Low-rank statFEM for reaction-diffusion models

This repo accompanies our JCP paper Low-rank statistical finite elements for scalable model-data synthesis, which can be cited as:

@article{duffin2022lowrank,
  title = {Low-Rank Statistical Finite Elements for Scalable Model-Data Synthesis},
  author = {Duffin, Connor and Cripps, Edward and Stemler, Thomas and Girolami, Mark},
  year = {2022},
  month = aug,
  journal = {Journal of Computational Physics},
  volume = {463},
  issn = {0021-9991},
  doi = {10.1016/j.jcp.2022.111261}
}

The paper focuses on low-rank methods for scaling up statistical finite element methods to high-dimensional problems. The architecture of this repo consists of the statbz package, found in the statbz directory, and three separate directories for each of the case studies (1-cells, 2-spiral-wave, 3-oscillatory). Each of these accord to different models that we study in the paper.

To run the examples, code is contained in a Makefile in each subdirectory to run the examples. Consult the relevant Makefile in each subdirectory to see what needs to be done for each example.

Getting started

To get started, first cd into this directory and setup the Conda environment through using the provided environment.yml file:

conda env create -f environment.yml

This should install all the requisite packages, into the environment reacdiff. Activate this environment through conda activate reacdiff. Then install the local statbz package locally:

pip install -e statbz

If you wanted, you can run the unit tests through doing (from this directory)

cd statbz
python3 -m pytest tests

Getting the data

For the cells example, you need to download the data from:

Simpson, M. J., Baker, R. E., Vittadello, S. T., & Maclaren, O. J. (2020). Practical parameter identifiability for spatio-temporal models of cell invasion. Journal of The Royal Society Interface, 17(164), 20200055. (https://doi.org/10.1098/rsif.2020.0055)

This should then be saved as 1-cells/data/rsif-data.xlsx, to accord with the local Makefile.

Running the examples

With all this set up, you should be able to run the examples from the Makefile in the local directories. For example, for the cells example, running (from this directory)

cd 1-cells
make outputs/cell-post.h5

Will run a statFEM model for the 1D cells example, computing the posterior distribution of the FEM coefficients using the extended Kalman filter. To run the low-rank statFEM, for the cells example, with 32 modes, simply do:

make outputs/cell-post-lr-32-modes.h5

The other examples are similar. All directories have a Makefile from which all the examples should be able to be run.

Generating the figures

Having run the requisite results for each example, the figures can now be generated. Using the Makefile, once again for the cells example, these can be generated via

make plots_cell

Again, the other examples are similar. Just check the local Makefile in each.