Python tools for solving data-constrained finite element problems
This package provides a Python implementation of the Statistical Finite Element Method (FEM) as described in the paper by Girolami et al. [1] to use data observations to constrain FEM models. The package builds on top of Firedrake [2] to assemble the underlying FEM system and uses PETSc [3-4] to perform the sparse linear algebra routines. These tools should allow the user to create efficient, scalable solvers based on high level Python code to address challenging problems in data-driven numerical analysis.
stat-fem requires a working Firedrake installation. The easiest way to obtain Firedrake is to
follow the installation instructions on the firedrake homepage.
Once you have installed Firedrake, activate the virtual environment that was created as part of
the installation process. Within the running virtual environment, switch to the main stat-fem
directory and proceed with the installation by entering:
$ pip install -r requirements.txt
$ python setup.py installThis will use pip to install any missing dependencies (notably Scipy) and install the stat-fem
package within the Firedrake virtual environment.
Alternatively, we provide a working Firedrake Docker container that has the stat-fem code
and dependencies installed within the Firedrake virtual environment. See the docker
directory in the stat-fem repository.
The code comes with a full suite of unit tests. Running the test suite uses pytest and pytest-mpi
to collect and run the tests. To run the tests on a single process, simply enter pytest into
the running virtual environment from any location in the stat-fem directory. To run the test
suite in parallel, enter mpiexec -n 2 python -m pytest --with-mpi or
mpiexec -n 4 python -m pytest --with-mpi depending on the number of desired
processes to be used. Tests have only been written for 2 and 4 processes, so
you may get a failure if you attempt to use other choices for the number
of processes.
An example illustrating the various code capabilities and features is included in
the stat-fem/examples directory.
This software was written by Eric Daub as part of a project with the Research Engineering Group at the Alan Turing Institute.
Any bugs or issues should be filed in the issue tracker on the main Github page.
[1] Mark Girolami, Alastair Gregory, Ge Yin, and Fehmi Cirak. The Statistical Finite Element Method. 2019. URL: http://arxiv.org/abs/1905.06391, arXiv:1905.06391.
[2] Florian Rathgeber, David A. Ham, Lawrence Mitchell, Michael Lange, Fabio Luporini, Andrew T. T. Mcrae, Gheorghe-Teodor Bercea, Graham R. Markall, and Paul H. J. Kelly. Firedrake: automating the finite element method by composing abstractions. ACM Trans. Math. Softw., 43(3):24:1–24:27, 2016. URL: http://arxiv.org/abs/1501.01809, arXiv:1501.01809, doi:10.1145/2998441.
[3] L. Dalcin, P. Kler, R. Paz, and A. Cosimo, Parallel Distributed Computing using Python, Advances in Water Resources, 34(9):1124-1139, 2011. http://dx.doi.org/10.1016/j.advwatres.2011.04.013
[4] S. Balay, S. Abhyankar, M. Adams, J. Brown, P. Brune, K. Buschelman, L. Dalcin, A. Dener, V. Eijkhout, W. Gropp, D. Karpeyev, D. Kaushik, M. Knepley, D. May, L. Curfman McInnes, R. Mills, T. Munson, K. Rupp, P. Sanan, B. Smith, S. Zampini, H. Zhang, and H. Zhang, PETSc Users Manual, ANL-95/11 - Revision 3.12, 2019. http://www.mcs.anl.gov/petsc/petsc-current/docs/manual.pdf