.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "examples_basic_geology/2-thickness_problem_gempy.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note :ref:`Go to the end ` to download the full example code .. rst-class:: sphx-glr-example-title .. _sphx_glr_examples_basic_geology_2-thickness_problem_gempy.py: 2.2 - Including GemPy ===================== Complex probabilistic model --------------------------- .. GENERATED FROM PYTHON SOURCE LINES 8-29 .. code-block:: Python import os import numpy as np import matplotlib.pyplot as plt import torch import pyro import pyro.distributions as dist from pyro.infer import MCMC, NUTS, Predictive from pyro.infer.autoguide import init_to_mean import gempy as gp import gempy_engine import gempy_viewer as gpv from gempy.modules.data_manipulation.engine_factory import interpolation_input_from_structural_frame from gempy_engine.core.backend_tensor import BackendTensor import arviz as az from gempy_engine.core.data.interpolation_input import InterpolationInput from gempy_probability.plot_posterior import default_red, default_blue # sphinx_gallery_thumbnail_number = -1 .. GENERATED FROM PYTHON SOURCE LINES 30-31 Set the data path .. GENERATED FROM PYTHON SOURCE LINES 31-34 .. code-block:: Python data_path = os.path.abspath('../') .. GENERATED FROM PYTHON SOURCE LINES 35-36 Define a function for plotting geological settings with wells .. GENERATED FROM PYTHON SOURCE LINES 36-62 .. code-block:: Python def plot_geo_setting_well(geo_model): """ This function plots the geological settings along with the well locations. It uses gempy_viewer to create 2D plots of the model. """ # Define well and device locations device_loc = np.array([[6e3, 0, 3700]]) well_1 = 3.41e3 well_2 = 3.6e3 # Create a 2D plot p2d = gpv.plot_2d(geo_model, show_topography=False, legend=False, show=False) # Add well and device markers to the plot p2d.axes[0].scatter([3e3], [well_1], marker='^', s=400, c='#71a4b3', zorder=10) p2d.axes[0].scatter([9e3], [well_2], marker='^', s=400, c='#71a4b3', zorder=10) p2d.axes[0].scatter(device_loc[:, 0], device_loc[:, 2], marker='x', s=400, c='#DA8886', zorder=10) # Add vertical lines to represent wells p2d.axes[0].vlines(3e3, .5e3, well_1, linewidth=4, color='gray') p2d.axes[0].vlines(9e3, .5e3, well_2, linewidth=4, color='gray') # Show the plot p2d.fig.show() .. GENERATED FROM PYTHON SOURCE LINES 63-67 Creating the Geological Model ----------------------------- Here we create a geological model using GemPy. The model defines the spatial extent, resolution, and geological information derived from orientations and surface points data. .. GENERATED FROM PYTHON SOURCE LINES 67-78 .. code-block:: Python geo_model = gp.create_geomodel( project_name='Wells', extent=[0, 12000, -500, 500, 0, 4000], refinement=3, importer_helper=gp.data.ImporterHelper( path_to_orientations=data_path + "/data/2-layers/2-layers_orientations.csv", path_to_surface_points=data_path + "/data/2-layers/2-layers_surface_points.csv" ) ) .. GENERATED FROM PYTHON SOURCE LINES 79-83 Configuring the Model --------------------- We configure the interpolation options for the geological model. These options determine how the model interpolates between data points. .. GENERATED FROM PYTHON SOURCE LINES 83-88 .. code-block:: Python geo_model.interpolation_options.uni_degree = 0 geo_model.interpolation_options.mesh_extraction = False geo_model.interpolation_options.sigmoid_slope = 1100. .. GENERATED FROM PYTHON SOURCE LINES 89-93 Setting up a Custom Grid ------------------------ A custom grid is set for the model, defining specific points in space where geological formations will be evaluated. .. GENERATED FROM PYTHON SOURCE LINES 93-100 .. code-block:: Python x_loc = 6000 y_loc = 0 z_loc = np.linspace(0, 4000, 100) xyz_coord = np.array([[x_loc, y_loc, z] for z in z_loc]) gp.set_custom_grid(geo_model.grid, xyz_coord=xyz_coord) .. rst-class:: sphx-glr-script-out .. code-block:: none Active grids: GridTypes.NONE|CUSTOM|OCTREE .. GENERATED FROM PYTHON SOURCE LINES 101-105 Plotting the Initial Geological Setting --------------------------------------- Before running any probabilistic analysis, we first visualize the initial geological setting. This step ensures that our model is correctly set up with the initial data. .. GENERATED FROM PYTHON SOURCE LINES 105-109 .. code-block:: Python # Plot initial geological settings plot_geo_setting_well(geo_model=geo_model) .. image-sg:: /examples_basic_geology/images/sphx_glr_2-thickness_problem_gempy_001.png :alt: Cell Number: mid Direction: y :srcset: /examples_basic_geology/images/sphx_glr_2-thickness_problem_gempy_001.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 110-114 Interpolating the Initial Guess ------------------------------- The model interpolates an initial guess for the geological formations. This step is crucial to provide a starting point for further probabilistic analysis. .. GENERATED FROM PYTHON SOURCE LINES 114-121 .. code-block:: Python gp.compute_model( gempy_model=geo_model, engine_config=gp.data.GemPyEngineConfig(backend=gp.data.AvailableBackends.numpy) ) plot_geo_setting_well(geo_model=geo_model) .. image-sg:: /examples_basic_geology/images/sphx_glr_2-thickness_problem_gempy_002.png :alt: Cell Number: mid Direction: y :srcset: /examples_basic_geology/images/sphx_glr_2-thickness_problem_gempy_002.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none Setting Backend To: AvailableBackends.numpy .. GENERATED FROM PYTHON SOURCE LINES 122-127 Probabilistic Geomodeling with Pyro ----------------------------------- In this section, we introduce a probabilistic approach to geological modeling. By using Pyro, a probabilistic programming language, we define a model that integrates geological data with uncertainty quantification. .. GENERATED FROM PYTHON SOURCE LINES 127-135 .. code-block:: Python type_ = gempy_engine.core.data.interpolation_input.InterpolationInput interpolation_input_copy: type_ = interpolation_input_from_structural_frame(geo_model) sp_coords_copy = interpolation_input_copy.surface_points.sp_coords # Change the backend to PyTorch for probabilistic modeling BackendTensor.change_backend_gempy(engine_backend=gp.data.AvailableBackends.PYTORCH) .. rst-class:: sphx-glr-script-out .. code-block:: none Setting Backend To: AvailableBackends.PYTORCH .. GENERATED FROM PYTHON SOURCE LINES 136-141 Defining the Probabilistic Model -------------------------------- The Pyro model represents the probabilistic aspects of the geological model. It defines a prior distribution for the top layer's location and computes the thickness of the geological layer as an observed variable. .. GENERATED FROM PYTHON SOURCE LINES 141-175 .. code-block:: Python def model(y_obs_list): """ This Pyro model represents the probabilistic aspects of the geological model. It defines a prior distribution for the top layer's location and computes the thickness of the geological layer as an observed variable. """ # Define prior for the top layer's location: prior_mean = sp_coords_copy[0, 2] mu_top = pyro.sample(r'$\mu_{top}$', dist.Normal(prior_mean, torch.tensor(0.02, dtype=torch.float64))) # Update the model with the new top layer's location interpolation_input = interpolation_input_from_structural_frame(geo_model) interpolation_input.surface_points.sp_coords = torch.index_put( interpolation_input.surface_points.sp_coords, (torch.tensor([0]), torch.tensor([2])), mu_top ) # Compute the geological model 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, ) # Compute and observe the thickness of the geological layer simulated_well = geo_model.solutions.octrees_output[0].last_output_center.custom_grid_values thickness = simulated_well.sum() pyro.deterministic(r'$\mu_{thickness}$', thickness.detach()) y_thickness = pyro.sample(r'$y_{thickness}$', dist.Normal(thickness, 50), obs=y_obs_list) .. GENERATED FROM PYTHON SOURCE LINES 176-180 Running Prior Sampling and Visualization ---------------------------------------- Prior sampling is an essential step in probabilistic modeling. It helps in understanding the distribution of our prior assumptions before observing any data. .. GENERATED FROM PYTHON SOURCE LINES 182-183 Prepare observation data .. GENERATED FROM PYTHON SOURCE LINES 183-185 .. code-block:: Python y_obs_list = torch.tensor([200, 210, 190]) .. GENERATED FROM PYTHON SOURCE LINES 186-187 Run prior sampling and visualization .. GENERATED FROM PYTHON SOURCE LINES 187-192 .. code-block:: Python prior = Predictive(model, num_samples=50)(y_obs_list) data = az.from_pyro(prior=prior) az.plot_trace(data.prior) plt.show() .. image-sg:: /examples_basic_geology/images/sphx_glr_2-thickness_problem_gempy_003.png :alt: $\mu_{thickness}$, $\mu_{thickness}$, $\mu_{top}$, $\mu_{top}$, $y_{thickness}$, $y_{thickness}$ :srcset: /examples_basic_geology/images/sphx_glr_2-thickness_problem_gempy_003.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 193-198 Sampling from the Posterior using MCMC -------------------------------------- We use Markov Chain Monte Carlo (MCMC) with the NUTS (No-U-Turn Sampler) algorithm to sample from the posterior distribution. This gives us an understanding of the distribution of our model parameters after considering the observed data. .. GENERATED FROM PYTHON SOURCE LINES 200-201 Run MCMC using NUTS to sample from the posterior .. GENERATED FROM PYTHON SOURCE LINES 201-206 .. code-block:: Python pyro.primitives.enable_validation(is_validate=True) nuts_kernel = NUTS(model, step_size=0.0085, adapt_step_size=True, target_accept_prob=0.9, max_tree_depth=10, init_strategy=init_to_mean) mcmc = MCMC(nuts_kernel, num_samples=200, warmup_steps=50, disable_validation=False) mcmc.run(y_obs_list) .. rst-class:: sphx-glr-script-out .. code-block:: none Warmup: 0%| | 0/250 [00:00, ?it/s] Warmup: 0%| | 1/250 [00:00, 3.93it/s, step size=7.14e-02, acc. prob=0.041] Warmup: 1%| | 3/250 [00:00, 7.20it/s, step size=4.08e-03, acc. prob=0.347] Warmup: 2%|▏ | 4/250 [00:00, 4.81it/s, step size=3.95e-03, acc. prob=0.510] Warmup: 2%|▏ | 6/250 [00:01, 6.18it/s, step size=5.25e-03, acc. prob=0.673] Warmup: 3%|▎ | 7/250 [00:01, 5.55it/s, step size=6.63e-03, acc. prob=0.719] Warmup: 3%|▎ | 8/250 [00:01, 5.57it/s, step size=8.65e-03, acc. prob=0.754] Warmup: 4%|▎ | 9/250 [00:01, 5.95it/s, step size=1.09e-02, acc. prob=0.779] Warmup: 4%|▍ | 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GENERATED FROM PYTHON SOURCE LINES 207-211 Posterior Predictive Checks --------------------------- After obtaining the posterior samples, we perform posterior predictive checks. This step is crucial to evaluate the performance and validity of our probabilistic model. .. GENERATED FROM PYTHON SOURCE LINES 213-214 Sample from posterior predictive and visualize .. GENERATED FROM PYTHON SOURCE LINES 214-220 .. code-block:: Python posterior_samples = mcmc.get_samples() posterior_predictive = Predictive(model, posterior_samples)(y_obs_list) data = az.from_pyro(posterior=mcmc, prior=prior, posterior_predictive=posterior_predictive) az.plot_trace(data) plt.show() .. image-sg:: /examples_basic_geology/images/sphx_glr_2-thickness_problem_gempy_004.png :alt: $\mu_{top}$, $\mu_{top}$ :srcset: /examples_basic_geology/images/sphx_glr_2-thickness_problem_gempy_004.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none /home/leguark/.virtualenvs/gempy_dependencies/lib/python3.10/site-packages/arviz/data/io_pyro.py:158: UserWarning: Could not get vectorized trace, log_likelihood group will be omitted. Check your model vectorization or set log_likelihood=False warnings.warn( .. GENERATED FROM PYTHON SOURCE LINES 221-226 Density Plot of Posterior Predictive ------------------------------------ A density plot provides a visual representation of the distribution of the posterior predictive checks. It helps in comparing the prior and posterior distributions and in assessing the impact of our observed data on the model. .. GENERATED FROM PYTHON SOURCE LINES 228-229 Plot density of posterior predictive and prior predictive .. GENERATED FROM PYTHON SOURCE LINES 229-237 .. code-block:: Python az.plot_density( data=[data.posterior_predictive, data.prior_predictive], shade=.9, var_names=[r'$\mu_{thickness}$'], data_labels=["Posterior Predictive", "Prior Predictive"], colors=[default_red, default_blue], ) plt.show() .. image-sg:: /examples_basic_geology/images/sphx_glr_2-thickness_problem_gempy_005.png :alt: $\mu_{thickness}$ :srcset: /examples_basic_geology/images/sphx_glr_2-thickness_problem_gempy_005.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 19.883 seconds) .. _sphx_glr_download_examples_basic_geology_2-thickness_problem_gempy.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: 2-thickness_problem_gempy.ipynb <2-thickness_problem_gempy.ipynb>` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: 2-thickness_problem_gempy.py <2-thickness_problem_gempy.py>` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_