Scripts and notebooks for simulations on unadjusted Langevin (ULA) and preconditioned unadjusted Langevin samplers (pULA), for the statistical finite element method (statFEM). This uses Fenics for FEM. Based on the work of Akyildiz, Duffin, Sabanis, and Girolami (2022). You can cite this via:
@article{akyildiz2022statistical,
author = {Akyildiz, \"{O}mer Deniz and Duffin, Connor and Sabanis, Sotirios and Girolami, Mark},
title = {Statistical Finite Elements via Langevin Dynamics},
journal = {SIAM/ASA Journal on Uncertainty Quantification},
volume = {10},
number = {4},
pages = {1560-1585},
year = {2022},
doi = {10.1137/21M1463094}
}
Included in this repository is the environment.yml file, that contains all the necessary packages that need to be installed in a conda environment in order to be run our code. Let me know if any are missing!
To setup the environment run
conda env create --file environment.yml
which will install all the required packages. The main thing is Fenics, a finite element library that allows us to build the necessary matrices for our PDE problem. It also does way more than this, but for our purposes, this is really all we use it for.
Then, with the conda environment active, to install the package that contains the Langevin samplers, run pip3 install -e sfmcmc, which will install a local copy of the sfmcmc package. This will enable you to now run the notebooks and scripts, as well as generate the plots.
Probably the thing of most interest are the notebooks, which are in the docs/ directory. To use the notebooks, run jupyter notebook from this directory, and navigate into the docs/ subdirectory from the Jupyter interface. Then choose the notebook of interest, and it should be good to go.
All notebooks have been designed to be run-able from this directory, so hopefully this works OK. Let me know if there are any issues.
The main code is hosted in the package sfmcmc, which contains all the code for ULA, MALA, etc. We also have notebooks, hosted in the docs/ directory, which illustrate the algorithms. To replicate our results, we have also included various running and plotting scripts, and the Makefile which we use to run the results.
The Makefile has the full details of the simulations, with simulation settings and parameters, etc.
Included in the package is a set of unit tests, under the sfmcmc/tests directory. To run these tests, first make sure the langevin-statfem environment is active. Then from the sfmcmc directory, run
python3 -m pytest .
This will run unit tests for the modules samplers and utils.