| Summary: | Perennially frozen ground, typically referred to as permafrost, plays a significant role in Arctic environments. Monitoring its response to rapid climate change is challenging, however, due to the limited availability of high quality, long-term observations of subsurface hydrothermal conditions, e.g. measurements of soil temperature and moisture. Numerical models are thus an indispensable tool for understanding how permafrost is changing at larger scales, but simulating the hydrothermal processes impacting it is difficult due to the nonlinear effects of phase change in porous media. The computational cost of such simulations is prohibitive, particularly for sensitivity analysis and parameter estimation tasks which require a large number of simulations with different parameter settings. To address this issue, we examine possible applications of physics-informed machine learning (PIML) methods in improving and accelerating dynamical models of permafrost processes. We assess the viability of recently developed PIML methods such as physics-informed operator networks in resolving dynamics across spatiotemporal scales and thus bridging the gap between scalable, low-resolution numerical simulations and costly high-resolution simulations of nonlinear hydrothermal dynamics. We highlight the strengths and weaknesses of PIML in this effort and the primary challenges that still need to be overcome.
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