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Geosystems are geological formations altered by humans activities such as fossil energy exploration, waste disposal, geologic carbon sequestration, and renewable energy generation. Geosystems also represent a critical link in the global water-energy nexus, providing both the source and buffering mechanisms for enabling societal adaptation to climate variability and change. The responsible use and exploration of geosystems are thus critical to the geosystem governance, which in turn depends on the efficient monitoring, risk assessment, and decision support tools for practical implementation. Large-scale, physics-based models have long been developed and used for geosystem management by incorporating geological domain knowledge such as stratigraphy, governing equations of flow and mass transport in porous media, geological and initial/boundary constraints, and field observations. Spatial heterogeneities and the multiscale nature of geological formations, however, pose significant challenges to the conventional numerical models, especially when used in a simulation-based optimization framework for decision support. Fast advances in machine learning (ML) algorithms and novel sensing technologies in recent years have presented new opportunities for the subsurface research community to improve the efficacy and transparency of geosystem governance. Although recent studies have shown the great promise of scientific ML (SciML) models, questions remain on how to best leverage ML in the management of geosystems, which are typified by multiscality, high-dimensionality, and data resolution inhomogeneity. This survey will provide a systematic review of the recent development and applications of domain-aware SciML in geosystem researches, with an emphasis on how the accuracy, interpretability, scalability, defensibility, and generalization skill of ML approaches can be improved to better serve the geoscientific community.

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