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.

南极冰盖和北极冰盖的大量流失导致海平面上升，海洋环流变化，从而导致沿海洪涝，并危及全球数千万人的家园和生计。为了解决冰川行为的复杂问题，文献中提出了物理模型和数据驱动模型。然而，传统的物理模型在产生高分辨率结果方面存在局限性；另一方面，数据驱动方法需要大量高质量且标记的数据，而这在极地地区很少见。因此，作为一种充分利用物理模型和数据驱动方法优势的有希望的框架，物理顺应机器学习（PIML）在近年来得到广泛研究。本文综述了现有的PIML算法，根据融合物理和数据驱动方法的方式提供了自己的分类，并分析了PIML在准确性和效率方面的优势。此外，我们的调研还讨论了一些当前的挑战和未来的机会，包括海冰研究中的PIML、不同组合方法和骨干网络的PIML以及神经操作器方法。

极地冰上的物理感知机器学习：一项调查