QEP Modeling with Derivatives
===============================================

Here are some examples of QEP modeling with derivative information in QPyTorch.


QEPs with Derivatives
----------------------

Like GP, QEP can also model the derivative information when it is available.
See the `1D derivatives QEP example`_ and the `2D derivatives QEP example`_ for **exact** QEP with derivatives.
See the `variational QEP with 2nd order derivatives`_ notebook for an example of **variational** QEP with up to second order derivatives.

.. toctree::
   :glob:
   :maxdepth: 1
   :hidden:

   Simple_QEP_Regression_Derivative_Information_1d.ipynb
   Simple_QEP_Regression_Derivative_Information_2d.ipynb
   SVQEP_Regression_Derivative_Information_2d.ipynb


Solving and Learning PDE with QEP
----------------------------------

Due to the enhanced capability to handle inhomogeneity, QEP can be used to solve and learn partial differential equations (PDEs).
We demonstrate in `Yu and Lan (2025)`_ QEP model with `q=1` as a superior probabilistic compared with GP.
See this `solving PDE with QEP`_ example for a demonstration with Burgers' equation.


.. toctree::
   :glob:
   :maxdepth: 1
   :hidden:

   Solve_PDE_with_QEP.ipynb


.. _1D derivatives QEP example:
  Simple_QEP_Regression_Derivative_Information_1d.ipynb

.. _2D derivatives QEP example:
  Simple_QEP_Regression_Derivative_Information_2d.ipynb

.. _variational QEP with 2nd order derivatives:
  SVQEP_Regression_Derivative_Information_2d.ipynb

.. _solving PDE with QEP:
  Solve_PDE_with_QEP.ipynb

.. _Yu and Lan (2025):
  https://openreview.net/pdf?id=WjhS0EpJH7