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The intersection of physics and machine learning has given rise to thephysics-enhanced machine learning (PEML) paradigm, aiming to improve thecapabilities and reduce the individual shortcomings of data- or physics-onlymethods. In this paper, the spectrum of physics-enhanced machine learningmethods, expressed across the defining axes of physics and data, is discussedby engaging in a comprehensive exploration of its characteristics, usage, andmotivations. In doing so, we present a survey of recent applications anddevelopments of PEML techniques, revealing the potency of PEML in addressingcomplex challenges. We further demonstrate application of select such schemeson the simple working example of a single degree-of-freedom Duffing oscillator,which allows to highlight the individual characteristics and motivations ofdifferent `genres' of PEML approaches. To promote collaboration andtransparency, and to provide practical examples for the reader, the codegenerating these working examples is provided alongside this paper. As afoundational contribution, this paper underscores the significance of PEML inpushing the boundaries of scientific and engineering research, underpinned bythe synergy of physical insights and machine learning capabilities.

Discussing the Spectrum of Physics-Enhanced Machine Learning; a Survey on Structural Mechanics Applications