:orphan:

.. _Calibration:

Calibration
===========



.. raw:: html

    <div class="sphx-glr-thumbnails">

.. thumbnail-parent-div-open

.. thumbnail-parent-div-close

.. raw:: html

    </div>


Least squares and gaussian calibration
--------------------------------------



.. raw:: html

    <div class="sphx-glr-thumbnails">

.. thumbnail-parent-div-open

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="In this example we are interested in the calibration of the flooding model &lt;use-case-flood-model&gt;. We show how to produce the observations that we use in the calibration model of Calibration of the flooding model &lt;/auto_calibration/least_squares_and_gaussian_calibration/plot_calibration_flooding&gt;.">

.. only:: html

  .. image:: /auto_calibration/least_squares_and_gaussian_calibration/images/thumb/sphx_glr_plot_generate_flooding_thumb.png
    :alt:

  :ref:`sphx_glr_auto_calibration_least_squares_and_gaussian_calibration_plot_generate_flooding.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Generate flooding model observations</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="In this example we present the calibration of a parametric module. To do this, we show how to define the observations. Then we create a Python function and create the parametric model that is to be calibrated. Finally, we calibrate the parameters of the model using least squares and we validate the hypotheses of the method.">

.. only:: html

  .. image:: /auto_calibration/least_squares_and_gaussian_calibration/images/thumb/sphx_glr_plot_calibration_quickstart_thumb.png
    :alt:

  :ref:`sphx_glr_auto_calibration_least_squares_and_gaussian_calibration_plot_calibration_quickstart.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Calibrate a parametric model: a quick-start guide to calibration</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="In this example we present the simulation of noisy observations of the Chaboche model. A detailed explanation of this mechanical law is presented use-case-chaboche. We show how to produce the observations that we use in the calibration model of Calibration of the Chaboche model &lt;/auto_calibration/least_squares_and_gaussian_calibration/plot_calibration_chaboche&gt;.">

.. only:: html

  .. image:: /auto_calibration/least_squares_and_gaussian_calibration/images/thumb/sphx_glr_plot_generate_chaboche_thumb.png
    :alt:

  :ref:`sphx_glr_auto_calibration_least_squares_and_gaussian_calibration_plot_generate_chaboche.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Generate observations of the Chaboche mechanical model</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Calibration without observed inputs">

.. only:: html

  .. image:: /auto_calibration/least_squares_and_gaussian_calibration/images/thumb/sphx_glr_plot_calibration_withoutobservedinputs_thumb.png
    :alt:

  :ref:`sphx_glr_auto_calibration_least_squares_and_gaussian_calibration_plot_calibration_withoutobservedinputs.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Calibration without observed inputs</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="We present a calibration study of the logistic growth model defined use-case-logistic. The data set that we use is the U.S. population from 1790 to 2000. One of the specific properties of this study is that the observations that we use are real world observations. Hence when we calibrate the model on the data, there is a discrepancy that will be seen. In this example, we calibrate the parameters of a model which predicts the dynamics of the size of a population. This shows how we can calibrate a model which predicts a time dependent output. The output of the model is a time series representing the evolution of the population. This requires a transpose of the sample, so that we can benefit from the visualization methods.">

.. only:: html

  .. image:: /auto_calibration/least_squares_and_gaussian_calibration/images/thumb/sphx_glr_plot_calibration_logistic_thumb.png
    :alt:

  :ref:`sphx_glr_auto_calibration_least_squares_and_gaussian_calibration_plot_calibration_logistic.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Calibration of the logistic model</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="In this example, we calibrate the deflection of a tube as described in the use cases &lt;use-case-deflection-tube&gt; section. More precisely, we calibrate the mechanical parameters of a physical model which computes the vertical deflection of a tube and two deflection angles. This example shows how to calibrate a computer code which has several outputs.">

.. only:: html

  .. image:: /auto_calibration/least_squares_and_gaussian_calibration/images/thumb/sphx_glr_plot_calibration_deflection_tube_thumb.png
    :alt:

  :ref:`sphx_glr_auto_calibration_least_squares_and_gaussian_calibration_plot_calibration_deflection_tube.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Calibration of the deflection of a tube</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="In this example we are interested in the calibration of the flooding model &lt;use-case-flood-model&gt;. We calibrate the parameters of a flooding model where only the difference between the downstream and upstream riverbed levels can be calibrated. This example shows how to manage the lack of identifiability in a calibration problem.">

.. only:: html

  .. image:: /auto_calibration/least_squares_and_gaussian_calibration/images/thumb/sphx_glr_plot_calibration_flooding_thumb.png
    :alt:

  :ref:`sphx_glr_auto_calibration_least_squares_and_gaussian_calibration_plot_calibration_flooding.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Calibration of the flooding model</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="In this example we present calibration methods on the Chaboche model. A detailed explanation of this mechanical law is presented use-case-chaboche. As we are going to see, this model is relatively simple to calibrate: its parameters are identifiable and the output is relatively sensitive to the variation of the parameters. Hence, all methods perform correctly in this case.">

.. only:: html

  .. image:: /auto_calibration/least_squares_and_gaussian_calibration/images/thumb/sphx_glr_plot_calibration_chaboche_thumb.png
    :alt:

  :ref:`sphx_glr_auto_calibration_least_squares_and_gaussian_calibration_plot_calibration_chaboche.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Calibration of the Chaboche mechanical model</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>


Bayesian calibration
--------------------



.. raw:: html

    <div class="sphx-glr-thumbnails">

.. thumbnail-parent-div-open

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Gibbs sampling of the posterior distribution">

.. only:: html

  .. image:: /auto_calibration/bayesian_calibration/images/thumb/sphx_glr_plot_gibbs_thumb.png
    :alt:

  :ref:`sphx_glr_auto_calibration_bayesian_calibration_plot_gibbs.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Gibbs sampling of the posterior distribution</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="This example is drawn from [1].">

.. only:: html

  .. image:: /auto_calibration/bayesian_calibration/images/thumb/sphx_glr_plot_imh_python_distribution_thumb.png
    :alt:

  :ref:`sphx_glr_auto_calibration_bayesian_calibration_plot_imh_python_distribution.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Sampling from an unnormalized probability density</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Posterior sampling using a PythonDistribution">

.. only:: html

  .. image:: /auto_calibration/bayesian_calibration/images/thumb/sphx_glr_plot_rwmh_python_distribution_thumb.png
    :alt:

  :ref:`sphx_glr_auto_calibration_bayesian_calibration_plot_rwmh_python_distribution.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Posterior sampling using a PythonDistribution</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Bayesian calibration of a computer code">

.. only:: html

  .. image:: /auto_calibration/bayesian_calibration/images/thumb/sphx_glr_plot_bayesian_calibration_thumb.png
    :alt:

  :ref:`sphx_glr_auto_calibration_bayesian_calibration_plot_bayesian_calibration.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Bayesian calibration of a computer code</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Bayesian calibration of the flooding model">

.. only:: html

  .. image:: /auto_calibration/bayesian_calibration/images/thumb/sphx_glr_plot_bayesian_calibration_flooding_thumb.png
    :alt:

  :ref:`sphx_glr_auto_calibration_bayesian_calibration_plot_bayesian_calibration_flooding.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Bayesian calibration of the flooding model</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="This simple example shows how you can build your own variant of the Metropolis-Hastings algorithm.">

.. only:: html

  .. image:: /auto_calibration/bayesian_calibration/images/thumb/sphx_glr_plot_ackley_distribution_thumb.png
    :alt:

  :ref:`sphx_glr_auto_calibration_bayesian_calibration_plot_ackley_distribution.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Customize your Metropolis-Hastings algorithm</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Linear Regression with interval-censored observations">

.. only:: html

  .. image:: /auto_calibration/bayesian_calibration/images/thumb/sphx_glr_plot_gibbs_simus_thumb.png
    :alt:

  :ref:`sphx_glr_auto_calibration_bayesian_calibration_plot_gibbs_simus.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Linear Regression with interval-censored observations</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Bayesian calibration of hierarchical fission gas release models">

.. only:: html

  .. image:: /auto_calibration/bayesian_calibration/images/thumb/sphx_glr_plot_hierarchical_calibration_fission_gas_thumb.png
    :alt:

  :ref:`sphx_glr_auto_calibration_bayesian_calibration_plot_hierarchical_calibration_fission_gas.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Bayesian calibration of hierarchical fission gas release models</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>


.. toctree::
   :hidden:
   :includehidden:


   /auto_calibration/least_squares_and_gaussian_calibration/index.rst
   /auto_calibration/bayesian_calibration/index.rst


.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-gallery

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download all examples in Python source code: auto_calibration_python.zip </auto_calibration/auto_calibration_python.zip>`

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download all examples in Jupyter notebooks: auto_calibration_jupyter.zip </auto_calibration/auto_calibration_jupyter.zip>`