def predict_and_plot(hyperp, options, filepaths):
#=== Load Observation Indices ===#
if options.obs_type == 'full':
obs_dimensions = options.mesh_dimensions
obs_indices = []
if options.obs_type == 'obs':
obs_dimensions = options.num_obs_points
print('Loading Boundary Indices')
df_obs_indices = pd.read_csv(filepaths.project.obs_indices + '.csv')
obs_indices = df_obs_indices.to_numpy()
#=== Data and Latent Dimensions of Autoencoder ===#
input_dimensions = obs_dimensions
latent_dimensions = options.parameter_dimensions
#=== Prepare Data ===#
data = DataHandler(hyperp, options, filepaths, obs_indices,
options.parameter_dimensions, obs_dimensions,
options.mesh_dimensions)
data.load_data_test()
if options.add_noise == 1:
data.add_noise_qoi_test()
parameter_test = data.poi_test
state_obs_test = data.qoi_test
#=== Load Trained Neural Network ===#
nn = VAE(hyperp, options, input_dimensions, latent_dimensions, None, None,
tf.identity)
nn.load_weights(filepaths.trained_nn)
#=== Construct Forward Model ===#
forward_operator = load_forward_operator_tf(options, filepaths)
forward_model =\
SolveForward1D(options, filepaths, forward_operator, obs_indices)
if options.discrete_polynomial == True:
forward_model_solve = forward_model.discrete_polynomial
if options.discrete_exponential == True:
forward_model_solve = forward_model.discrete_exponential
#=== Selecting Samples ===#
sample_number = 4
parameter_test_sample = np.expand_dims(parameter_test[sample_number, :], 0)
state_obs_test_sample = np.expand_dims(state_obs_test[sample_number, :], 0)
#=== Predictions ===#
post_mean_pred, log_post_std_pred, post_cov_chol_pred = nn.encoder(
state_obs_test_sample)
n_samples = 1000
posterior_pred_draws = np.zeros((n_samples, post_mean_pred.shape[1]),
dtype=np.float32)
state_obs_pred_draws = np.zeros(
(n_samples, state_obs_test_sample.shape[1]), dtype=np.float32)
for n in range(0, n_samples):
posterior_pred_draws[n, :] = nn.reparameterize(post_mean_pred,
post_cov_chol_pred)
if options.model_aware == True:
state_obs_pred_draws = nn.decoder(posterior_pred_draws)
else:
state_obs_pred_draws = forward_model_solve(posterior_pred_draws)
#=== Plotting Prediction ===#
print('================================')
print(' Plotting Predictions ')
print('================================')
n_bins = 100
for n in range(0, post_mean_pred.shape[1]):
#=== Posterior Histogram ===#
plt.hist(posterior_pred_draws[:, n],
density=True,
range=[3, 5],
bins=n_bins)
#=== True Parameter Value ===#
plt.axvline(parameter_test_sample[0, n],
color='r',
linestyle='dashed',
linewidth=3,
label="True Parameter Value")
#=== Predicted Posterior Mean ===#
plt.axvline(post_mean_pred[0, n],
color='b',
linestyle='dashed',
linewidth=1,
label="Predicted Posterior Mean")
#=== Probability Density Function ===#
mn, mx = plt.xlim()
plt.xlim(mn, mx)
kde_xs = np.linspace(mn, mx, 301)
kde = st.gaussian_kde(posterior_pred_draws[:, n])
#=== Title and Labels ===#
plt.plot(kde_xs, kde.pdf(kde_xs))
plt.legend(loc="upper left")
plt.ylabel('Probability')
plt.xlabel('Parameter Value')
plt.title("Marginal Posterior Parameter_%d" % (n))
#=== Save and Close Figure ===#
plt.savefig(filepaths.figure_parameter_pred + '_%d' % (n))
plt.close()
print('Predictions plotted')
###############################################################################
# Compare Covariance #
###############################################################################
#=== Construct Likelihood Matrix ===#
if options.add_noise == True:
noise_regularization_matrix = data.construct_noise_regularization_matrix_test(
)
noise_regularization_matrix = np.expand_dims(
noise_regularization_matrix, axis=0)
else:
noise_regularization_matrix = np.ones((1, obs_dimensions),
dtype=np.float32)
measurement_matrix = data.construct_measurement_matrix()
likelihood_matrix = tf.linalg.matmul(
tf.transpose(tf.linalg.matmul(measurement_matrix, forward_operator)),
tf.linalg.matmul(
tf.linalg.diag(tf.squeeze(noise_regularization_matrix)),
tf.linalg.matmul(measurement_matrix, forward_operator)))
#=== Construct Inverse of Prior Matrix ===#
prior = PriorHandler(hyperp, options, filepaths,
options.parameter_dimensions)
prior_mean = prior.load_prior_mean()
prior_cov_inv = prior.load_prior_covariance_inverse()
#=== Construct True Posterior ===#
post_cov_true = np.linalg.inv(likelihood_matrix + prior_cov_inv)
post_cov_pred = np.matmul(
np.reshape(
post_cov_chol_pred,
(options.parameter_dimensions, options.parameter_dimensions)),
np.transpose(
np.reshape(
post_cov_chol_pred,
(options.parameter_dimensions, options.parameter_dimensions))))
#=== Construct True Mean ===#
post_mean_true = np.matmul(post_cov_true,
np.matmul(
np.transpose(np.matmul(measurement_matrix,forward_operator)),
np.matmul(np.diag(noise_regularization_matrix.flatten()),
np.transpose(state_obs_test_sample))) +\
np.matmul(prior_cov_inv, np.expand_dims(prior_mean, axis=1)))
#=== Relative Error of Matrices ===#
relative_error = np.linalg.norm(post_cov_true - post_cov_pred, ord='fro')\
/np.linalg.norm(post_cov_true, ord='fro')
print('relative error = %.4f' % (relative_error))
def predict_and_plot(hyperp, options, filepaths):
#=== Load Observation Indices ===#
if options.obs_type == 'full':
obs_dimensions = options.mesh_dimensions
obs_indices = []
if options.obs_type == 'obs':
obs_dimensions = options.num_obs_points
print('Loading Boundary Indices')
df_obs_indices = pd.read_csv(filepaths.project.obs_indices + '.csv')
obs_indices = df_obs_indices.to_numpy()
#=== Data and Latent Dimensions of Autoencoder ===#
input_dimensions = obs_dimensions
latent_dimensions = options.parameter_dimensions
#=== Prepare Data ===#
data = DataHandler(hyperp, options, filepaths, obs_indices,
options.parameter_dimensions, obs_dimensions,
options.mesh_dimensions)
data.load_data_test()
if options.add_noise == 1:
data.add_noise_qoi_test()
parameter_test = data.poi_test
state_obs_test = data.qoi_test
#=== Load Trained Neural Network ===#
nn = VAE(hyperp, options, input_dimensions, latent_dimensions, None, None,
tf.identity)
nn.load_weights(filepaths.trained_nn)
#=== Construct Forward Model ===#
if options.model_augmented == True:
forward_operator = load_forward_operator_tf(options, filepaths)
forward_model =\
SolveForward1D(options, filepaths, forward_operator, obs_indices)
if options.discrete_polynomial == True:
forward_model_solve = forward_model.discrete_polynomial
if options.discrete_exponential == True:
forward_model_solve = forward_model.discrete_exponential
#=== Selecting Samples ===#
sample_number = 105
parameter_test_sample = np.expand_dims(parameter_test[sample_number, :], 0)
state_obs_test_sample = np.expand_dims(state_obs_test[sample_number, :], 0)
#=== Predictions ===#
post_mean_pred, log_post_std_pred, post_cov_chol_pred = nn.encoder(
state_obs_test_sample)
n_samples = 1000
posterior_pred_draws = np.zeros((n_samples, post_mean_pred.shape[1]),
dtype=np.float32)
state_obs_pred_draws = np.zeros(
(n_samples, state_obs_test_sample.shape[1]), dtype=np.float32)
for n in range(0, n_samples):
posterior_pred_draws[n, :] = nn.reparameterize(post_mean_pred,
post_cov_chol_pred)
if options.model_aware == True:
state_obs_pred_draws = nn.decoder(posterior_pred_draws)
else:
state_obs_pred_draws = forward_model_solve(posterior_pred_draws)
#=== Plotting Prediction ===#
print('================================')
print(' Plotting Predictions ')
print('================================')
n_bins = 100
for n in range(0, post_mean_pred.shape[1]):
#=== Posterior Histogram ===#
plt.hist(posterior_pred_draws[:, n],
density=True,
range=[-1, 10],
bins=n_bins)
#=== True Parameter Value ===#
plt.axvline(parameter_test_sample[0, n],
color='r',
linestyle='dashed',
linewidth=3,
label="True Parameter Value")
#=== Predicted Posterior Mean ===#
plt.axvline(post_mean_pred[0, n],
color='b',
linestyle='dashed',
linewidth=1,
label="Predicted Posterior Mean")
#=== Probability Density Function ===#
mn, mx = plt.xlim()
plt.xlim(mn, mx)
kde_xs = np.linspace(mn, mx, 301)
kde = st.gaussian_kde(posterior_pred_draws[:, n])
#=== Title and Labels ===#
plt.plot(kde_xs, kde.pdf(kde_xs))
plt.legend(loc="upper left")
plt.ylabel('Probability')
plt.xlabel('Parameter Value')
plt.title("Marginal Posterior Parameter_%d" % (n))
#=== Save and Close Figure ===#
plt.savefig(filepaths.figure_parameter_pred + '_%d' % (n))
plt.close()
print('Predictions plotted')