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.

本文讨论了物理增强机器学习（PEML）的特点、用途和动机，并通过对PEML技术的最近应用和发展的全面探索，展示了PEML在解决复杂挑战中的潜力。通过对单自由度Duffing振子的简单工作示例的应用，突出了不同PEML方法的个体特征和动机。提供这些工作示例的代码，以促进合作和透明度，并为读者提供实用的示例。作为基础性贡献，本文强调了物理洞察力和机器学习能力的协同作用，在推动科学和工程研究的边界上的重要性。

通过结构力学应用的调查讨论物理增强机器学习的光谱