Review of Physics-Informed Machine Learning Inversion of Geophysical Data

We review five types of physics-informed machine learning (PIML) algorithms for inversion and modeling of geophysical data. Such algorithms use the combination of a data-driven machine learning (ML) method and the equations of physics to model and/or invert geophysical data. By incorporating the constraints of physics, PIML algorithms can effectively reduce the size of the solution space for machine learning models, enabling them to be trained on smaller datasets. This is especially advantageous in scenarios where data availability may be limited or expensive to obtain.In this review we restrict the {\it physics} to be that from the governing wave equation, either as a constraint that must be satisfied or by using numerical solutions to the wave equation for both modeling and inversion.#xD;This approach ensures that the resulting models adhere to physical principles while leveraging the power of machine learning to analyze and interpret complex geophysical data.#xD;The key challenge with PIML methods is to strike a balance between computational efficiency and predictive accuracy. While PIML algorithms may offer computational advantages over standard numerical methods, their accuracy must justify the trade-off. In cases where PIML models are efficient but somewhat inaccurate, they can still serve valuable purposes, such as providing initial velocity models for more accurate techniques like Full Waveform Inversion (FWI).