CUQIpy-FEniCS

CUQIpy-FEniCS is a plugin for CUQIpy software package. It provides an interface between FEniCS PDE models and CUQIpy modules. The documentation for CUQIpy-FEniCS can be found here.

Installation

First install FEniCS, we recommend using Anaconda from the available installation options. Then install CUQIpy-FEniCS with pip:

pip install cuqipy-fenics

If CUQIpy is not installed, it will be installed automatically. We provide additional information about FEniCS installation, below, in case the above approach was problematic.

Quickstart

import numpy as np
import matplotlib.pyplot as plt
import cuqi
import cuqipy_fenics

# Load a fenics forward model and data from testproblem library
model, y_data, info = cuqipy_fenics.testproblem.FEniCSDiffusion1D(
    dim=20,
    endpoint=1,
    exactSolution='smooth_step',
    mapping='exponential',
    SNR=10000,
    left_bc=0,
    right_bc=8
).get_components()

# Set up Bayesian model
x = cuqi.distribution.GMRF(np.zeros(model.domain_dim),
                           25, 1, 'zero', geometry=model.domain_geometry)
# y ~ N(model(x), 0.01^2)
y = cuqi.distribution.Gaussian(mean=model(x), cov=0.05**2)

# Set up Bayesian Problem object
BP = cuqi.problem.BayesianProblem(y, x).set_data(y=y_data)

# Sample from the posterior
samples = BP.sample_posterior(5000)

# Analyze the samples
samples.burnthin(1000).plot_ci(95, plot_par=True,
                               exact=info.exactSolution, linestyle='-', marker='.')

For more examples, see the demos folder.

More on using and installing FEniCS

FEniCS on Google Colaboratory

If you do not wish to install FEniCS on your machine or you have difficulty doing so, one option is to install FEniCS on Google Colaboratory (Colab) Jupyter Notebook service. We show below how to achieve this using FEM on Colab packages. First open a notebook in Google Colab (an introduction to Colab can be found here) and write in a cell:

try:
    import dolfin
except ImportError:
    !wget "https://fem-on-colab.github.io/releases/fenics-install.sh" -O "/tmp/fenics-install.sh" && bash "/tmp/fenics-install.sh"
    import dolfin

Then in a following cell use pip to install cuqipy-fenics as follows:

!pip install cuqipy-fenics

Test that you can import cuqi and cuqipy_fenics

import cuqi
import cuqipy_fenics

Create a Docker image for FEniCS

Here is another approach of installing FEniCS that could be useful in some cases (e.g. MAC M1 machines). We create a Docker image that contains a conda environment for FEniCS.

Run the following command lines to create a directory named, for example, my_dir.

mkdir my_dir
cd my_dir

In my_dir, run the following command lines to create the files needed for the Docker image and to pull a base image continuumio/miniconda3.

touch Dockerfile
touch environment.yml
docker pull continuumio/miniconda3

Edit the file Dockerfile you just created to have the following lines:

# Define base image
FROM continuumio/miniconda3

# Set working directory for the project
WORKDIR /app

# Create Conda environment from the YAML file
COPY environment.yml .
RUN conda env create -f environment.yml

Edit the file environment.yml you just created to have the following lines

name: env
channels:
   - conda-forge
dependencies:
   - python=3.10
   - fenics
   - pip
   - pip:
   # works for regular pip packages
     - cuqipy-fenics

(consider also python=3.8 if python=3.10 turn out to be problematic)

Build the docker image, named my_image for example, by running the following command inside my_dir (this might take a little while):

docker build -t my_image .

Run the docker image:

docker run --entrypoint=/bin/bash -it -p 127.0.0.1:8090:8000 -v $(pwd):/app -w /app my_image

Inside the Docker container, activate the conda environment and run python:

conda activate env
python

Run the following python commands to make sure FEniCS and cuqipy-fenics are installed

import fenics
import cuqi
import cuqipy_fenics