stat-fem

Python tools for solving data-constrained finite element problems

Overview

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.

Installation

Installing stat-fem

stat-fem requires a working Firedrake installation. The easiest way to obtain Firedrake is to use the installation script provided by the Firedrake project on the firedrake homepage.

bash curl -O https://raw.githubusercontent.com/firedrakeproject/firedrake/master/scripts/firedrake-install python3 firedrake-install --install git+https://github.com/alan-turing-institute/stat-fem#egg=stat-fem

This will install Firedrake and install the stat-fem library inside the Firedrake virtual environment. If this does not work, details on manual installation are provided in the documentation.

Using a Docker Container

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.

Testing the installation

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.

Example Scripts

An example illustrating the various code capabilities and features is included in the stat-fem/examples directory.

Contact

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.

References

[1] Mark Girolami, Eky Febrianto, Ge Yin, and Fehmi Cirak. The statistical finite element method (statFEM) for coherent synthesis of observation data and model predictions. Computer Methods in Applied Mechanics and Engineering, Volume 375, 2021, 113533, https://doi.org/10.1016/j.cma.2020.113533.

[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