  Uncertainty quantification (UQ) in machine learning is currently drawing
increasing research interest, driven by the rapid deployment of deep neural
networks across different fields, such as computer vision, natural language
processing, and the need for reliable tools in risk-sensitive applications.
Recently, various machine learning models have also been developed to tackle
problems in the field of scientific computing with applications to
computational science and engineering (CSE). Physics-informed neural networks
and deep operator networks are two such models for solving partial differential
equations and learning operator mappings, respectively. In this regard, a
comprehensive study of UQ methods tailored specifically for scientific machine
learning (SciML) models has been provided in [45]. Nevertheless, and despite
their theoretical merit, implementations of these methods are not
straightforward, especially in large-scale CSE applications, hindering their
broad adoption in both research and industry settings. In this paper, we
present an open-source Python library (https://github.com/Crunch-UQ4MI), termed
NeuralUQ and accompanied by an educational tutorial, for employing UQ methods
for SciML in a convenient and structured manner. The library, designed for both
educational and research purposes, supports multiple modern UQ methods and
SciML models. It is based on a succinct workflow and facilitates flexible
employment and easy extensions by the users. We first present a tutorial of
NeuralUQ and subsequently demonstrate its applicability and efficiency in four
diverse examples, involving dynamical systems and high-dimensional parametric
and time-dependent PDEs.
