Exploring physics-informed machine learning for accelerated simulation of permafrost processes

Permafrost, i.e. ground material that remains perennially frozen, plays a key role in Arctic ecosystems. Monitoring the response of permafrost to rapid climate change remains difficult due to the sparse availability of long-term, high quality measurements of the subsurface. Numerical models are therefore an indispensable tool for understanding the evolution of Arctic permafrost. However, large scale simulation of the hydrothermal processes affecting permafrost is challenging due to the highly nonlinear effects of phase change in porous media. The resulting computational cost of such simulations is especially prohibitive for sensitivity analysis and parameter estimation tasks where a large number of simulations may be necessary for robust inference of quantities such as temperature, water fluxes, and soil properties. In this work, we explore the applicability of recently developed physics-informed machine learning (PIML) methods for accelerating numerical models of permafrost hydrothermal dynamics. We present a preliminary assessment of two possible applications of PIML in this context: (1) linearization of the nonlinear PDE system according to Koopman operator theory in order to reduce the computational burden of large scale simulations, and (2) efficient parameterization of the surface energy balance and snow dynamics on the subsurface hydrothermal regime. By combining the predictive power of machine learning with the underlying conservation laws, PIML can potentially enable researchers and practitioners interested in permafrost to explore complex process interactions at larger spatiotemporal scales.