[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-123774-en":3,"doc-seo-123774-105":30,"detail-sidebar-cat-0-en-105":91},{"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":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},123774,1649267921044,"Ava Thompson","https://us-avatar.wpscdn.com/avatar/1800007509477c92dfb?_k=1782875107921204101",8,"Research & Report","Differentiable modeling to unify machine learning and physical models for geosciences","Process-based modelling delivers interpretability and physical consistency across geosciences, but it struggles to exploit large datasets efficiently. Purely data-driven machine learning can predict strongly, yet it cannot reliably answer specific scientific questions. The perspective introduces differentiable modelling as a bridge between process-based models and machine learning, enabled by accurate gradient computation and by integrating prior physical knowledge into neural networks. Examples from hydrological modelling show gains in interpretability, generalizability, extrapolation, data efficiency, and robust performance under data-scarce conditions.","Differentiable modeling to unify machine learning and physical models and advance Geosciences  \nChaopeng Shen 1*, Alison P. Appling2, Pierre Gentine3, Toshiyuki Bandai4, Hoshin Gupta5, Alexandre Tartakovsky6, Marco Baity-Jesi7, Fabrizio Fenicia7, Daniel Kifer8, Li Li 1, Xiaofeng Liu 1, Wei Ren9, Yi Zheng 10, Ciaran J. Harman 11, Martyn Clark 12, Matthew Farthing 13, Dapeng Feng 1, Praveen Kumar6,14, Doaa Aboelyazeed 1, Farshid Rahmani 1, Hylke E. Beck 15, Tadd Bindas 1, Dipankar Dwivedi 16, Kuai Fang 17, Marvin Höge7, Chris Rackauckas 18, Tirthankar Roy 19, Chonggang Xu20, Binayak Mohanty21, Kathryn Lawson 1  \n1 Civil and Environmental Engineering, The Pennsylvania State University, University Park, PA, USA.  \n2 U. S. Geological Survey, Water Mission Area, Integrated Modeling and Prediction Division, Reston, VA, USA  \n3 National Science Foundation Science and Technology Center for Learning the Earth with Artificial Intelligence and Physics (LEAP), Columbia University, New York, NY USA  \n4 Life and Environmental Science Department, University of California, Merced, CA, USA  \n5 Hydrology and Atmospheric Sciences, The University of Arizona, Tucson, AZ, USA.  \n6 Civil and Environmental Engineering, University of Illinois, Urbana Champaign, IL, USA  \n7 Eawag: Swiss Federal Institute of Aquatic Science and Technology, Dübendorf, Switzerland  \n8 Computer Science and Engineering, The Pennsylvania State University, University Park, PA, USA  \n9 Department of Natural Resources and the Environment, University of Connecticut, Storrs, CT, USA  \n10 Southern University of Science and Technology, Shenzhen, Guangdong Province, China  \n11 Department of Environmental Health and Engineering, Johns Hopkins University, Baltimore, MD, USA  \n12 Global Institute for Water Security, University of Saskatchewan, Canmore, Alberta, Canada  \n13 US Army Engineer Research and Development Center, Vicksburg, MS, USA  \n14 Prairie Research Institute, University of Illinois, Urbana Champaign, IL, USA  \n15 Physical Science and Engineering Division, King Abdullah University of Science and Technology, Thuwal, Saudi Arabia  \n16 Lawrence Berkeley National Laboratory, Berkeley, CA, USA  \n17 Department of Earth System Science, Stanford University, Stanford, CA, USA  \n18 Computer Science and Artificial Intelligence Laboratory (CSAIL), Massachusetts Institute of Technology, Massachusetts, USA  \n19 Civil and Environmental Engineering, University of Nebraska-Lincoln, NE, USA  \n20 Earth and Environmental Divisions, Los Alamos National Laboratory, NM, USA  \n21 Department of Biological and Agricultural Engineering, Texas A&M University, College Station, TX, USA  \n* Corresponding author, email [cshen@engr.psu.edu](cshen@engr.psu.edu)  \nThe final accepted paper has been published in Nature Reviews Earth & Environment with doi:  \n10.1038/s43017-023-00450-9. The link to the paper is [https://www.nature.com/articles/s43017-023-](https://www.nature.com/articles/s43017-023-)[ ](https://www.nature.com/articles/s43017-023-)00450-9. The link to the Open Access online PDF is: [https://t.co/qyuAzYPA6Y](https://t.co/qyuAzYPA6Y. If you need a journal)[. If you need a journal](https://t.co/qyuAzYPA6Y. If you need a journal)[ ](https://t.co/qyuAzYPA6Y. If you need a journal)[printout version of the PDF](printout version of the PDF), [please write to the corresponding author. Correct citation for the paper is:](please write to the corresponding author. Correct citation for the paper is:)  \nChaopeng Shen, Alison P. Appling, Pierre Gentine, Toshiyuki Bandai, Hoshin Gupta, Alexandre Tartakovsky, Marco Baity-Jesi, Fabrizio Fenicia, Daniel Kifer, Li Li, Xiaofeng Liu, Wei Ren, Yi Zheng, Ciaran J. Harman, Martyn Clark, Matthew Farthing, Dapeng Feng*, Praveen Kumar, Doaa  \nAboelyazeed*, Farshid Rahmani*, Yalan Song*, Hylke E. Beck, Tadd Bindas*, Dipankar Dwivedi, Kuai Fang, Marvin Höge, Chris Rackauckas, Binayak Mohanty, Tirthankar Roy, Chonggang Xu and Kathryn Lawson*, Differentiable modelling to unify","cbCaijxgXjFFiZkF","https://ap.wps.com/l/cbCaijxgXjFFiZkF","pdf",1667859,1,39,"English","en",105,"# Abstract\n# Introduction","[{\"question\":\"What problem does differentiable modelling aim to solve in geosciences?\",\"answer\":\"It targets the barrier between process-based modelling, which is interpretable but data-inefficient, and machine learning, which predicts well but struggles with answering scientific questions. Differentiable modelling links physics-based constraints with neural networks to improve scientific usefulness.\"},{\"question\":\"What does “differentiable” mean in this perspective?\",\"answer\":\"It means accurately and efficiently computing gradients with respect to model variables or parameters. This capability helps discover high-dimensional unknown relationships during model training and inference.\"},{\"question\":\"How does differentiable modelling compare with purely data-driven machine learning?\",\"answer\":\"It can provide better interpretability, generalizability, and extrapolation, while achieving similar accuracy with less training data. The perspective also notes strong scaling in performance and efficiency as data volume increases.\"}]","Differentiable modeling to unify machine learning and physical models for geosciences | PDF",1785818483,98,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"differentiable-modeling-to-unify-machine-learning-and-physical-models-for-geosciences","",{"@graph":36,"@context":85},[37,54,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/differentiable-modeling-to-unify-machine-learning-and-physical-models-for-geosciences/123774/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":62,"encodingFormat":61,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-04",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What problem does differentiable modelling aim to solve in geosciences?","Question",{"text":75,"@type":76},"It targets the barrier between process-based modelling, which is interpretable but data-inefficient, and machine learning, which predicts well but struggles with answering scientific questions. Differentiable modelling links physics-based constraints with neural networks to improve scientific usefulness.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What does “differentiable” mean in this perspective?",{"text":80,"@type":76},"It means accurately and efficiently computing gradients with respect to model variables or parameters. This capability helps discover high-dimensional unknown relationships during model training and inference.",{"name":82,"@type":73,"acceptedAnswer":83},"How does differentiable modelling compare with purely data-driven machine learning?",{"text":84,"@type":76},"It can provide better interpretability, generalizability, and extrapolation, while achieving similar accuracy with less training data. 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