On top of machine learning models, uncertainty quantification (UQ) functions as an essential layer of safety assurance that could lead to more principled decision making by enabling sound risk assessment and management. The safety and reliability improvement of ML models empowered by UQ has the potential to significantly facilitate the broad adoption of ML solutions in high-stakes decision settings, such as healthcare, manufacturing, and aviation, to name a few. In this tutorial, we aim to provide a holistic lens on emerging UQ methods for ML models with a particular focus on neural networks and the applications of these UQ methods in tackling engineering design as well as prognostics and health management problems. Toward this goal, we start with a comprehensive classification of uncertainty types, sources, and causes pertaining to UQ of ML models. Next, we provide a tutorial-style description of several state-of-the-art UQ methods: Gaussian process regression, Bayesian neural network, neural network ensemble, and deterministic UQ methods focusing on spectral-normalized neural Gaussian process. Established upon the mathematical formulations, we subsequently examine the soundness of these UQ methods quantitatively and qualitatively (by a toy regression example) to examine their strengths and shortcomings from different dimensions. Then, we review quantitative metrics commonly used to assess the quality of predictive uncertainty in classification and regression problems. Afterward, we discuss the increasingly important role of UQ of ML models in solving challenging problems in engineering design and health prognostics. Two case studies with source codes available on GitHub are used to demonstrate these UQ methods and compare their performance in the life prediction of lithium-ion batteries at the early stage and the remaining useful life prediction of turbofan engines.

翻译：在机器学习模型基础上，不确定性量化（UQ）作为安全保障的关键层，通过支持可靠的风险评估与管理，能够实现更具原则性的决策。由UQ驱动的机器学习模型安全性与可靠性提升，有望显著促进其在医疗、制造、航空等高风险决策场景中的广泛部署。本教程旨在全面审视面向机器学习模型（特别是神经网络）的新兴UQ方法，以及这些方法在解决工程设计与预测性健康管理问题中的应用。为此，我们首先对机器学习模型UQ相关的不确定性类型、来源及成因进行系统性分类。继而以教程形式详述若干前沿UQ方法：高斯过程回归、贝叶斯神经网络、神经网络集成，以及聚焦于谱归一化神经高斯过程的确定性UQ方法。基于数学形式化表达，我们通过玩具回归示例对这些UQ方法进行定量与定性验证，从多维度审视其优势与局限。随后，我们系统梳理常用于评估分类与回归问题中预测不确定性质量的量化指标。在此基础上，探讨机器学习模型UQ在解决工程设计及健康预测领域挑战性问题中日益重要的角色。通过GitHub开源代码的两项案例研究，我们展示上述UQ方法在锂离子电池早期寿命预测与涡轮风扇发动机剩余寿命预测中的性能对比。