Despite the growing availability of sensing and data in general, we remain unable to fully characterise many in-service engineering systems and structures from a purely data-driven approach. The vast data and resources available to capture human activity are unmatched in our engineered world, and, even in cases where data could be referred to as ``big,'' they will rarely hold information across operational windows or life spans. This paper pursues the combination of machine learning technology and physics-based reasoning to enhance our ability to make predictive models with limited data. By explicitly linking the physics-based view of stochastic processes with a data-based regression approach, a spectrum of possible Gaussian process models are introduced that enable the incorporation of different levels of expert knowledge of a system. Examples illustrate how these approaches can significantly reduce reliance on data collection whilst also increasing the interpretability of the model, another important consideration in this context.

翻译：尽管传感和数据的可用性日益增长，我们仍无法完全通过纯数据驱动方法全面表征许多在役工程系统与结构。用于捕捉人类活动的大量数据与资源在工程领域难以匹敌，即便在某些可称为"大数据"的情形下，这些数据也极少涵盖运行窗口或全生命周期的信息。本文致力于融合机器学习技术与基于物理的推理，以增强在有限数据条件下构建预测模型的能力。通过将基于物理的随机过程观点与数据驱动的回归方法明确关联，引入了一系列高斯过程模型，这些模型能够融合不同层级的系统专家知识。实例表明，这些方法不仅能显著降低对数据采集的依赖，同时还能提升模型的可解释性——而这在该领域中同样是重要的考量因素。