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

Physics-Informed Machine Learning On Polar Ice: A Survey

Given multi-model ensemble climate projections, the goal is to accurately and
reliably predict future sea-level rise while lowering the uncertainty. This
problem is important because sea-level rise affects millions of people in
coastal communities and beyond due to climate change's impacts on polar ice
sheets and the ocean. This problem is challenging due to spatial variability
and unknowns such as possible tipping points (e.g., collapse of Greenland or
West Antarctic ice-shelf), climate feedback loops (e.g., clouds, permafrost
thawing), future policy decisions, and human actions. Most existing climate
modeling approaches use the same set of weights globally, during either
regression or deep learning to combine different climate projections. Such
approaches are inadequate when different regions require different weighting
schemes for accurate and reliable sea-level rise predictions. This paper
proposes a zonal regression model which addresses spatial variability and model
inter-dependency. Experimental results show more reliable predictions using the
weights learned via this approach on a regional scale.

利用多模型集合气候预测，通过降低不确定性精确可靠地预测未来海平面上升是一个重要问题，本文提出了一个区域回归模型来解决空间变异性和模型相互依赖性，并通过实验结果表明该方法在区域尺度上能给出更可靠的预测。