pyMOR is a software library for building model order reduction applications with the Python programming language. All algorithms in pyMOR are formulated in terms of abstract interfaces, allowing generic implementations to work with different backends, from NumPy/SciPy to external partial differential equation solver packages.

• Reduced basis methods for parametric linear and non-linear problems.
• System-theoretic methods for linear time-invariant systems.
• Neural network-based methods for parametric problems.
• Proper orthogonal decomposition.
• Dynamic mode decomposition.
• Rational interpolation of data (Loewner, AAA).
• Numerical linear algebra (Gram-Schmidt, time-stepping, ...).
• Pure Python implementations of finite element and finite volume discretizations using the NumPy/SciPy scientific computing stack.

pyMOR is licensed under BSD-2-clause. See LICENSE.txt.

If you use pyMOR for academic work, please consider citing our publication:

R. Milk, S. Rave, F. Schindler
pyMOR - Generic Algorithms and Interfaces for Model Order Reduction
SIAM J. Sci. Comput., 38(5), pp. S194--S216, 2016

We recommend installation of pyMOR in a virtual environment.

pyMOR can easily be installed with the pip command. Please note that pip versions prior to 21.1 might have problems resolving all dependencies, so running the following first is recommended:

pip install --upgrade pip

If you are not operating in a virtual environment, you can pass the optional --user argument to pip. pyMOR will then only be installed for your local user, not requiring administrator privileges.

For an installation with minimal dependencies, run

pip install pymor

Note that most included demo scripts additionally require Qt bindings such as pyside2 to function. Therefore we recommend install pyMOR with the gui extra:

pip install pymor[gui]  # 2023.1 and later

The following installs the latest release of pyMOR on your system with most optional dependencies:

pip install pymor[full]

There are some optional packages not included with pymor[full] because they need additional setup on your system:

• mpi4py: support of MPI distributed models and parallelization of greedy algorithms (requires MPI development headers and a C compiler):

  pip install mpi4py
  

• Slycot: dense matrix equation solvers for system-theoretic methods and H-infinity norm calculation (requires OpenBLAS headers and a Fortran compiler):

  pip install slycot
  

  Note that building Slycot might fail for the following reasons:

  • The Slycot package contains a cmake check which fails when it detects multiply NumPy include directories. This will cause the build to fail in venvs with any Python interpreter that has NumPy globally installed. To circumvent this problem, use another Python interpreter. If you do not want to build CPython yourself, you can use pyenv, uv or mise-en-place to easily install another interpreter.
  • Slycot's build environment contains numpy>=2. However, scikit-builds's FindF2PY.cmake will select any globally installed f2py3 executable to generate the Fortran wrapper code. On most systems, an older NumPy version is installed, whose f2py will generate incorrect wrapper code for numpy>=2. To mitigate this issue, install numpy>=2 into your venv and link f2py3 to f2py its /bin directory.
  • Building Slycot on Windows is challenging. We recommend using conda-forge packages instead. If you do not want to install the pyMOR conda-forge package, you can also pip install pyMOR into an existing conda environment.

  If you are on Linux and don't want to build Slycot yourself, you can try our experimental manylinux wheels for Slycot.

To install the latest development version of pyMOR, execute

pip install 'pymor[full] @ git+https://github.com/pymor/pymor'

which requires that the git version control system is installed on your system.

From time to time, the main branch of pyMOR undergoes major changes and things might break (this is usually announced in our discussion forum), so you might prefer to install pyMOR from the current release branch:

pip install 'pymor[full] @ git+https://github.com/pymor/[email protected]'

Release branches will always stay stable and will only receive bugfix commits after the corresponding release has been made.

pyMOR is packaged in conda-forge and can be installed by running

conda install -c conda-forge pymor

This will install pyMOR with its core dependencies into the current active conda environment. To replicate an environment with most optional dependencies, which is also used in our continuous integration tests, you can use the conda-linux-64.lock, conda-osx-64.lock, conda-win-64.lock lock files from the pyMOR repository:

conda create -n pymorenv --file ./conda-{linux,osx,win}-64.lock
conda activate pymorenv
conda install pymor

Documentation is available online. We recommend starting with getting started, tutorials, and technical overview.

To build the documentation locally, run the following from inside the root directory of the pyMOR source tree:

make docs

This will generate HTML documentation in docs/_build/html.

pyMOR has been designed with easy integration of external PDE solvers in mind.

We provide bindings for the following solver libraries:

• FEniCS

  MPI-compatible wrapper classes for dolfin linear algebra data structures are shipped with pyMOR (pymor.bindings.fenics). For an example see pymordemos.thermalblock, pymordemos.thermalblock_simple. It is tested using FEniCS version 2019.1.0.

• deal.II

  Python bindings and pyMOR wrapper classes can be found here.

• NGSolve

  Wrapper classes for the NGSolve finite element library are shipped with pyMOR (pymor.bindings.ngsolve). For an example see pymordemos.thermalblock_simple. It is tested using NGSolve version v6.2.2104.

A simple example for direct integration of pyMOR with a a custom solver can be found in pymordemos.minimal_cpp_demo.

An alternative approach is to import system matrices from file and use scipy.sparse-based solvers.

Please see the Developer Documentation.

Should you have any questions regarding pyMOR or wish to contribute, do not hesitate to send us an email at

[email protected]