Computational Uncertainty Quantification for Inverse Problems in python

CUQIpy stands for Computational Uncertainty Quantification for Inverse Problems in python. It's a robust Python package designed for modeling and solving inverse problems using Bayesian inference. Here's what it brings to the table:

A straightforward high-level interface for UQ analysis.
Complete control over the models and methods.
An array of predefined distributions, samplers, models, and test problems.
Easy extendability for your unique needs.

CUQIpy is part of the CUQI project supported by the Villum Foundation.

📚 Resources

Documentation: CUQIpy website
Papers: CUQIpy on ArXiv - Part I & Part II
Training: Demo & training notebooks

🚀 Quickstart

Install CUQIpy using pip:

pip install cuqipy

For more detailed instructions, see the Getting Started guide.

🧪 Quick Example - UQ in a few lines of code

Experience the simplicity and power of CUQIpy with this Image deconvolution example. Getting started with UQ takes just a few lines of code:

# Imports
import matplotlib.pyplot as plt
from cuqi.testproblem import Deconvolution2D
from cuqi.distribution import Gaussian, LMRF, Gamma
from cuqi.problem import BayesianProblem

# Step 1: Set up forward model and data, y = Ax
A, y_data, info = Deconvolution2D(dim=256, phantom="cookie").get_components()

# Step 2: Define distributions for parameters
d = Gamma(1, 1e-4)
s = Gamma(1, 1e-4)
x = LMRF(0, lambda d: 1/d, geometry=A.domain_geometry)
y = Gaussian(A@x, lambda s: 1/s)

# Step 3: Combine into Bayesian Problem and sample posterior
BP = BayesianProblem(y, x, d, s)
BP.set_data(y=y_data)
samples = BP.sample_posterior(200)

# Step 4: Analyze results
info.exactSolution.plot(); plt.title("Sharp image (exact solution)")
y_data.plot(); plt.title("Blurred and noisy image (data)")
samples["x"].plot_mean(); plt.title("Estimated image (posterior mean)")
samples["x"].plot_std(); plt.title("Uncertainty (posterior standard deviation)")
samples["s"].plot_trace(); plt.suptitle("Noise level (posterior trace)")
samples["d"].plot_trace(); plt.suptitle("Regularization parameter (posterior trace)")

🔌 Plugins

CUQIpy can be extended with additional functionality by installing optional plugins. We currently offer the following plugins:

CUQIpy-CIL A plugin for the Core Imaging Library (CIL) providing access to forward models for X-ray computed tomography.
CUQIpy-FEniCS: A plugin providing access to the finite element modelling tool FEniCS, which is used for solving PDE-based inverse problems.
CUQIpy-PyTorch: A plugin providing access to the automatic differentiation framework of PyTorch within CUQIpy. It allows gradient-based sampling methods without manually providing derivative information of distributions and forward models.