[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-125962-en":3,"doc-seo-125962-105":31,"detail-sidebar-cat-0-en-105":93},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":28,"seo_description":14,"update_tm":29,"read_time":30},125962,137451207643,"Noah","https://ap-avatar.wpscdn.com/davatar_3d24733baf745e90a7e4bdd5f77d97b2",8,"Research & Report","Physics-Informed Machine Learning On Polar Ice - A Survey","Polar ice-sheet mass loss drives sea-level rise and alters ocean circulation, increasing coastal flooding risks worldwide. To better model complex ice behavior, the literature uses both physical models and data-driven models, yet physical approaches can be costly for high resolution and data-driven methods struggle with scarce labeled data in polar regions. Physics-informed machine learning (PIML) combines both paradigms to improve accuracy and efficiency. This survey reviews PIML algorithms, proposes a taxonomy, and analyzes current challenges and future directions, including sea-ice studies and neural operator methods.","arXiv :2404 . 19536v1 [ cs .LG] 30 Apr 2024  \nPhysics-Informed Machine Learning On Polar Ice: A Survey  \nZESHENG LIU, Department of Computer Science and Engineering, Lehigh University, USA  \nYOUNGHYUN KOO, Department of Computer Science and Engineering, Lehigh University, USA MARYAM RAHNEMOONFAR∗ , Department of Computer Science and Engineering, Department of Civil and Environmental Engineering, Lehigh University, USA  \nThe 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 oftens 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.  \nAdditional Key Words and Phrases: Land ice, Sea ice, Physics model, Data-driven model, Physics-informed neural network, Neural operator, Polar region  \n1 INTRODUCTION  \nAs the global climate has been warming due to anthropogenic CO2 emissions, Greenland and the Antarctic ice sheets have undergone significant mass loss during the last few centuries. Ice losses from Greenland and Antarctic ice sheets have reached more than 7500 Gt since 1992, contributing to 21 mm of global sea level rise [94] . Although these trends exhibit large inter-annual variability for various regions and climate conditions, accelerated mass losses have been found in most studies [27, 91, 107, 147] for both Greenland and the Antarctic. In general, ice dynamics is the primary driver of mass loss in Greenland [14, 91], whereas ice melting on floating ice shelves contributes more to mass loss in the Antarctic [4] . If the current CO2 emissions and ice loss trends continue, the global mean sea level will rise by 0.7-1.3 m by 2100 [115] . Meanwhile, Arctic sea ice extent and thickness have decreased over the last few decades [60, 93], showing a loss of more than 8 . 000 km2 of volume [111] . As a result, the Arctic Ocean will likely be ice-free by the 2030s [21]. Although the Antarctic sea ice extent showed an increasing trend from the 1970s to 2016, it has also recently experienced a dramatic reduction after 2016 [23] . Considering such changes in polar ice have significant impacts on global climate, it is essential to accurately predict polar ice behavior.  \nBased on the fundamental physical laws stacked for the last few decades, many numerical models have been developed to explain the physical behavior of ice sheets and sea ice. These physical models solve the continuous equations on numerical grids by considering complex interactions between the atmosphere, ocean, snow/ice surface, and bed topography. However, solving these physical models is computationally expensive due to the complexity of  \n∗ Corresponding author  \nAuthors’ addresses: Zesheng Liu, Department of Computer Science and Engineering, Lehigh University, Bethlehem, Pennsylvania, USA, [zel220@lehigh.edu](zel220@lehigh.edu); YoungHyun Koo, Department of Computer Science and Engineering, Lehigh University, Bethlehem, Pennsylvan","cbCainnvmmqYIYfH","https://ap.wps.com/l/cbCainnvmmqYIYfH","pdf",18794388,7,1,35,"English","en",105,"# Introduction\n## Polar ice mass loss and climate impacts\n## Physical models for ice dynamics\n## Limitations of physical and data-driven approaches\n## Physics-informed machine learning (PIML)\n# Survey scope and taxonomy\n## Algorithms review\n## Accuracy and efficiency analysis\n## Challenges and future opportunities","[{\"question\":\"Why is modeling polar ice behavior challenging?\",\"answer\":\"Polar ice mass loss strongly affects climate and sea level, while accurate prediction requires handling complex ice dynamics and physical interactions. Physical models are computationally expensive at high resolution, and data-driven methods often lack sufficient labeled data in polar regions.\"},{\"question\":\"What does physics-informed machine learning aim to address?\",\"answer\":\"PIML leverages the strengths of physical models and data-driven learning by embedding physical understanding into machine learning. This helps improve physical consistency while aiming for better accuracy and efficiency.\"},{\"question\":\"What does the survey include beyond algorithm review?\",\"answer\":\"The survey provides a taxonomy for combining physics and data-driven approaches, analyzes advantages in accuracy and efficiency, and discusses current challenges and future opportunities. It also highlights directions such as PIML for sea ice studies and neural operator methods.\"}]","Physics-Informed Machine Learning On Polar Ice - A Survey | PDF",1785902259,88,{"code":4,"msg":32,"data":33},"ok",{"site_id":25,"language":24,"slug":34,"title":13,"keywords":35,"description":14,"schema_data":36,"social_meta":88,"head_meta":90,"extra_data":92,"updated_unix":29},"physics-informed-machine-learning-on-polar-ice-a-survey","",{"@graph":37,"@context":87},[38,55,70],{"@type":39,"itemListElement":40},"BreadcrumbList",[41,45,49,52],{"item":42,"name":43,"@type":44,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":46,"name":47,"@type":44,"position":48},"https://docshare.wps.com/document/","Document",2,{"item":50,"name":12,"@type":44,"position":51},"https://docshare.wps.com/document/research-report/",3,{"item":53,"name":13,"@type":44,"position":54},"https://docshare.wps.com/document/physics-informed-machine-learning-on-polar-ice-a-survey/125962/",4,{"url":53,"name":13,"@type":56,"author":57,"headline":13,"publisher":59,"fileFormat":62,"inLanguage":24,"description":14,"dateModified":63,"datePublished":64,"encodingFormat":62,"isAccessibleForFree":65,"interactionStatistic":66},"DigitalDocument",{"name":9,"@type":58},"Person",{"url":42,"name":60,"@type":61},"DocShare","Organization","application/pdf","2026-08-23","2026-08-05",true,{"@type":67,"interactionType":68,"userInteractionCount":20},"InteractionCounter",{"@type":69},"ViewAction",{"@type":71,"mainEntity":72},"FAQPage",[73,79,83],{"name":74,"@type":75,"acceptedAnswer":76},"Why is modeling polar ice behavior challenging?","Question",{"text":77,"@type":78},"Polar ice mass loss strongly affects climate and sea level, while accurate prediction requires handling complex ice dynamics and physical interactions. Physical models are computationally expensive at high resolution, and data-driven methods often lack sufficient labeled data in polar regions.","Answer",{"name":80,"@type":75,"acceptedAnswer":81},"What does physics-informed machine learning aim to address?",{"text":82,"@type":78},"PIML leverages the strengths of physical models and data-driven learning by embedding physical understanding into machine learning. This helps improve physical consistency while aiming for better accuracy and efficiency.",{"name":84,"@type":75,"acceptedAnswer":85},"What does the survey include beyond algorithm review?",{"text":86,"@type":78},"The survey provides a taxonomy for combining physics and data-driven approaches, analyzes advantages in accuracy and efficiency, and discusses current challenges and future opportunities. 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