This paper introduces CUQIpy, a versatile open-source Python package for computational uncertainty quantification (UQ) in inverse problems, presented as Part I of a two-part series. CUQIpy employs a Bayesian framework, integrating prior knowledge with observed data to produce posterior probability distributions that characterize the uncertainty in computed solutions to inverse problems. The package offers a high-level modeling framework with concise syntax, allowing users to easily specify their inverse problems, prior information, and statistical assumptions. CUQIpy supports a range of efficient sampling strategies and is designed to handle large-scale problems. Notably, the automatic sampler selection feature analyzes the problem structure and chooses a suitable sampler without user intervention, streamlining the process. With a selection of probability distributions, test problems, computational methods, and visualization tools, CUQIpy serves as a powerful, flexible, and adaptable tool for UQ in a wide selection of inverse problems. Part II of the series focuses on the use of CUQIpy for UQ in inverse problems with partial differential equations (PDEs).

翻译：本文介绍CUQIpy，一个用于反问题计算不确定性量化（UQ）的通用开源Python软件包，作为两篇系列论文的第一部分。CUQIpy采用贝叶斯框架，将先验知识与观测数据相结合，生成后验概率分布，以表征反问题计算解的不确定性。该软件包提供具有简洁语法的高层次建模框架，使用户能够轻松指定其反问题、先验信息和统计假设。CUQIpy支持多种高效采样策略，并设计用于处理大规模问题。值得注意的是，其自动采样器选择功能可分析问题结构并自动选取合适的采样器，无需用户干预，从而简化流程。通过提供概率分布、测试问题、计算方法及可视化工具的选择，CUQIpy成为广泛反问题中UQ的强大、灵活且适应性强的工具。本系列的第二部分专注于CUQIpy在含偏微分方程（PDE）的反问题UQ中的应用。