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：本文介绍了CUQIpy，一个用于反问题计算不确定性量化的多功能开源Python软件包，作为两部分系列的第一部分。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，以表征反问题求解结果的不确定性。该软件包提供具有简洁语法的高级建模框架，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，并专为处理大规模问题而设计。值得注意的是，自动采样器选择功能可分析问题结构并在无需用户干预的情况下选择合适的采样器，从而简化流程。通过一系列概率分布、测试问题、计算方法及可视化工具，CUQIpy成为适用于各类反问题的强大、灵活且可调的不确定性量化工具。本系列第二部分聚焦于CUQIpy在含偏微分方程的反问题不确定性量化中的应用。