chiSmall=0.5, # ask for twice as much clustering (target value is /2)
)
# add learned mref in smooth once stable
MrefInSmooth = directives.PGI_AddMrefInSmooth(
wait_till_stable=True,
verbose=True,
)
# update the parameters in smallness (L2-approx of PGI)
update_smallness = directives.PGI_UpdateParameters(
update_gmm=True, # update the GMM each iteration
kappa=np.c_[ # confidences in each mean phys. prop. of each cluster
1e10 * np.ones(
2
), # fixed background at 0 density, 0 mag. susc. (high confidences of 1e10)
[
0,
1e10,
], # density-contrasting cluster: updatable density mean, fixed mag. susc.
[
1e10,
0,
], # magnetic-contrasting cluster: fixed density mean, updatable mag. susc.
].T,
)
# pre-conditioner
update_Jacobi = directives.UpdatePreconditioner()
# iteratively balance the scaling of the data misfits
scaling_init = directives.ScalingMultipleDataMisfits_ByEig(
chi0_ratio=[1.0, 100.0])
scale_schedule = directives.JointScalingSchedule(verbose=True)
# Create inverse problem
n_pw_iter=10)
scaling_schedule = directives.JointScalingSchedule(verbose=True)
alpha0_ratio = np.r_[np.zeros(len(reg_simple.objfcts[0].objfcts)),
100.0 * np.ones(len(reg_simple.objfcts[1].objfcts)),
1.0 * np.ones(len(reg_simple.objfcts[2].objfcts)), ]
alphas = directives.AlphasSmoothEstimate_ByEig(alpha0_ratio=alpha0_ratio,
n_pw_iter=10,
verbose=True)
beta = directives.BetaEstimate_ByEig(beta0_ratio=1e-5, n_pw_iter=10)
betaIt = directives.PGI_BetaAlphaSchedule(
verbose=True,
coolingFactor=2.0,
progress=0.2,
)
targets = directives.MultiTargetMisfits(verbose=True)
petrodir = directives.PGI_UpdateParameters(update_gmm=False)
# Setup Inversion
inv = inversion.BaseInversion(
invProb,
directiveList=[
alphas, scales, beta, petrodir, targets, betaIt, scaling_schedule
],
)
mcluster_map = inv.run(minit)
# Inversion with no nonlinear mapping
reg_simple_no_map = utils.make_SimplePGI_regularization(
mesh=mesh,
gmmref=clfnomapping,
1e-4 * np.ones(len(reg.objfcts[1].objfcts)),
100.0 * 1e-4 * np.ones(len(reg.objfcts[2].objfcts)),
]
Alphas = directives.AlphasSmoothEstimate_ByEig(alpha0_ratio=alpha0_ratio, verbose=True)
# initialize beta and beta/alpha_s schedule
beta = directives.BetaEstimate_ByEig(beta0_ratio=1e-2)
betaIt = directives.PGI_BetaAlphaSchedule(
verbose=True, coolingFactor=2.0, tolerance=0.2, progress=0.2,
)
# geophy. and petro. target misfits
targets = directives.MultiTargetMisfits(verbose=True,)
# add learned mref in smooth once stable
MrefInSmooth = directives.PGI_AddMrefInSmooth(wait_till_stable=True, verbose=True,)
# update the parameters in smallness (L2-approx of PGI)
update_smallness = directives.PGI_UpdateParameters(
update_gmm=False # keep GMM model fixed
)
# pre-conditioner
update_Jacobi = directives.UpdatePreconditioner()
# iteratively balance the scaling of the data misfits
scaling_init = directives.ScalingMultipleDataMisfits_ByEig(chi0_ratio=[1.0, 100.0])
scale_schedule = directives.JointScalingSchedule(verbose=True)
# Create inverse problem
# Optimization
# set lower and upper bounds
lowerbound = np.r_[-2.0 * np.ones(actvMap.nP), 0.0 * np.ones(actvMap.nP)]
upperbound = np.r_[0.0 * np.ones(actvMap.nP), 1e-1 * np.ones(actvMap.nP)]
opt = optimization.ProjectedGNCG(
maxIter=30,
lower=lowerbound,
# Setup new inverse problem
invProb = inverse_problem.BaseInvProblem(dmis, reg, opt)
# directives
Alphas = directives.AlphasSmoothEstimate_ByEig(alpha0_ratio=10.0, verbose=True)
beta = directives.BetaEstimate_ByEig(beta0_ratio=1e-6)
betaIt = directives.PGI_BetaAlphaSchedule(
verbose=True,
coolingFactor=2.0,
warmingFactor=1.0,
tolerance=0.1,
update_rate=1,
progress=0.2,
)
targets = directives.MultiTargetMisfits(verbose=True)
petrodir = directives.PGI_UpdateParameters()
addmref = directives.PGI_AddMrefInSmooth(verbose=True)
# Setup Inversion
inv = inversion.BaseInversion(
invProb, directiveList=[Alphas, beta, petrodir, targets, addmref, betaIt])
# Initial model same as for Tikhonov
mcluster = inv.run(m0)
# Final Plot
fig, axes = plt.subplots(1, 3, figsize=(12 * 1.2, 4 * 1.2))
for i in range(prob.G.shape[0]):
axes[0].plot(prob.G[i, :])
axes[0].set_title("Columns of matrix G")