Physics-Informed Machine Learning On Polar Ice: A Survey

TL;DR

The existing algorithms of PIML are reviewed, a taxonomy based on the methods of combining physics and data-driven approaches is provided, and the advantages of PIML in the aspects of accuracy and efficiency are analyzed.

Abstract

The mass loss of the polar ice sheets contributes considerably to ongoing sea-level rise and changing ocean circulation, leading to coastal flooding and risking the homes and livelihoods of tens of millions of people globally. To address the complex problem of ice behavior, physical models and data-driven models have been proposed in the literature. Although traditional physical models can guarantee physically meaningful results, they have limitations in producing high-resolution results. On the other hand, data-driven approaches require large amounts of high-quality and labeled data, which is rarely available in the polar regions. Hence, as a promising framework that leverages the advantages of physical models and data-driven methods, physics-informed machine learning (PIML) has been widely studied in recent years. In this paper, we review the existing algorithms of PIML, provide our own taxonomy based on the methods of combining physics and data-driven approaches, and analyze the advantages of PIML in the aspects of accuracy and efficiency. Further, our survey discusses some current challenges and highlights future opportunities, including PIML on sea ice studies, PIML with different combination methods and backbone networks, and neural operator methods.

Figures (13)

• Figure 1: Roadmap of physics-driven, data-driven, and physics-informed machine learning studies for polar ice
• Figure 2: (a): A comparison of 1D interpolation result showing the importance of mass conservation constraint. (b): A comparison between the result of the network proposed by Teisberg et al. and BedMachine result. Overlaid lines represent the used radar data locations, with red indicating that the predicted thickness exceeds the measured radar thickness. Figure reproduced from the original paperteisberg.
• Figure 3: Network architecture diagram and loss function design for inferring the slip mechanism. Reproduced from original paperslip.
• Figure 4: Network Architecture and workflow for estimating ice viscosity. Reproduced from original paperrheologyiceshelf.
• Figure 5: Network Prediction Verification. a. Comparison between observation and prediction of ice velocity and thickness. b. Verification of equation residual, showing that the PINN predictions satisfy the shallow-shelf approximation equation. c. Estimation of ice stress based on strain rate and ice viscosity. Reproduced from original paperrheologyiceshelf.