Bayesian approach to inverse Robin problems

Scripts and notebooks to run and analyse the Bayesian computational routine to tackle the inverse problems of estimating a Robin boundary coefficient in Laplace Stokes PDE problems. Based on work by Mark Girolami, Ieva Kazlauskaite, Alsel K. Rasmussen and Fanny Seizilles.

Set up

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 run our code (exported from MacOS). To setup the environment run:

conda env create --name robin --file environment.yml
conda activate robin

Contents

In addition to the environment file, this repository contains 2 python files and a notebook.

• With the python file icesheet_functions.py, all functions necessary to run the experiments are defined (PDE solver via FenicsX for FEM, MCMC)
• With the python file run.py, we set the parameters of the experiment (prior type, number of observations...) and run it. For every experiment, a dictionary is created and stored in a .pkl file
• With the notebook Postprocessing.ipynb, we define all the functions needed to analyse the results of the experiment once it has finished running. The .pkl file is retrieved and we can analyse the chains, compute the posterior mean and make reconstructions of the basal drag.