig('optimisation_progress_dJdm_linf',
plot_dir,
extensions=plot.extensions)
fig, axes = plt.subplots(figsize=(8, 6))
for level in range(levels):
fname = os.path.join(
def dJdm(m):
djdm = 2 * rescaling * sum([(np.dot(g[i, :], m) - f[i]) * g[i, :]
for i in range(N)])
self.print_debug("INTERPOLATION: gradient = {:8.6e}".format(
vecnorm(djdm, order=np.Inf)))
return djdm
control_trajectory = np.load(fname.format('ctrl') + '.npy')
functional_trajectory = np.load(fname.format('func') + '.npy')
gradient_trajectory = np.load(fname.format('grad') + '.npy')
line_search_trajectory = np.load(fname.format('ls') + '.npy')
i = 0
indices = [0]
for j, ctrl in enumerate(control_trajectory):
if i == len(line_search_trajectory):
break
if np.allclose(ctrl, line_search_trajectory[i]):
indices.append(j)
i += 1
functional_trajectory = [functional_trajectory[i] for i in indices]
gradient_trajectory = [gradient_trajectory[i] for i in indices]
gradient_norm_trajectory = [
vecnorm(g, order=np.Inf) for g in gradient_trajectory
]
fig, axes = plt.subplots(figsize=(8, 8))
axes.loglog(functional_trajectory)
axes.set_xlabel("Iteration")
axes.set_ylabel("Quantity of Interest")
axes.grid(True, which='both')
savefig("qoi_progress_{:d}_{:s}".format(level, categories),
"plots",
extensions=["pdf"])
fig, axes = plt.subplots(figsize=(8, 8))
axes.loglog(gradient_norm_trajectory)
axes.set_xlabel("Iteration")
axes.set_ylabel("Computed gradient")