The intersection of physics and machine learning has given rise to a paradigm that we refer to here as physics-enhanced machine learning (PEML), aiming to improve the capabilities and reduce the individual shortcomings of data- or physics-only methods. In this paper, the spectrum of physics-enhanced machine learning methods, expressed across the defining axes of physics and data, is discussed by engaging in a comprehensive exploration of its characteristics, usage, and motivations. In doing so, this paper offers a survey of recent applications and developments of PEML techniques, revealing the potency of PEML in addressing complex challenges. We further demonstrate application of select such schemes on the simple working example of a single-degree-of-freedom Duffing oscillator, which allows to highlight the individual characteristics and motivations of different `genres' of PEML approaches. To promote collaboration and transparency, and to provide practical examples for the reader, the code of these working examples is provided alongside this paper. As a foundational contribution, this paper underscores the significance of PEML in pushing the boundaries of scientific and engineering research, underpinned by the synergy of physical insights and machine learning capabilities.

翻译：物理与机器学习的交叉催生了一种我们称之为物理增强机器学习（PEML）的范式，旨在提升纯数据驱动或纯物理驱动方法的性能，并弥补各自缺陷。本文围绕物理与数据这两大核心维度，对物理增强机器学习方法的频谱进行了深入探讨，系统梳理了其特征、用途及内在动机。为此，本文综述了PEML技术的最新应用与发展，揭示了其在应对复杂挑战中的潜力。我们进一步在单自由度杜芬振子这一简单工作实例上展示了若干典型方案的运用，从而凸显不同“流派”PEML方法的个性特征与设计动机。为促进合作与透明性，并为读者提供实践参考，本文随附了这些工作实例的代码。作为一项基础性贡献，本文强调了PEML在物理洞见与机器学习能力协同作用下，对推动科学与工程研究边界拓展的重要意义。