Getting started

Code for the numerical experiments demonstrating our error analysis of the statFEM method.

Overview

This repo contains code accompanying our error analysis of the Statistical Finite Element Method (StatFEM) as described in the paper by Girolami et al. [1]. The code accompanies [2].

The folder scripts contains the scripts for the numerical experiments from our paper [2].

Installation

The code can be run in a Docker container.

Prerequisites: Docker must be installed and set up following these instructions.

Recommended method (Docker image):

Steps:

• Clone the repo.
• Navigate to the repo directory: cd statFEM_analysis
• A Docker image is available online. To use run the following command, remembering to replace my-name with your desired image/container name.

docker run -ti --name my-name -w /home/fenics -v $(pwd):/home/fenics/shared -p 8888:8888 yannipapandreou/statfem_analysis

Alternative method (Building Docker container locally) :

Steps:

• Clone the repo.
• Navigate to the repo directory: cd statFEM_analysis
• Build the Docker image: docker build .
• Docker will build the container using the instructions in the Dockerfile. After the build is complete Docker will output a hash, e.g.:

  Successfully built 10c79a08651f

• Use this to tag your container for future use:

  docker tag 10c79 quay.io/my-user/my-docker-image

• Run the Docker container with the repo directory mounted in :bash:/home/fenics/shared:

  docker run -ti --name my-name -w /home/fenics -v $(pwd):/home/fenics/shared -p 8888:8888 quay.io/my-user/my-docker-image

Running the code

Once the Docker image is pulled/built and running, you will be in a Docker container running Ubuntu. The recommended way for running code is to either:

• Run scripts using python3 run script.py
• Launch a Jupyter lab session using:

  jupyter lab --ip 0.0.0.0 --port 8888 --no-browser --allow-root

  • The Jupyter lab session can then be accessed by opening http://localhost:8888/lab in your browser and pasting the token written in the Docker container.

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] Yanni Papandreou, Jon Cockayne, Mark Girolami, and Andrew B. Duncan. "Theoretical Guarantees for the Statistical Finite Element Method." arXiv preprint arXiv:2111.07691 (2021), https://arxiv.org/abs/2111.07691.