Probabilistic Inversion Example: Geological Model

This example demonstrates a probabilistic inversion of a geological model using Bayesian methods.

import time
import os
import numpy as np
import xarray as xr
import pandas as pd
import torch
import pyro
import pyro.distributions as dist
import gempy as gp
import gempy_viewer as gpv
from matplotlib import pyplot as plt
from dotenv import dotenv_values
from pyro.infer import MCMC, NUTS, Predictive
import arviz as az

from gempy_probability.plot_posterior import default_red, default_blue
from vector_geology.bayesian_helpers import calculate_scale_shift, gaussian_kernel
from vector_geology.model_1_builder import initialize_geo_model, setup_geophysics
from vector_geology.omf_to_gempy import process_file
from vector_geology.utils import extend_box
import gempy_engine
from gempy_engine.core.backend_tensor import BackendTensor

/home/leguark/subsurface/subsurface/reader/__init__.py:14: UserWarning: Welly or Striplog not installed. No well reader possible.
  warnings.warn("Welly or Striplog not installed. No well reader possible.")

Start the timer for benchmarking purposes

start_time = time.time()

Load necessary configuration and paths from environment variables

config = dotenv_values()
path = config.get("PATH_TO_MODEL_1_Subsurface")

Initialize lists to store structural elements for the geological model

structural_elements = []
global_extent = None
color_gen = gp.data.ColorsGenerator()

Process each .nc file in the specified directory for model construction

for filename in os.listdir(path):
    base, ext = os.path.splitext(filename)
    if ext == '.nc':
        structural_element, global_extent = process_file(os.path.join(path, filename), global_extent, color_gen)
        structural_elements.append(structural_element)

Configure GemPy for geological modeling with PyTorch backend

BackendTensor.change_backend_gempy(engine_backend=gp.data.AvailableBackends.PYTORCH, dtype="float64")
geo_model = initialize_geo_model(
    structural_elements=structural_elements,
    extent=(np.array(global_extent)),
    topography=(xr.open_dataset(os.path.join(path, "Topography.nc"))),
    load_nuggets=True
)

Setting Backend To: AvailableBackends.PYTORCH
Active grids: ['regular' 'topography']

Setup geophysics configuration for the model

geophysics_input = setup_geophysics(
    env_path="PATH_TO_MODEL_1_BOUGUER",
    geo_model=geo_model
)

Active grids: ['regular' 'topography' 'centered']

Adjust interpolation options for geological modeling

interpolation_options = geo_model.interpolation_options
interpolation_options.kernel_options.range = .7
interpolation_options.kernel_options.c_o = 3
interpolation_options.kernel_options.compute_condition_number = True

Compute the geological model

sol = gp.compute_model(
    gempy_model=geo_model,
    engine_config=gp.data.GemPyEngineConfig(
        backend=gp.data.AvailableBackends.PYTORCH,
        dtype='float64'
    )
)

Setting Backend To: AvailableBackends.PYTORCH
/home/leguark/gempy/gempy/core/data/geo_model.py:183: UserWarning: You are using refinement and passing a regular grid. The resolution of the regular grid will be overwritten
  warnings.warn(

Visualize the computed geological model in 3D

gempy_vista = gpv.plot_3d(
    model=geo_model,
    show=True,
    kwargs_plot_structured_grid={'opacity': 0.8},
    image=True
)

Calculate and adapt the observed gravity data for model comparison

grav = sol.gravity
s, c = calculate_scale_shift(
    a=geophysics_input["Bouguer_267_complete"].values,
    b=(grav.detach().numpy())
)
adapted_observed_grav = s * geophysics_input["Bouguer_267_complete"] + c

Plot the 2D gravity data for visualization

plot2d = gpv.plot_2d(geo_model, show_topography=True, section_names=["topography"], show=False)
sc = plot2d.axes[0].scatter(
    geophysics_input['X'],
    geophysics_input['Y'],
    c=adapted_observed_grav,
    cmap='viridis',
    s=100,
    zorder=10000
)
plt.colorbar(sc, label="mGal")
plt.show()

/home/leguark/gempy_viewer/gempy_viewer/API/_plot_2d_sections_api.py:104: UserWarning: Section contacts not implemented yet. We need to pass scalar field for the sections grid
  warnings.warn(

Define hyperparameters for the Bayesian geological model

length_scale_prior = torch.tensor(1_000.0)
variance_prior = torch.tensor(25.0 ** 2)
covariance_matrix = gaussian_kernel(geophysics_input[['X', 'Y']], length_scale_prior, variance_prior)

Configure the Pyro model for geological data

prior_tensor = BackendTensor.t.array([2.61, 2.92, 3.1, 2.92, 2.61, 2.61]).to(torch.float64)
geo_model.geophysics_input = gp.data.GeophysicsInput(
    tz=geo_model.geophysics_input.tz,
    densities=prior_tensor,
)

Define the Pyro probabilistic model for inversion

def model(y_obs_list, interpolation_input):
    """
    Pyro model representing the probabilistic aspects of the geological model.
    """
    prior_mean = 2.62
    mu_density = pyro.sample(
        name=r'$\mu_{density}$',
        fn=dist.Normal(prior_mean, torch.tensor(0.5, dtype=torch.float64))
    )
    geo_model.geophysics_input.densities = torch.index_put(
        input=prior_tensor,
        indices=(torch.tensor([3]),),
        values=mu_density
    )
    geo_model.solutions = gempy_engine.compute_model(
        interpolation_input=interpolation_input,
        options=geo_model.interpolation_options,
        data_descriptor=geo_model.input_data_descriptor,
        geophysics_input=geo_model.geophysics_input
    )
    simulated_geophysics = geo_model.solutions.gravity
    pyro.deterministic(r'$\mu_{gravity}$', simulated_geophysics)
    pyro.sample(
        name="obs",
        fn=dist.MultivariateNormal(simulated_geophysics, covariance_matrix),
        obs=y_obs_list
    )

Prepare observed data for Pyro model and optimize mesh settings

y_obs_list = torch.tensor(adapted_observed_grav.values).view(1, 17)
interpolation_options.mesh_extraction = False
interpolation_options.number_octree_levels = 1
geo_model.grid.set_inactive("topography")
geo_model.grid.set_inactive("regular")

array([False, False, False, False,  True])

Perform prior sampling and visualize the results

if True:
    prior = Predictive(model, num_samples=50)(y_obs_list, interpolation_input=geo_model.interpolation_input)
    data = az.from_pyro(prior=prior)
    az.plot_trace(data.prior)
    plt.show()

Final Iteration 584, Residual Norm: 1.0496041889313497e-07
/home/leguark/.virtualenvs/gempy-geotop-pilot/lib/python3.10/site-packages/arviz/utils.py:184: NumbaDeprecationWarning: The 'nopython' keyword argument was not supplied to the 'numba.jit' decorator. The implicit default value for this argument is currently False, but it will be changed to True in Numba 0.59.0. See https://numba.readthedocs.io/en/stable/reference/deprecation.html#deprecation-of-object-mode-fall-back-behaviour-when-using-jit for details.
  numba_fn = numba.jit(**self.kwargs)(self.function)
/home/leguark/.virtualenvs/gempy-geotop-pilot/lib/python3.10/site-packages/arviz/stats/density_utils.py:487: UserWarning: Your data appears to have a single value or no finite values
  warnings.warn("Your data appears to have a single value or no finite values")

Run Markov Chain Monte Carlo (MCMC) using the NUTS algorithm for probabilistic inversion

pyro.primitives.enable_validation(is_validate=True)
nuts_kernel = NUTS(model)
mcmc = MCMC(nuts_kernel, num_samples=1000, warmup_steps=300)
mcmc.run(y_obs_list, interpolation_input=geo_model.interpolation_input)

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Warmup:  13%|#3        | 171/1300 [00:43,  4.42it/s, step size=1.97e+00, acc. prob=0.783]
Warmup:  13%|#3        | 173/1300 [00:43,  5.00it/s, step size=3.90e+00, acc. prob=0.785]
Warmup:  13%|#3        | 175/1300 [00:44,  4.12it/s, step size=7.13e-01, acc. prob=0.781]
Warmup:  14%|#3        | 176/1300 [00:44,  3.65it/s, step size=9.43e-01, acc. prob=0.782]
Warmup:  14%|#3        | 177/1300 [00:44,  3.76it/s, step size=1.42e+00, acc. prob=0.783]
Warmup:  14%|#3        | 178/1300 [00:44,  3.85it/s, step size=6.75e-01, acc. prob=0.781]
Warmup:  14%|#3        | 179/1300 [00:45,  3.93it/s, step size=1.19e+00, acc. prob=0.783]
Warmup:  14%|#3        | 181/1300 [00:45,  5.55it/s, step size=5.67e-01, acc. prob=0.781]
Warmup:  14%|#4        | 182/1300 [00:45,  5.15it/s, step size=9.62e-01, acc. prob=0.782]
Warmup:  14%|#4        | 184/1300 [00:45,  5.53it/s, step size=2.85e+00, acc. prob=0.785]
Warmup:  14%|#4        | 186/1300 [00:46,  5.78it/s, step size=6.14e-01, acc. prob=0.782]
Warmup:  14%|#4        | 188/1300 [00:46,  5.93it/s, step size=1.71e+00, acc. prob=0.784]
Warmup:  15%|#4        | 190/1300 [00:47,  4.08it/s, step size=5.41e-01, acc. prob=0.782]
Warmup:  15%|#4        | 191/1300 [00:47,  4.08it/s, step size=9.02e-01, acc. prob=0.783]
Warmup:  15%|#4        | 192/1300 [00:47,  4.11it/s, step size=1.17e+00, acc. prob=0.783]
Warmup:  15%|#4        | 193/1300 [00:48,  4.11it/s, step size=1.47e+00, acc. prob=0.784]
Warmup:  15%|#4        | 194/1300 [00:48,  4.13it/s, step size=2.42e+00, acc. prob=0.785]
Warmup:  15%|#5        | 196/1300 [00:48,  4.81it/s, step size=1.24e+00, acc. prob=0.784]
Warmup:  15%|#5        | 197/1300 [00:48,  4.65it/s, step size=1.85e+00, acc. prob=0.785]
Warmup:  15%|#5        | 198/1300 [00:49,  4.53it/s, step size=1.16e+00, acc. prob=0.784]
Warmup:  15%|#5        | 199/1300 [00:49,  4.43it/s, step size=1.84e+00, acc. prob=0.785]
Warmup:  15%|#5        | 201/1300 [00:49,  5.03it/s, step size=9.44e-01, acc. prob=0.783]
Warmup:  16%|#5        | 202/1300 [00:49,  4.80it/s, step size=1.40e+00, acc. prob=0.784]
Warmup:  16%|#5        | 203/1300 [00:50,  4.61it/s, step size=2.16e+00, acc. prob=0.785]
Warmup:  16%|#5        | 204/1300 [00:50,  4.50it/s, step size=3.43e+00, acc. prob=0.786]
Warmup:  16%|#5        | 206/1300 [00:51,  3.78it/s, step size=8.66e-01, acc. prob=0.783]
Warmup:  16%|#5        | 207/1300 [00:51,  3.85it/s, step size=1.38e+00, acc. prob=0.784]
Warmup:  16%|#6        | 208/1300 [00:51,  3.93it/s, step size=1.94e+00, acc. prob=0.785]
Warmup:  16%|#6        | 210/1300 [00:51,  4.64it/s, step size=2.47e+00, acc. prob=0.786]
Warmup:  16%|#6        | 211/1300 [00:52,  4.51it/s, step size=1.21e+00, acc. prob=0.784]
Warmup:  16%|#6        | 213/1300 [00:52,  6.02it/s, step size=2.95e+00, acc. prob=0.786]
Warmup:  17%|#6        | 215/1300 [00:52,  7.43it/s, step size=7.40e-01, acc. prob=0.784]
Warmup:  17%|#6        | 216/1300 [00:52,  4.49it/s, step size=1.10e+00, acc. prob=0.784]
Warmup:  17%|#6        | 217/1300 [00:53,  4.41it/s, step size=1.48e+00, acc. prob=0.785]
Warmup:  17%|#6        | 219/1300 [00:53,  4.99it/s, step size=1.01e+00, acc. prob=0.784]
Warmup:  17%|#6        | 220/1300 [00:53,  4.78it/s, step size=1.55e+00, acc. prob=0.785]
Warmup:  17%|#7        | 221/1300 [00:53,  4.63it/s, step size=1.74e+00, acc. prob=0.786]
Warmup:  17%|#7        | 223/1300 [00:54,  4.44it/s, step size=5.12e-01, acc. prob=0.783]
Warmup:  17%|#7        | 224/1300 [00:54,  4.37it/s, step size=7.80e-01, acc. prob=0.784]
Warmup:  17%|#7        | 225/1300 [00:55,  3.70it/s, step size=1.17e+00, acc. prob=0.785]
Warmup:  17%|#7        | 226/1300 [00:55,  3.81it/s, step size=1.49e+00, acc. prob=0.786]
Warmup:  17%|#7        | 227/1300 [00:55,  3.91it/s, step size=1.51e+00, acc. prob=0.786]
Warmup:  18%|#7        | 229/1300 [00:56,  3.55it/s, step size=1.47e+00, acc. prob=0.786]
Warmup:  18%|#7        | 231/1300 [00:56,  4.88it/s, step size=9.00e-01, acc. prob=0.785]
Warmup:  18%|#7        | 232/1300 [00:56,  4.70it/s, step size=1.34e+00, acc. prob=0.786]
Warmup:  18%|#7        | 233/1300 [00:56,  4.56it/s, step size=1.88e+00, acc. prob=0.786]
Warmup:  18%|#8        | 235/1300 [00:57,  5.11it/s, step size=2.50e+00, acc. prob=0.787]
Warmup:  18%|#8        | 237/1300 [00:57,  6.51it/s, step size=2.27e+00, acc. prob=0.787]
Warmup:  18%|#8        | 239/1300 [00:57,  6.41it/s, step size=8.49e-01, acc. prob=0.785]
Warmup:  18%|#8        | 240/1300 [00:57,  5.76it/s, step size=1.25e+00, acc. prob=0.786]
Warmup:  19%|#8        | 241/1300 [00:58,  5.31it/s, step size=1.80e+00, acc. prob=0.787]
Warmup:  19%|#8        | 243/1300 [00:58,  5.66it/s, step size=1.23e+00, acc. prob=0.786]
Warmup:  19%|#8        | 245/1300 [00:58,  5.86it/s, step size=1.78e+00, acc. prob=0.787]
Warmup:  19%|#9        | 247/1300 [00:58,  7.15it/s, step size=2.29e+00, acc. prob=0.787]
Warmup:  19%|#9        | 249/1300 [00:59,  4.22it/s, step size=3.84e+00, acc. prob=0.784]
Warmup:  19%|#9        | 251/1300 [00:59,  5.35it/s, step size=8.84e-01, acc. prob=0.778]
Warmup:  19%|#9        | 252/1300 [01:00,  5.07it/s, step size=8.10e-01, acc. prob=0.778]
Warmup:  19%|#9        | 253/1300 [01:00,  4.86it/s, step size=1.01e+00, acc. prob=0.779]
Warmup:  20%|#9        | 254/1300 [01:00,  4.68it/s, step size=1.53e+00, acc. prob=0.780]
Warmup:  20%|#9        | 255/1300 [01:00,  4.55it/s, step size=1.05e+00, acc. prob=0.780]
Warmup:  20%|#9        | 256/1300 [01:01,  4.44it/s, step size=1.48e+00, acc. prob=0.780]
Warmup:  20%|#9        | 258/1300 [01:01,  5.09it/s, step size=1.85e+00, acc. prob=0.781]
Warmup:  20%|##        | 260/1300 [01:02,  3.28it/s, step size=5.08e-01, acc. prob=0.779]
Warmup:  20%|##        | 261/1300 [01:03,  2.79it/s, step size=9.60e-01, acc. prob=0.780]
Warmup:  20%|##        | 262/1300 [01:03,  3.03it/s, step size=1.65e+00, acc. prob=0.781]
Warmup:  20%|##        | 264/1300 [01:03,  4.36it/s, step size=3.56e+00, acc. prob=0.782]
Warmup:  20%|##        | 266/1300 [01:04,  3.78it/s, step size=1.72e+00, acc. prob=0.781]
Warmup:  21%|##        | 268/1300 [01:04,  4.97it/s, step size=4.18e+00, acc. prob=0.782]
Warmup:  21%|##        | 269/1300 [01:04,  4.80it/s, step size=3.92e-01, acc. prob=0.779]
Warmup:  21%|##        | 270/1300 [01:05,  3.50it/s, step size=7.18e-01, acc. prob=0.780]
Warmup:  21%|##        | 271/1300 [01:05,  3.20it/s, step size=1.20e+00, acc. prob=0.781]
Warmup:  21%|##        | 272/1300 [01:05,  3.39it/s, step size=1.23e+00, acc. prob=0.781]
Warmup:  21%|##1       | 273/1300 [01:05,  3.57it/s, step size=2.26e+00, acc. prob=0.782]
Warmup:  21%|##1       | 275/1300 [01:06,  3.37it/s, step size=6.80e-01, acc. prob=0.780]
Warmup:  21%|##1       | 276/1300 [01:07,  2.78it/s, step size=1.15e+00, acc. prob=0.781]
Warmup:  21%|##1       | 277/1300 [01:07,  3.04it/s, step size=1.99e+00, acc. prob=0.782]
Warmup:  21%|##1       | 278/1300 [01:07,  3.28it/s, step size=3.42e+00, acc. prob=0.782]
Warmup:  22%|##1       | 280/1300 [01:08,  2.89it/s, step size=6.97e-01, acc. prob=0.780]
Warmup:  22%|##1       | 281/1300 [01:08,  3.11it/s, step size=1.23e+00, acc. prob=0.781]
Warmup:  22%|##1       | 282/1300 [01:08,  3.32it/s, step size=1.48e+00, acc. prob=0.782]
Warmup:  22%|##1       | 283/1300 [01:09,  3.49it/s, step size=2.58e+00, acc. prob=0.782]
Warmup:  22%|##1       | 285/1300 [01:09,  3.34it/s, step size=5.56e-01, acc. prob=0.780]
Warmup:  22%|##2       | 286/1300 [01:10,  2.77it/s, step size=9.55e-01, acc. prob=0.781]
Warmup:  22%|##2       | 287/1300 [01:10,  3.03it/s, step size=1.56e+00, acc. prob=0.782]
Warmup:  22%|##2       | 288/1300 [01:10,  3.27it/s, step size=2.67e+00, acc. prob=0.783]
Warmup:  22%|##2       | 290/1300 [01:10,  4.79it/s, step size=6.51e-01, acc. prob=0.781]
Warmup:  22%|##2       | 292/1300 [01:11,  4.00it/s, step size=1.63e+00, acc. prob=0.782]
Warmup:  23%|##2       | 293/1300 [01:11,  4.04it/s, step size=2.72e+00, acc. prob=0.783]
Warmup:  23%|##2       | 295/1300 [01:12,  4.69it/s, step size=2.31e+00, acc. prob=0.783]
Warmup:  23%|##2       | 297/1300 [01:12,  6.01it/s, step size=5.71e-01, acc. prob=0.781]
Warmup:  23%|##2       | 298/1300 [01:12,  4.67it/s, step size=9.37e-01, acc. prob=0.781]
Warmup:  23%|##3       | 299/1300 [01:12,  4.56it/s, step size=1.16e+00, acc. prob=0.781]
Warmup:  23%|##3       | 300/1300 [01:13,  4.46it/s, step size=1.16e+00, acc. prob=0.782]
Warmup:  23%|##3       | 301/1300 [01:13,  4.40it/s, step size=1.16e+00, acc. prob=1.000]
Sample:  23%|##3       | 303/1300 [01:13,  5.03it/s, step size=1.16e+00, acc. prob=0.951]
Sample:  23%|##3       | 304/1300 [01:14,  4.13it/s, step size=1.16e+00, acc. prob=0.960]
Sample:  23%|##3       | 305/1300 [01:14,  4.13it/s, step size=1.16e+00, acc. prob=0.968]
Sample:  24%|##3       | 306/1300 [01:14,  4.13it/s, step size=1.16e+00, acc. prob=0.972]
Sample:  24%|##3       | 307/1300 [01:14,  4.15it/s, step size=1.16e+00, acc. prob=0.974]
Sample:  24%|##3       | 308/1300 [01:15,  4.15it/s, step size=1.16e+00, acc. prob=0.970]
Sample:  24%|##3       | 309/1300 [01:15,  4.17it/s, step size=1.16e+00, acc. prob=0.955]
Sample:  24%|##3       | 311/1300 [01:15,  4.92it/s, step size=1.16e+00, acc. prob=0.946]
Sample:  24%|##4       | 312/1300 [01:15,  4.70it/s, step size=1.16e+00, acc. prob=0.943]
Sample:  24%|##4       | 313/1300 [01:16,  4.50it/s, step size=1.16e+00, acc. prob=0.948]
Sample:  24%|##4       | 314/1300 [01:16,  4.39it/s, step size=1.16e+00, acc. prob=0.951]
Sample:  24%|##4       | 315/1300 [01:16,  4.32it/s, step size=1.16e+00, acc. prob=0.943]
Sample:  24%|##4       | 316/1300 [01:16,  4.28it/s, step size=1.16e+00, acc. prob=0.929]
Sample:  24%|##4       | 318/1300 [01:16,  6.07it/s, step size=1.16e+00, acc. prob=0.929]
Sample:  25%|##4       | 319/1300 [01:17,  5.43it/s, step size=1.16e+00, acc. prob=0.933]
Sample:  25%|##4       | 320/1300 [01:17,  5.02it/s, step size=1.16e+00, acc. prob=0.923]
Sample:  25%|##4       | 321/1300 [01:17,  4.74it/s, step size=1.16e+00, acc. prob=0.922]
Sample:  25%|##4       | 323/1300 [01:17,  6.47it/s, step size=1.16e+00, acc. prob=0.928]
Sample:  25%|##4       | 324/1300 [01:18,  5.72it/s, step size=1.16e+00, acc. prob=0.931]
Sample:  25%|##5       | 325/1300 [01:18,  5.24it/s, step size=1.16e+00, acc. prob=0.932]
Sample:  25%|##5       | 326/1300 [01:18,  4.85it/s, step size=1.16e+00, acc. prob=0.934]
Sample:  25%|##5       | 327/1300 [01:18,  4.65it/s, step size=1.16e+00, acc. prob=0.929]
Sample:  25%|##5       | 328/1300 [01:19,  4.49it/s, step size=1.16e+00, acc. prob=0.931]
Sample:  25%|##5       | 330/1300 [01:19,  6.28it/s, step size=1.16e+00, acc. prob=0.936]
Sample:  26%|##5       | 332/1300 [01:19,  6.26it/s, step size=1.16e+00, acc. prob=0.929]
Sample:  26%|##5       | 333/1300 [01:19,  5.66it/s, step size=1.16e+00, acc. prob=0.931]
Sample:  26%|##5       | 334/1300 [01:20,  5.22it/s, step size=1.16e+00, acc. prob=0.923]
Sample:  26%|##5       | 335/1300 [01:20,  4.92it/s, step size=1.16e+00, acc. prob=0.924]
Sample:  26%|##5       | 336/1300 [01:20,  4.70it/s, step size=1.16e+00, acc. prob=0.923]
Sample:  26%|##6       | 338/1300 [01:20,  5.24it/s, step size=1.16e+00, acc. prob=0.926]
Sample:  26%|##6       | 339/1300 [01:21,  4.96it/s, step size=1.16e+00, acc. prob=0.928]
Sample:  26%|##6       | 340/1300 [01:21,  4.75it/s, step size=1.16e+00, acc. prob=0.929]
Sample:  26%|##6       | 341/1300 [01:21,  4.57it/s, step size=1.16e+00, acc. prob=0.931]
Sample:  26%|##6       | 342/1300 [01:21,  4.47it/s, step size=1.16e+00, acc. prob=0.930]
Sample:  26%|##6       | 344/1300 [01:22,  5.11it/s, step size=1.16e+00, acc. prob=0.929]
Sample:  27%|##6       | 346/1300 [01:22,  5.52it/s, step size=1.16e+00, acc. prob=0.927]
Sample:  27%|##6       | 347/1300 [01:22,  5.17it/s, step size=1.16e+00, acc. prob=0.928]
Sample:  27%|##6       | 348/1300 [01:22,  4.88it/s, step size=1.16e+00, acc. prob=0.928]
Sample:  27%|##6       | 349/1300 [01:23,  4.67it/s, step size=1.16e+00, acc. prob=0.929]
Sample:  27%|##6       | 350/1300 [01:23,  4.55it/s, step size=1.16e+00, acc. prob=0.930]
Sample:  27%|##7       | 352/1300 [01:23,  5.15it/s, step size=1.16e+00, acc. prob=0.929]
Sample:  27%|##7       | 353/1300 [01:23,  4.86it/s, step size=1.16e+00, acc. prob=0.930]
Sample:  27%|##7       | 354/1300 [01:24,  4.58it/s, step size=1.16e+00, acc. prob=0.931]
Sample:  27%|##7       | 355/1300 [01:24,  4.47it/s, step size=1.16e+00, acc. prob=0.932]
Sample:  27%|##7       | 356/1300 [01:24,  4.35it/s, step size=1.16e+00, acc. prob=0.933]
Sample:  27%|##7       | 357/1300 [01:24,  4.31it/s, step size=1.16e+00, acc. prob=0.934]
Sample:  28%|##7       | 358/1300 [01:25,  4.27it/s, step size=1.16e+00, acc. prob=0.931]
Sample:  28%|##7       | 359/1300 [01:25,  4.22it/s, step size=1.16e+00, acc. prob=0.932]
Sample:  28%|##7       | 360/1300 [01:25,  4.21it/s, step size=1.16e+00, acc. prob=0.933]
Sample:  28%|##7       | 362/1300 [01:25,  6.04it/s, step size=1.16e+00, acc. prob=0.934]
Sample:  28%|##7       | 363/1300 [01:26,  5.42it/s, step size=1.16e+00, acc. prob=0.933]
Sample:  28%|##8       | 365/1300 [01:26,  7.06it/s, step size=1.16e+00, acc. prob=0.933]
Sample:  28%|##8       | 367/1300 [01:26,  8.45it/s, step size=1.16e+00, acc. prob=0.933]
Sample:  28%|##8       | 369/1300 [01:26,  9.54it/s, step size=1.16e+00, acc. prob=0.934]
Sample:  29%|##8       | 371/1300 [01:27,  6.61it/s, step size=1.16e+00, acc. prob=0.936]
Sample:  29%|##8       | 372/1300 [01:27,  5.95it/s, step size=1.16e+00, acc. prob=0.936]
Sample:  29%|##8       | 373/1300 [01:27,  5.44it/s, step size=1.16e+00, acc. prob=0.937]
Sample:  29%|##8       | 374/1300 [01:27,  5.07it/s, step size=1.16e+00, acc. prob=0.934]
Sample:  29%|##8       | 375/1300 [01:27,  4.79it/s, step size=1.16e+00, acc. prob=0.935]
Sample:  29%|##9       | 377/1300 [01:28,  5.29it/s, step size=1.16e+00, acc. prob=0.936]
Sample:  29%|##9       | 378/1300 [01:28,  4.98it/s, step size=1.16e+00, acc. prob=0.935]
Sample:  29%|##9       | 379/1300 [01:28,  4.74it/s, step size=1.16e+00, acc. prob=0.936]
Sample:  29%|##9       | 381/1300 [01:29,  5.28it/s, step size=1.16e+00, acc. prob=0.937]
Sample:  29%|##9       | 382/1300 [01:29,  5.01it/s, step size=1.16e+00, acc. prob=0.935]
Sample:  29%|##9       | 383/1300 [01:29,  4.79it/s, step size=1.16e+00, acc. prob=0.933]
Sample:  30%|##9       | 384/1300 [01:29,  4.63it/s, step size=1.16e+00, acc. prob=0.933]
Sample:  30%|##9       | 385/1300 [01:30,  4.49it/s, step size=1.16e+00, acc. prob=0.932]
Sample:  30%|##9       | 386/1300 [01:30,  4.40it/s, step size=1.16e+00, acc. prob=0.933]
Sample:  30%|##9       | 388/1300 [01:30,  6.16it/s, step size=1.16e+00, acc. prob=0.934]
Sample:  30%|##9       | 389/1300 [01:30,  5.53it/s, step size=1.16e+00, acc. prob=0.935]
Sample:  30%|###       | 390/1300 [01:30,  5.12it/s, step size=1.16e+00, acc. prob=0.934]
Sample:  30%|###       | 392/1300 [01:31,  5.52it/s, step size=1.16e+00, acc. prob=0.934]
Sample:  30%|###       | 393/1300 [01:31,  5.12it/s, step size=1.16e+00, acc. prob=0.934]
Sample:  30%|###       | 394/1300 [01:31,  4.85it/s, step size=1.16e+00, acc. prob=0.935]
Sample:  30%|###       | 395/1300 [01:31,  4.66it/s, step size=1.16e+00, acc. prob=0.932]
Sample:  30%|###       | 396/1300 [01:32,  4.52it/s, step size=1.16e+00, acc. prob=0.933]
Sample:  31%|###       | 397/1300 [01:32,  4.41it/s, step size=1.16e+00, acc. prob=0.933]
Sample:  31%|###       | 398/1300 [01:32,  4.36it/s, step size=1.16e+00, acc. prob=0.934]
Sample:  31%|###       | 399/1300 [01:32,  4.29it/s, step size=1.16e+00, acc. prob=0.934]
Sample:  31%|###       | 400/1300 [01:33,  4.25it/s, step size=1.16e+00, acc. prob=0.934]
Sample:  31%|###       | 401/1300 [01:33,  4.24it/s, step size=1.16e+00, acc. prob=0.935]
Sample:  31%|###       | 402/1300 [01:33,  4.21it/s, step size=1.16e+00, acc. prob=0.936]
Sample:  31%|###1      | 403/1300 [01:33,  4.20it/s, step size=1.16e+00, acc. prob=0.935]
Sample:  31%|###1      | 404/1300 [01:34,  4.18it/s, step size=1.16e+00, acc. prob=0.936]
Sample:  31%|###1      | 405/1300 [01:34,  4.16it/s, step size=1.16e+00, acc. prob=0.936]
Sample:  31%|###1      | 407/1300 [01:34,  4.93it/s, step size=1.16e+00, acc. prob=0.937]
Sample:  31%|###1      | 408/1300 [01:34,  4.71it/s, step size=1.16e+00, acc. prob=0.938]
Sample:  31%|###1      | 409/1300 [01:35,  4.54it/s, step size=1.16e+00, acc. prob=0.938]
Sample:  32%|###1      | 410/1300 [01:35,  4.44it/s, step size=1.16e+00, acc. prob=0.938]
Sample:  32%|###1      | 411/1300 [01:35,  4.35it/s, step size=1.16e+00, acc. prob=0.938]
Sample:  32%|###1      | 413/1300 [01:35,  6.13it/s, step size=1.16e+00, acc. prob=0.939]
Sample:  32%|###1      | 414/1300 [01:36,  5.49it/s, step size=1.16e+00, acc. prob=0.939]
Sample:  32%|###1      | 415/1300 [01:36,  5.11it/s, step size=1.16e+00, acc. prob=0.938]
Sample:  32%|###2      | 416/1300 [01:36,  4.82it/s, step size=1.16e+00, acc. prob=0.938]
Sample:  32%|###2      | 418/1300 [01:36,  6.53it/s, step size=1.16e+00, acc. prob=0.939]
Sample:  32%|###2      | 419/1300 [01:36,  5.75it/s, step size=1.16e+00, acc. prob=0.939]
Sample:  32%|###2      | 421/1300 [01:37,  5.96it/s, step size=1.16e+00, acc. prob=0.939]
Sample:  33%|###2      | 423/1300 [01:37,  6.05it/s, step size=1.16e+00, acc. prob=0.939]
Sample:  33%|###2      | 424/1300 [01:37,  5.52it/s, step size=1.16e+00, acc. prob=0.939]
Sample:  33%|###2      | 426/1300 [01:38,  5.76it/s, step size=1.16e+00, acc. prob=0.939]
Sample:  33%|###2      | 428/1300 [01:38,  7.09it/s, step size=1.16e+00, acc. prob=0.939]
Sample:  33%|###3      | 430/1300 [01:38,  6.77it/s, step size=1.16e+00, acc. prob=0.938]
Sample:  33%|###3      | 432/1300 [01:38,  7.94it/s, step size=1.16e+00, acc. prob=0.939]
Sample:  33%|###3      | 433/1300 [01:39,  6.81it/s, step size=1.16e+00, acc. prob=0.939]
Sample:  33%|###3      | 434/1300 [01:39,  6.03it/s, step size=1.16e+00, acc. prob=0.937]
Sample:  33%|###3      | 435/1300 [01:39,  5.46it/s, step size=1.16e+00, acc. prob=0.937]
Sample:  34%|###3      | 436/1300 [01:39,  5.06it/s, step size=1.16e+00, acc. prob=0.937]
Sample:  34%|###3      | 437/1300 [01:39,  4.79it/s, step size=1.16e+00, acc. prob=0.938]
Sample:  34%|###3      | 439/1300 [01:40,  5.33it/s, step size=1.16e+00, acc. prob=0.936]
Sample:  34%|###3      | 440/1300 [01:40,  5.01it/s, step size=1.16e+00, acc. prob=0.937]
Sample:  34%|###3      | 441/1300 [01:40,  4.75it/s, step size=1.16e+00, acc. prob=0.937]
Sample:  34%|###4      | 442/1300 [01:41,  4.58it/s, step size=1.16e+00, acc. prob=0.937]
Sample:  34%|###4      | 443/1300 [01:41,  4.45it/s, step size=1.16e+00, acc. prob=0.935]
Sample:  34%|###4      | 444/1300 [01:41,  4.34it/s, step size=1.16e+00, acc. prob=0.936]
Sample:  34%|###4      | 445/1300 [01:41,  4.30it/s, step size=1.16e+00, acc. prob=0.936]
Sample:  34%|###4      | 446/1300 [01:41,  4.28it/s, step size=1.16e+00, acc. prob=0.936]
Sample:  34%|###4      | 447/1300 [01:42,  4.24it/s, step size=1.16e+00, acc. prob=0.935]
Sample:  34%|###4      | 448/1300 [01:42,  4.22it/s, step size=1.16e+00, acc. prob=0.935]
Sample:  35%|###4      | 449/1300 [01:42,  4.21it/s, step size=1.16e+00, acc. prob=0.936]
Sample:  35%|###4      | 450/1300 [01:42,  4.17it/s, step size=1.16e+00, acc. prob=0.936]
Sample:  35%|###4      | 451/1300 [01:43,  4.14it/s, step size=1.16e+00, acc. prob=0.936]
Sample:  35%|###4      | 452/1300 [01:43,  4.15it/s, step size=1.16e+00, acc. prob=0.935]
Sample:  35%|###4      | 453/1300 [01:43,  4.16it/s, step size=1.16e+00, acc. prob=0.934]
Sample:  35%|###4      | 454/1300 [01:43,  4.09it/s, step size=1.16e+00, acc. prob=0.934]
Sample:  35%|###5      | 456/1300 [01:44,  4.85it/s, step size=1.16e+00, acc. prob=0.934]
Sample:  35%|###5      | 457/1300 [01:44,  4.69it/s, step size=1.16e+00, acc. prob=0.935]
Sample:  35%|###5      | 458/1300 [01:44,  4.54it/s, step size=1.16e+00, acc. prob=0.935]
Sample:  35%|###5      | 459/1300 [01:44,  4.44it/s, step size=1.16e+00, acc. prob=0.935]
Sample:  35%|###5      | 460/1300 [01:45,  4.35it/s, step size=1.16e+00, acc. prob=0.935]
Sample:  36%|###5      | 462/1300 [01:45,  5.03it/s, step size=1.16e+00, acc. prob=0.935]
Sample:  36%|###5      | 463/1300 [01:45,  4.80it/s, step size=1.16e+00, acc. prob=0.935]
Sample:  36%|###5      | 464/1300 [01:46,  4.59it/s, step size=1.16e+00, acc. prob=0.936]
Sample:  36%|###5      | 465/1300 [01:46,  4.47it/s, step size=1.16e+00, acc. prob=0.936]
Sample:  36%|###5      | 466/1300 [01:46,  4.37it/s, step size=1.16e+00, acc. prob=0.936]
Sample:  36%|###6      | 468/1300 [01:46,  5.01it/s, step size=1.16e+00, acc. prob=0.936]
Sample:  36%|###6      | 469/1300 [01:47,  4.75it/s, step size=1.16e+00, acc. prob=0.936]
Sample:  36%|###6      | 470/1300 [01:47,  4.59it/s, step size=1.16e+00, acc. prob=0.937]
Sample:  36%|###6      | 471/1300 [01:47,  4.48it/s, step size=1.16e+00, acc. prob=0.937]
Sample:  36%|###6      | 472/1300 [01:47,  4.39it/s, step size=1.16e+00, acc. prob=0.937]
Sample:  36%|###6      | 473/1300 [01:48,  4.32it/s, step size=1.16e+00, acc. prob=0.935]
Sample:  37%|###6      | 475/1300 [01:48,  5.02it/s, step size=1.16e+00, acc. prob=0.936]
Sample:  37%|###6      | 477/1300 [01:48,  5.42it/s, step size=1.16e+00, acc. prob=0.935]
Sample:  37%|###6      | 479/1300 [01:48,  5.67it/s, step size=1.16e+00, acc. prob=0.935]
Sample:  37%|###6      | 480/1300 [01:49,  5.29it/s, step size=1.16e+00, acc. prob=0.936]
Sample:  37%|###7      | 481/1300 [01:49,  4.99it/s, step size=1.16e+00, acc. prob=0.935]
Sample:  37%|###7      | 483/1300 [01:49,  5.43it/s, step size=1.16e+00, acc. prob=0.936]
Sample:  37%|###7      | 485/1300 [01:50,  5.71it/s, step size=1.16e+00, acc. prob=0.936]
Sample:  37%|###7      | 486/1300 [01:50,  5.30it/s, step size=1.16e+00, acc. prob=0.936]
Sample:  37%|###7      | 487/1300 [01:50,  5.01it/s, step size=1.16e+00, acc. prob=0.937]
Sample:  38%|###7      | 489/1300 [01:50,  6.57it/s, step size=1.16e+00, acc. prob=0.937]
Sample:  38%|###7      | 490/1300 [01:50,  5.86it/s, step size=1.16e+00, acc. prob=0.937]
Sample:  38%|###7      | 492/1300 [01:51,  6.01it/s, step size=1.16e+00, acc. prob=0.937]
Sample:  38%|###8      | 494/1300 [01:51,  7.36it/s, step size=1.16e+00, acc. prob=0.937]
Sample:  38%|###8      | 495/1300 [01:51,  6.39it/s, step size=1.16e+00, acc. prob=0.937]
Sample:  38%|###8      | 496/1300 [01:51,  5.70it/s, step size=1.16e+00, acc. prob=0.937]
Sample:  38%|###8      | 497/1300 [01:52,  5.23it/s, step size=1.16e+00, acc. prob=0.936]
Sample:  38%|###8      | 498/1300 [01:52,  4.92it/s, step size=1.16e+00, acc. prob=0.936]
Sample:  38%|###8      | 499/1300 [01:52,  4.69it/s, step size=1.16e+00, acc. prob=0.936]
Sample:  39%|###8      | 501/1300 [01:52,  5.27it/s, step size=1.16e+00, acc. prob=0.936]
Sample:  39%|###8      | 502/1300 [01:53,  4.95it/s, step size=1.16e+00, acc. prob=0.936]
Sample:  39%|###8      | 504/1300 [01:53,  6.54it/s, step size=1.16e+00, acc. prob=0.936]
Sample:  39%|###8      | 505/1300 [01:53,  5.81it/s, step size=1.16e+00, acc. prob=0.936]
Sample:  39%|###9      | 507/1300 [01:53,  6.01it/s, step size=1.16e+00, acc. prob=0.937]
Sample:  39%|###9      | 509/1300 [01:54,  7.36it/s, step size=1.16e+00, acc. prob=0.936]
Sample:  39%|###9      | 510/1300 [01:54,  6.39it/s, step size=1.16e+00, acc. prob=0.937]
Sample:  39%|###9      | 511/1300 [01:54,  5.67it/s, step size=1.16e+00, acc. prob=0.936]
Sample:  39%|###9      | 512/1300 [01:54,  5.22it/s, step size=1.16e+00, acc. prob=0.936]
Sample:  39%|###9      | 513/1300 [01:55,  4.86it/s, step size=1.16e+00, acc. prob=0.936]
Sample:  40%|###9      | 514/1300 [01:55,  4.67it/s, step size=1.16e+00, acc. prob=0.936]
Sample:  40%|###9      | 516/1300 [01:55,  5.23it/s, step size=1.16e+00, acc. prob=0.935]
Sample:  40%|###9      | 518/1300 [01:55,  6.71it/s, step size=1.16e+00, acc. prob=0.935]
Sample:  40%|###9      | 519/1300 [01:56,  5.95it/s, step size=1.16e+00, acc. prob=0.935]
Sample:  40%|####      | 521/1300 [01:56,  7.43it/s, step size=1.16e+00, acc. prob=0.935]
Sample:  40%|####      | 523/1300 [01:56,  6.95it/s, step size=1.16e+00, acc. prob=0.933]
Sample:  40%|####      | 524/1300 [01:56,  6.11it/s, step size=1.16e+00, acc. prob=0.934]
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Sample:  41%|####      | 527/1300 [01:57,  6.41it/s, step size=1.16e+00, acc. prob=0.933]
Sample:  41%|####      | 529/1300 [01:57,  6.34it/s, step size=1.16e+00, acc. prob=0.932]
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Sample:  41%|####1     | 533/1300 [01:58,  4.72it/s, step size=1.16e+00, acc. prob=0.932]
Sample:  41%|####1     | 535/1300 [01:58,  5.22it/s, step size=1.16e+00, acc. prob=0.932]
Sample:  41%|####1     | 536/1300 [01:58,  4.95it/s, step size=1.16e+00, acc. prob=0.932]
Sample:  41%|####1     | 537/1300 [01:59,  4.75it/s, step size=1.16e+00, acc. prob=0.933]
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Sample:  42%|####1     | 540/1300 [01:59,  4.37it/s, step size=1.16e+00, acc. prob=0.933]
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Sample:  42%|####1     | 543/1300 [02:00,  4.25it/s, step size=1.16e+00, acc. prob=0.931]
Sample:  42%|####1     | 544/1300 [02:00,  4.20it/s, step size=1.16e+00, acc. prob=0.932]
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Sample:  42%|####2     | 548/1300 [02:01,  5.39it/s, step size=1.16e+00, acc. prob=0.931]
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Sample:  43%|####2     | 557/1300 [02:02,  5.91it/s, step size=1.16e+00, acc. prob=0.932]
Sample:  43%|####3     | 559/1300 [02:03,  6.03it/s, step size=1.16e+00, acc. prob=0.932]
Sample:  43%|####3     | 561/1300 [02:03,  6.14it/s, step size=1.16e+00, acc. prob=0.931]
Sample:  43%|####3     | 563/1300 [02:03,  6.18it/s, step size=1.16e+00, acc. prob=0.931]
Sample:  43%|####3     | 564/1300 [02:03,  5.62it/s, step size=1.16e+00, acc. prob=0.932]
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Sample:  44%|####3     | 569/1300 [02:05,  4.38it/s, step size=1.16e+00, acc. prob=0.932]
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Sample:  44%|####4     | 573/1300 [02:05,  5.44it/s, step size=1.16e+00, acc. prob=0.931]
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Sample:  45%|####5     | 590/1300 [02:09,  6.09it/s, step size=1.16e+00, acc. prob=0.932]
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Sample:  46%|####5     | 594/1300 [02:09,  5.32it/s, step size=1.16e+00, acc. prob=0.933]
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Sample:  46%|####6     | 599/1300 [02:10,  8.01it/s, step size=1.16e+00, acc. prob=0.932]
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Sample:  47%|####6     | 609/1300 [02:12,  5.18it/s, step size=1.16e+00, acc. prob=0.932]
Sample:  47%|####6     | 610/1300 [02:12,  4.88it/s, step size=1.16e+00, acc. prob=0.931]
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Sample:  47%|####7     | 612/1300 [02:12,  4.53it/s, step size=1.16e+00, acc. prob=0.931]
Sample:  47%|####7     | 613/1300 [02:13,  4.42it/s, step size=1.16e+00, acc. prob=0.932]
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Sample:  47%|####7     | 617/1300 [02:13,  6.11it/s, step size=1.16e+00, acc. prob=0.932]
Sample:  48%|####7     | 619/1300 [02:14,  5.95it/s, step size=1.16e+00, acc. prob=0.931]
Sample:  48%|####7     | 620/1300 [02:14,  5.20it/s, step size=1.16e+00, acc. prob=0.932]
Sample:  48%|####7     | 622/1300 [02:14,  5.50it/s, step size=1.16e+00, acc. prob=0.932]
Sample:  48%|####8     | 624/1300 [02:15,  5.71it/s, step size=1.16e+00, acc. prob=0.932]
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Sample:  48%|####8     | 629/1300 [02:16,  5.07it/s, step size=1.16e+00, acc. prob=0.932]
Sample:  49%|####8     | 631/1300 [02:16,  5.48it/s, step size=1.16e+00, acc. prob=0.933]
Sample:  49%|####8     | 632/1300 [02:16,  5.12it/s, step size=1.16e+00, acc. prob=0.933]
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Sample:  49%|####8     | 636/1300 [02:17,  6.83it/s, step size=1.16e+00, acc. prob=0.932]
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Sample:  49%|####9     | 638/1300 [02:17,  5.48it/s, step size=1.16e+00, acc. prob=0.933]
Sample:  49%|####9     | 639/1300 [02:17,  5.09it/s, step size=1.16e+00, acc. prob=0.932]
Sample:  49%|####9     | 640/1300 [02:18,  4.81it/s, step size=1.16e+00, acc. prob=0.932]
Sample:  49%|####9     | 642/1300 [02:18,  6.50it/s, step size=1.16e+00, acc. prob=0.933]
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Sample:  50%|####9     | 645/1300 [02:19,  4.90it/s, step size=1.16e+00, acc. prob=0.933]
Sample:  50%|####9     | 646/1300 [02:19,  4.67it/s, step size=1.16e+00, acc. prob=0.933]
Sample:  50%|####9     | 647/1300 [02:19,  4.51it/s, step size=1.16e+00, acc. prob=0.933]
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Sample:  50%|####9     | 649/1300 [02:20,  4.33it/s, step size=1.16e+00, acc. prob=0.933]
Sample:  50%|#####     | 650/1300 [02:20,  4.29it/s, step size=1.16e+00, acc. prob=0.933]
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Sample:  50%|#####     | 652/1300 [02:20,  4.22it/s, step size=1.16e+00, acc. prob=0.932]
Sample:  50%|#####     | 654/1300 [02:21,  4.97it/s, step size=1.16e+00, acc. prob=0.933]
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Sample:  51%|#####     | 659/1300 [02:21,  6.01it/s, step size=1.16e+00, acc. prob=0.932]
Sample:  51%|#####     | 661/1300 [02:21,  7.44it/s, step size=1.16e+00, acc. prob=0.933]
Sample:  51%|#####     | 662/1300 [02:22,  6.40it/s, step size=1.16e+00, acc. prob=0.932]
Sample:  51%|#####1    | 663/1300 [02:22,  5.74it/s, step size=1.16e+00, acc. prob=0.932]
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Sample:  51%|#####1    | 667/1300 [02:23,  5.41it/s, step size=1.16e+00, acc. prob=0.932]
Sample:  51%|#####1    | 668/1300 [02:23,  5.06it/s, step size=1.16e+00, acc. prob=0.932]
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Sample:  52%|#####1    | 670/1300 [02:23,  4.61it/s, step size=1.16e+00, acc. prob=0.932]
Sample:  52%|#####1    | 672/1300 [02:24,  5.19it/s, step size=1.16e+00, acc. prob=0.933]
Sample:  52%|#####1    | 674/1300 [02:24,  5.49it/s, step size=1.16e+00, acc. prob=0.933]
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Sample:  52%|#####2    | 677/1300 [02:25,  5.32it/s, step size=1.16e+00, acc. prob=0.933]
Sample:  52%|#####2    | 679/1300 [02:25,  5.66it/s, step size=1.16e+00, acc. prob=0.933]
Sample:  52%|#####2    | 680/1300 [02:25,  5.27it/s, step size=1.16e+00, acc. prob=0.932]
Sample:  52%|#####2    | 681/1300 [02:25,  4.98it/s, step size=1.16e+00, acc. prob=0.931]
Sample:  52%|#####2    | 682/1300 [02:26,  4.75it/s, step size=1.16e+00, acc. prob=0.932]
Sample:  53%|#####2    | 683/1300 [02:26,  4.61it/s, step size=1.16e+00, acc. prob=0.932]
Sample:  53%|#####2    | 684/1300 [02:26,  4.46it/s, step size=1.16e+00, acc. prob=0.932]
Sample:  53%|#####2    | 685/1300 [02:26,  4.36it/s, step size=1.16e+00, acc. prob=0.932]
Sample:  53%|#####2    | 686/1300 [02:27,  4.28it/s, step size=1.16e+00, acc. prob=0.932]
Sample:  53%|#####2    | 687/1300 [02:27,  4.25it/s, step size=1.16e+00, acc. prob=0.932]
Sample:  53%|#####3    | 689/1300 [02:27,  4.97it/s, step size=1.16e+00, acc. prob=0.932]
Sample:  53%|#####3    | 690/1300 [02:27,  4.76it/s, step size=1.16e+00, acc. prob=0.932]
Sample:  53%|#####3    | 691/1300 [02:28,  4.57it/s, step size=1.16e+00, acc. prob=0.932]
Sample:  53%|#####3    | 692/1300 [02:28,  4.46it/s, step size=1.16e+00, acc. prob=0.932]
Sample:  53%|#####3    | 693/1300 [02:28,  4.38it/s, step size=1.16e+00, acc. prob=0.932]
Sample:  53%|#####3    | 694/1300 [02:28,  4.30it/s, step size=1.16e+00, acc. prob=0.932]
Sample:  53%|#####3    | 695/1300 [02:29,  4.26it/s, step size=1.16e+00, acc. prob=0.932]
Sample:  54%|#####3    | 696/1300 [02:29,  4.25it/s, step size=1.16e+00, acc. prob=0.932]
Sample:  54%|#####3    | 697/1300 [02:29,  4.23it/s, step size=1.16e+00, acc. prob=0.932]
Sample:  54%|#####3    | 698/1300 [02:29,  4.21it/s, step size=1.16e+00, acc. prob=0.932]
Sample:  54%|#####3    | 699/1300 [02:30,  4.19it/s, step size=1.16e+00, acc. prob=0.932]
Sample:  54%|#####3    | 701/1300 [02:30,  4.92it/s, step size=1.16e+00, acc. prob=0.932]
Sample:  54%|#####4    | 702/1300 [02:30,  4.69it/s, step size=1.16e+00, acc. prob=0.932]
Sample:  54%|#####4    | 703/1300 [02:30,  4.52it/s, step size=1.16e+00, acc. prob=0.932]
Sample:  54%|#####4    | 704/1300 [02:31,  4.39it/s, step size=1.16e+00, acc. prob=0.932]
Sample:  54%|#####4    | 705/1300 [02:31,  4.33it/s, step size=1.16e+00, acc. prob=0.931]
Sample:  54%|#####4    | 706/1300 [02:31,  4.28it/s, step size=1.16e+00, acc. prob=0.931]
Sample:  54%|#####4    | 707/1300 [02:31,  4.24it/s, step size=1.16e+00, acc. prob=0.931]
Sample:  54%|#####4    | 708/1300 [02:32,  4.18it/s, step size=1.16e+00, acc. prob=0.930]
Sample:  55%|#####4    | 709/1300 [02:32,  4.17it/s, step size=1.16e+00, acc. prob=0.930]
Sample:  55%|#####4    | 711/1300 [02:32,  4.81it/s, step size=1.16e+00, acc. prob=0.930]
Sample:  55%|#####4    | 712/1300 [02:32,  4.57it/s, step size=1.16e+00, acc. prob=0.930]
Sample:  55%|#####4    | 713/1300 [02:33,  4.45it/s, step size=1.16e+00, acc. prob=0.930]
Sample:  55%|#####4    | 714/1300 [02:33,  4.34it/s, step size=1.16e+00, acc. prob=0.929]
Sample:  55%|#####5    | 715/1300 [02:33,  4.19it/s, step size=1.16e+00, acc. prob=0.930]
Sample:  55%|#####5    | 716/1300 [02:33,  4.11it/s, step size=1.16e+00, acc. prob=0.929]
Sample:  55%|#####5    | 717/1300 [02:34,  4.07it/s, step size=1.16e+00, acc. prob=0.930]
Sample:  55%|#####5    | 718/1300 [02:34,  3.97it/s, step size=1.16e+00, acc. prob=0.929]
Sample:  55%|#####5    | 719/1300 [02:34,  3.94it/s, step size=1.16e+00, acc. prob=0.930]
Sample:  55%|#####5    | 720/1300 [02:35,  3.71it/s, step size=1.16e+00, acc. prob=0.930]
Sample:  55%|#####5    | 721/1300 [02:35,  3.79it/s, step size=1.16e+00, acc. prob=0.930]
Sample:  56%|#####5    | 722/1300 [02:35,  3.88it/s, step size=1.16e+00, acc. prob=0.930]
Sample:  56%|#####5    | 723/1300 [02:35,  3.90it/s, step size=1.16e+00, acc. prob=0.929]
Sample:  56%|#####5    | 724/1300 [02:36,  3.96it/s, step size=1.16e+00, acc. prob=0.929]
Sample:  56%|#####5    | 725/1300 [02:36,  3.92it/s, step size=1.16e+00, acc. prob=0.929]
Sample:  56%|#####5    | 726/1300 [02:36,  3.94it/s, step size=1.16e+00, acc. prob=0.930]
Sample:  56%|#####5    | 727/1300 [02:36,  4.01it/s, step size=1.16e+00, acc. prob=0.930]
Sample:  56%|#####6    | 728/1300 [02:37,  4.00it/s, step size=1.16e+00, acc. prob=0.930]
Sample:  56%|#####6    | 729/1300 [02:37,  3.99it/s, step size=1.16e+00, acc. prob=0.929]
Sample:  56%|#####6    | 730/1300 [02:37,  4.04it/s, step size=1.16e+00, acc. prob=0.929]
Sample:  56%|#####6    | 731/1300 [02:37,  4.07it/s, step size=1.16e+00, acc. prob=0.929]
Sample:  56%|#####6    | 733/1300 [02:38,  4.80it/s, step size=1.16e+00, acc. prob=0.929]
Sample:  56%|#####6    | 734/1300 [02:38,  4.60it/s, step size=1.16e+00, acc. prob=0.929]
Sample:  57%|#####6    | 735/1300 [02:38,  4.47it/s, step size=1.16e+00, acc. prob=0.929]
Sample:  57%|#####6    | 737/1300 [02:38,  5.06it/s, step size=1.16e+00, acc. prob=0.929]
Sample:  57%|#####6    | 738/1300 [02:39,  4.82it/s, step size=1.16e+00, acc. prob=0.929]
Sample:  57%|#####6    | 739/1300 [02:39,  4.64it/s, step size=1.16e+00, acc. prob=0.928]
Sample:  57%|#####6    | 740/1300 [02:39,  4.50it/s, step size=1.16e+00, acc. prob=0.928]
Sample:  57%|#####6    | 741/1300 [02:39,  4.41it/s, step size=1.16e+00, acc. prob=0.928]
Sample:  57%|#####7    | 742/1300 [02:40,  4.33it/s, step size=1.16e+00, acc. prob=0.928]
Sample:  57%|#####7    | 743/1300 [02:40,  4.25it/s, step size=1.16e+00, acc. prob=0.928]
Sample:  57%|#####7    | 744/1300 [02:40,  4.24it/s, step size=1.16e+00, acc. prob=0.928]
Sample:  57%|#####7    | 745/1300 [02:40,  4.22it/s, step size=1.16e+00, acc. prob=0.928]
Sample:  57%|#####7    | 746/1300 [02:41,  4.22it/s, step size=1.16e+00, acc. prob=0.929]
Sample:  58%|#####7    | 748/1300 [02:41,  6.04it/s, step size=1.16e+00, acc. prob=0.928]
Sample:  58%|#####7    | 750/1300 [02:41,  7.55it/s, step size=1.16e+00, acc. prob=0.928]
Sample:  58%|#####7    | 751/1300 [02:41,  6.40it/s, step size=1.16e+00, acc. prob=0.928]
Sample:  58%|#####7    | 752/1300 [02:41,  5.66it/s, step size=1.16e+00, acc. prob=0.928]
Sample:  58%|#####7    | 753/1300 [02:42,  5.15it/s, step size=1.16e+00, acc. prob=0.927]
Sample:  58%|#####8    | 754/1300 [02:42,  4.08it/s, step size=1.16e+00, acc. prob=0.927]
Sample:  58%|#####8    | 755/1300 [02:42,  4.09it/s, step size=1.16e+00, acc. prob=0.927]
Sample:  58%|#####8    | 756/1300 [02:43,  4.10it/s, step size=1.16e+00, acc. prob=0.927]
Sample:  58%|#####8    | 758/1300 [02:43,  4.84it/s, step size=1.16e+00, acc. prob=0.927]
Sample:  58%|#####8    | 759/1300 [02:43,  4.64it/s, step size=1.16e+00, acc. prob=0.927]
Sample:  58%|#####8    | 760/1300 [02:43,  4.49it/s, step size=1.16e+00, acc. prob=0.927]
Sample:  59%|#####8    | 761/1300 [02:44,  4.34it/s, step size=1.16e+00, acc. prob=0.927]
Sample:  59%|#####8    | 762/1300 [02:44,  4.26it/s, step size=1.16e+00, acc. prob=0.927]
Sample:  59%|#####8    | 764/1300 [02:44,  5.99it/s, step size=1.16e+00, acc. prob=0.927]
Sample:  59%|#####8    | 765/1300 [02:44,  5.39it/s, step size=1.16e+00, acc. prob=0.927]
Sample:  59%|#####8    | 766/1300 [02:44,  4.99it/s, step size=1.16e+00, acc. prob=0.926]
Sample:  59%|#####8    | 767/1300 [02:45,  4.71it/s, step size=1.16e+00, acc. prob=0.927]
Sample:  59%|#####9    | 768/1300 [02:45,  4.51it/s, step size=1.16e+00, acc. prob=0.927]
Sample:  59%|#####9    | 769/1300 [02:45,  4.33it/s, step size=1.16e+00, acc. prob=0.927]
Sample:  59%|#####9    | 770/1300 [02:45,  4.27it/s, step size=1.16e+00, acc. prob=0.927]
Sample:  59%|#####9    | 771/1300 [02:46,  4.21it/s, step size=1.16e+00, acc. prob=0.926]
Sample:  59%|#####9    | 773/1300 [02:46,  4.94it/s, step size=1.16e+00, acc. prob=0.926]
Sample:  60%|#####9    | 775/1300 [02:46,  5.32it/s, step size=1.16e+00, acc. prob=0.926]
Sample:  60%|#####9    | 776/1300 [02:47,  4.98it/s, step size=1.16e+00, acc. prob=0.925]
Sample:  60%|#####9    | 777/1300 [02:47,  4.76it/s, step size=1.16e+00, acc. prob=0.925]
Sample:  60%|#####9    | 779/1300 [02:47,  6.35it/s, step size=1.16e+00, acc. prob=0.926]
Sample:  60%|######    | 781/1300 [02:47,  7.73it/s, step size=1.16e+00, acc. prob=0.925]
Sample:  60%|######    | 782/1300 [02:47,  6.49it/s, step size=1.16e+00, acc. prob=0.925]
Sample:  60%|######    | 783/1300 [02:48,  5.77it/s, step size=1.16e+00, acc. prob=0.925]
Sample:  60%|######    | 784/1300 [02:48,  5.28it/s, step size=1.16e+00, acc. prob=0.925]
Sample:  60%|######    | 786/1300 [02:48,  6.93it/s, step size=1.16e+00, acc. prob=0.925]
Sample:  61%|######    | 787/1300 [02:48,  5.93it/s, step size=1.16e+00, acc. prob=0.925]
Sample:  61%|######    | 789/1300 [02:49,  5.95it/s, step size=1.16e+00, acc. prob=0.925]
Sample:  61%|######    | 790/1300 [02:49,  5.44it/s, step size=1.16e+00, acc. prob=0.925]
Sample:  61%|######    | 792/1300 [02:49,  6.92it/s, step size=1.16e+00, acc. prob=0.925]
Sample:  61%|######1   | 793/1300 [02:49,  6.03it/s, step size=1.16e+00, acc. prob=0.926]
Sample:  61%|######1   | 795/1300 [02:49,  7.36it/s, step size=1.16e+00, acc. prob=0.926]
Sample:  61%|######1   | 796/1300 [02:50,  6.19it/s, step size=1.16e+00, acc. prob=0.925]
Sample:  61%|######1   | 798/1300 [02:50,  6.15it/s, step size=1.16e+00, acc. prob=0.926]
Sample:  61%|######1   | 799/1300 [02:50,  5.49it/s, step size=1.16e+00, acc. prob=0.926]
Sample:  62%|######1   | 800/1300 [02:51,  5.08it/s, step size=1.16e+00, acc. prob=0.926]
Sample:  62%|######1   | 801/1300 [02:51,  4.73it/s, step size=1.16e+00, acc. prob=0.926]
Sample:  62%|######1   | 802/1300 [02:51,  4.57it/s, step size=1.16e+00, acc. prob=0.926]
Sample:  62%|######1   | 803/1300 [02:51,  4.42it/s, step size=1.16e+00, acc. prob=0.926]
Sample:  62%|######1   | 804/1300 [02:52,  4.29it/s, step size=1.16e+00, acc. prob=0.926]
Sample:  62%|######1   | 805/1300 [02:52,  4.10it/s, step size=1.16e+00, acc. prob=0.926]
Sample:  62%|######2   | 807/1300 [02:52,  4.75it/s, step size=1.16e+00, acc. prob=0.926]
Sample:  62%|######2   | 808/1300 [02:52,  4.53it/s, step size=1.16e+00, acc. prob=0.926]
Sample:  62%|######2   | 809/1300 [02:53,  4.44it/s, step size=1.16e+00, acc. prob=0.926]
Sample:  62%|######2   | 810/1300 [02:53,  4.31it/s, step size=1.16e+00, acc. prob=0.926]
Sample:  62%|######2   | 812/1300 [02:53,  4.94it/s, step size=1.16e+00, acc. prob=0.926]
Sample:  63%|######2   | 813/1300 [02:53,  4.70it/s, step size=1.16e+00, acc. prob=0.926]
Sample:  63%|######2   | 815/1300 [02:54,  6.27it/s, step size=1.16e+00, acc. prob=0.926]
Sample:  63%|######2   | 817/1300 [02:54,  7.68it/s, step size=1.16e+00, acc. prob=0.926]
Sample:  63%|######3   | 819/1300 [02:54,  7.03it/s, step size=1.16e+00, acc. prob=0.926]
Sample:  63%|######3   | 820/1300 [02:54,  6.18it/s, step size=1.16e+00, acc. prob=0.926]
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Sample:  97%|#########7| 1263/1300 [04:16,  4.75it/s, step size=1.16e+00, acc. prob=0.925]
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Sample:  97%|#########7| 1265/1300 [04:16,  4.45it/s, step size=1.16e+00, acc. prob=0.925]
Sample:  97%|#########7| 1266/1300 [04:17,  4.34it/s, step size=1.16e+00, acc. prob=0.925]
Sample:  98%|#########7| 1268/1300 [04:17,  6.13it/s, step size=1.16e+00, acc. prob=0.925]
Sample:  98%|#########7| 1270/1300 [04:17,  7.63it/s, step size=1.16e+00, acc. prob=0.925]
Sample:  98%|#########7| 1271/1300 [04:17,  6.44it/s, step size=1.16e+00, acc. prob=0.925]
Sample:  98%|#########7| 1272/1300 [04:17,  5.67it/s, step size=1.16e+00, acc. prob=0.925]
Sample:  98%|#########8| 1274/1300 [04:18,  5.88it/s, step size=1.16e+00, acc. prob=0.925]
Sample:  98%|#########8| 1275/1300 [04:18,  5.37it/s, step size=1.16e+00, acc. prob=0.925]
Sample:  98%|#########8| 1276/1300 [04:18,  5.00it/s, step size=1.16e+00, acc. prob=0.925]
Sample:  98%|#########8| 1277/1300 [04:19,  4.65it/s, step size=1.16e+00, acc. prob=0.925]
Sample:  98%|#########8| 1278/1300 [04:19,  4.51it/s, step size=1.16e+00, acc. prob=0.925]
Sample:  98%|#########8| 1280/1300 [04:19,  6.24it/s, step size=1.16e+00, acc. prob=0.925]
Sample:  99%|#########8| 1281/1300 [04:19,  5.59it/s, step size=1.16e+00, acc. prob=0.925]
Sample:  99%|#########8| 1283/1300 [04:19,  7.17it/s, step size=1.16e+00, acc. prob=0.925]
Sample:  99%|#########8| 1284/1300 [04:20,  6.19it/s, step size=1.16e+00, acc. prob=0.925]
Sample:  99%|#########8| 1286/1300 [04:20,  7.69it/s, step size=1.16e+00, acc. prob=0.925]
Sample:  99%|#########9| 1287/1300 [04:20,  6.48it/s, step size=1.16e+00, acc. prob=0.925]
Sample:  99%|#########9| 1288/1300 [04:20,  5.71it/s, step size=1.16e+00, acc. prob=0.925]
Sample:  99%|#########9| 1289/1300 [04:20,  5.21it/s, step size=1.16e+00, acc. prob=0.925]
Sample:  99%|#########9| 1291/1300 [04:21,  5.60it/s, step size=1.16e+00, acc. prob=0.925]
Sample:  99%|#########9| 1293/1300 [04:21,  5.82it/s, step size=1.16e+00, acc. prob=0.925]
Sample: 100%|#########9| 1294/1300 [04:21,  5.36it/s, step size=1.16e+00, acc. prob=0.925]
Sample: 100%|#########9| 1296/1300 [04:22,  6.80it/s, step size=1.16e+00, acc. prob=0.925]
Sample: 100%|#########9| 1297/1300 [04:22,  5.98it/s, step size=1.16e+00, acc. prob=0.925]
Sample: 100%|#########9| 1299/1300 [04:22,  6.10it/s, step size=1.16e+00, acc. prob=0.925]
Sample: 100%|##########| 1300/1300 [04:22,  4.95it/s, step size=1.16e+00, acc. prob=0.925]

Analyze posterior samples and predictives, and visualize the results

posterior_samples = mcmc.get_samples(50)
posterior_predictive = Predictive(model, posterior_samples)(y_obs_list, interpolation_input=geo_model.interpolation_input)
data = az.from_pyro(
    posterior=mcmc,
    prior=prior,
    posterior_predictive=posterior_predictive
)
az.plot_trace(data)
plt.show()

/home/leguark/.virtualenvs/gempy-geotop-pilot/lib/python3.10/site-packages/arviz/data/io_pyro.py:157: UserWarning: Could not get vectorized trace, log_likelihood group will be omitted. Check your model vectorization or set log_likelihood=False
  warnings.warn(
posterior predictive shape not compatible with number of chains and draws.This can mean that some draws or even whole chains are not represented.
posterior predictive shape not compatible with number of chains and draws.This can mean that some draws or even whole chains are not represented.

Create density plots for posterior and prior distributions These plots provide insights into the parameter distributions and their changes.

az.plot_density(
    data=[data, data.prior],
    shade=.9,
    hdi_prob=.99,
    data_labels=["Posterior", "Prior"],
    colors=[default_red, default_blue],
)
plt.show()

az.plot_density(
    data=[data.posterior_predictive, data.prior_predictive],
    shade=.9,
    var_names=[r'$\mu_{gravity}$'],
    data_labels=["Posterior Predictive", "Prior Predictive"],
    colors=[default_red, default_blue],
)
plt.show()

# sphinx_gallery_thumbnail_number = -1