# Create a low-fidelity model
lf_model = Model(
eval_fun=lambda x, samples=prior_pf_samples_lf: elliptic_pde.find_xy_pair(x, prior_samples, samples),
rv_samples=prior_samples[indices], rv_samples_pred=prior_samples[indices], n_evals=n_evals[0],
n_qoi=n_qoi, rv_name='$q_0$', label='Low-fidelity')
# Create a high-fidelity model
hf_model = Model(
eval_fun=lambda x, samples=prior_pf_samples_hf: elliptic_pde.find_xy_pair(x, prior_samples, samples),
n_evals=n_evals[-1], n_qoi=n_qoi, rv_name='$Q$', label='High-fidelity')
models = [lf_model, hf_model]
# Setup MFMC
mfmc = MFMC(models=models,
training_set_strategy=training_set_strategy, regression_type=regression_type)
# Apply MFMC
mfmc.apply_mfmc_framework(verbose=False)
prior_pf_samples = mfmc.get_samples()[-1, :, :]
p_prior_pf = Distribution(prior_pf_samples, rv_name='$Q$', label='Prior-PF')
# l1 error between prior push-forward and reference push-forward
l1_prior_pf_1hf_1lf.append(ref_p_prior_pf.calculate_l1_error(p_prior_pf))
# -------------- 1 HF, 2 LF
l1_prior_pf_1hf_2lf = []
for idx, n_evals in enumerate(n_evals_mfmc_hf_2lf):
n_evals = [n_evals_mfmc_lf_2lf[idx], n_evals_mfmc_mf_2lf[idx], n_evals]
indices = np.random.choice(range(prior_samples.shape[0]), size=n_evals[0], replace=False)
def get_prior_prior_pf_samples():
prior_samples, prior_pf_samples, obs_loc, obs_scale, prior_pf_mc_samples, mc_model, n_qoi = \
None, None, None, None, None, None, None
# Check push forward method
if fw_uq_method not in ['mc', 'mfmc']:
print('Unknown forward uq method: %r' % fw_uq_method)
exit()
if model == 'lambda_p':
n_qoi = 1
obs_loc = [0.25]
obs_scale = [0.1]
prior_samples = lambda_p.get_prior_samples(n_mc_ref)
# Create the Monte Carlo reference
mc_model = Model(eval_fun=lambda x: lambda_p.lambda_p(x, 5), rv_samples=prior_samples,
rv_samples_pred=prior_samples, n_evals=n_mc_ref, n_qoi=n_qoi, rv_name='$Q$',
label='MC reference')
if fw_uq_method == 'mc':
# Brute force Monte Carlo
prior_pf_samples = mc_model.evaluate()
prior_pf_samples = np.reshape(prior_pf_samples, (1, n_mc_ref, np.shape(prior_pf_samples)[1]))
prior_pf_mc_samples = prior_pf_samples
elif fw_uq_method == 'mfmc':
# Create a low-fidelity model
lf_model = Model(eval_fun=lambda x: lambda_p.lambda_p(x, 1), rv_samples=prior_samples[:n_evals[0]],
rv_samples_pred=prior_samples[:n_evals[0]], n_evals=n_evals[0], n_qoi=n_qoi,
rv_name='Low-fidelity: $q_0$', label='Low-fidelity')
# Create a high-fidelity model
if n_models == 3:
hf_label = 'Multi-fidelity (low, mid, high)'
elif n_models == 2:
hf_label = 'Multi-fidelity (low, high)'
else:
hf_label = 'Multi-fidelity'
hf_model = Model(eval_fun=lambda x: lambda_p.lambda_p(x, 5), n_evals=n_evals[-1],
n_qoi=n_qoi, rv_name='High-fidelity: $Q$', label=hf_label)
if n_models == 2:
models = [lf_model, hf_model]
# Create a mid fidelity model
elif n_models == 3:
mf_model = Model(eval_fun=lambda x: lambda_p.lambda_p(x, 3), n_evals=n_evals[1], n_qoi=n_qoi,
rv_name='Mid-fidelity: $q_1$', label='Multi-fidelity (low, mid)')
models = [lf_model, mf_model, hf_model]
else:
print('Unsupported number of models (%d) for lambda_p.' % n_models)
exit()
elif model in ['elliptic_pde', 'elliptic_pde_2d', 'elliptic_pde_3d']:
# Setup and load data
if model == 'elliptic_pde':
n_qoi = 1
obs_loc = [0.71]
obs_scale = [0.02]
elif model == 'elliptic_pde_2d':
n_qoi = 2
obs_loc = [0.71, 0.12]
obs_scale = [0.02, 0.02]
elif model == 'elliptic_pde_3d':
n_qoi = 3
obs_loc = [0.71, 0.12, 0.45]
obs_scale = [0.02, 0.02, 0.02]
prior_pf_samples = elliptic_pde.load_data()
prior_samples = np.reshape(range(n_mc_ref), (n_mc_ref, 1)) # we only need some id here
mc_model = Model(eval_fun=None, rv_samples=prior_samples, rv_samples_pred=prior_samples,
n_evals=n_mc_ref, n_qoi=n_qoi, rv_name='High-fidelity: $Q$', label='MC reference')
mc_model.set_model_evals(prior_pf_samples[-1][:n_mc_ref, 0:n_qoi])
if fw_uq_method == 'mc':
# Monte Carlo reference
prior_pf_samples = prior_pf_samples[-1][:n_mc_ref, 0:n_qoi]
prior_pf_samples = np.reshape(prior_pf_samples, (1, n_mc_ref, n_qoi))
prior_pf_mc_samples = prior_pf_samples
elif fw_uq_method == 'mfmc':
if n_models > 3:
print('elliptic_pde only supports up to 3 fidelity levels.')
exit()
# Create a low-fidelity model
samples = prior_pf_samples[0][:n_evals[0], 0:n_qoi]
samples = samples ** 1.2 # add a bias
lf_prior_samples = prior_samples[:n_evals[0]]
lf_model = Model(
eval_fun=lambda x, samples=samples: elliptic_pde.find_xy_pair(x, lf_prior_samples, samples),
rv_samples=lf_prior_samples, rv_samples_pred=lf_prior_samples, n_evals=n_evals[0],
n_qoi=n_qoi, rv_name='Low-fidelity: $q_0$', label='Low-fidelity')
# Create a high-fidelity model
if n_models == 3:
hf_label = 'Multi-fidelity (low, mid, high)'
elif n_models == 2:
hf_label = 'Multi-fidelity (low, high)'
else:
hf_label = 'Multi-fidelity'
samples = prior_pf_samples[-1][:n_evals[0], 0:n_qoi]
hf_model = Model(
eval_fun=lambda x, samples=samples: elliptic_pde.find_xy_pair(x, lf_prior_samples, samples),
n_evals=n_evals[-1], n_qoi=n_qoi, rv_name='High-fidelity: $Q$', label=hf_label)
if n_models == 3:
# Create a mid fidelity model
samples = prior_pf_samples[1][:n_evals[0], 0:n_qoi]
samples = samples ** 1.1 # add a bias
mf_model = Model(
eval_fun=lambda x, samples=samples: elliptic_pde.find_xy_pair(x, lf_prior_samples, samples),
n_evals=n_evals[1], n_qoi=n_qoi, rv_name='Mid-fidelity: $q_1$', label='Multi-fidelity (low, mid)')
models = [lf_model, mf_model, hf_model]
elif n_models == 2:
models = [lf_model, hf_model]
else:
print('Unsupported number of models (%d) for elliptic_pde.' % n_models)
exit()
elif model is 'linear_elasticity':
if training_set_strategy is not 'fixed':
print('This model only supports a fixed training set.')
exit()
n_qoi = 1
obs_loc = [0.95]
obs_scale = [0.01]
lf_data, hf_data, prior_samples = linear_elasticity.load_data()
if fw_uq_method == 'mc':
print('No MC reference available.')
elif fw_uq_method == 'mfmc':
if n_models > 2:
print('linear_elasticity only supports 2 fidelity levels.')
exit()
# Create a low-fidelity model
samples = lf_data[:n_evals[0]]
lf_prior_samples = prior_samples[:n_evals[0], 0:n_qoi]
lf_model = Model(eval_fun=lambda x, samples=samples: samples[x], rv_samples=lf_prior_samples,
rv_samples_pred=lf_prior_samples, n_evals=n_evals[0], n_qoi=n_qoi,
rv_name='Low-fidelity: $q$', label='Low-fidelity')
data = np.zeros((n_evals[0], 1))
data[:, 0] = samples
lf_model.set_model_evals(data)
# Create a high-fidelity model
samples = hf_data[:n_evals[-1]]
hf_model = Model(eval_fun=lambda x, samples=samples: samples[x],n_evals=n_evals[-1], n_qoi=n_qoi,
rv_name='High-fidelity: $Q$', label='Multi-fidelity (low, high)')
data = np.zeros((n_evals[-1], 1))
data[:, 0] = samples
hf_model.set_model_evals(data)
models = [lf_model, hf_model]
else:
print('Unknown model: %r' % model)
exit()
if fw_uq_method == 'mc':
print('')
print('########### MC statistics ###########')
print('')
print('MC mean:\t\t\t\t\t\t%s' % prior_pf_mc_samples[0, :, :].mean(axis=0))
print('MC std:\t\t\t\t\t\t\t%s' % prior_pf_mc_samples[0, :, :].std(axis=0))
print('')
print('########################################')
print('')
if fw_uq_method == 'mfmc':
# Setup MFMC
mfmc = MFMC(models=models, mc_model=mc_model,
training_set_strategy=training_set_strategy, regression_type=regression_type)
# Apply MFMC
mfmc.apply_mfmc_framework()
# Calculate Monte Carlo reference
if mc_model is not None:
mfmc.calculate_mc_reference()
mc = True
else:
mc = False
# Diagnostics
mfmc.print_stats(mc=mc)
# Plots
mfmc.plot_results(mc=mc)
mfmc.plot_regression_models()
mfmc.plot_joint_densities()
# Get prior push-forward samples
prior_pf_samples = mfmc.get_samples()
if mc:
prior_pf_mc_samples = mfmc.get_mc_samples()
return prior_samples, prior_pf_samples, obs_loc, obs_scale, prior_pf_mc_samples