[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-117246-en":3,"doc-seo-117246-105":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":4,"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},117246,2336464648322,"Aria","https://ap-avatar.wpscdn.com/avatar/2200025388227c56fec?_k=1778556882303663488",8,"Research & Report","Scientific Machine Learning - A Symbiosis","Editorial preface for the “Scientific Machine Learning” (SciML) special issue in AIMS Foundations of Data Science. Argues that SciML forms a symbiotic relationship between computational science and engineering (CSE) and machine learning (ML), noting CSE’s rigorous mathematical guarantees alongside ML’s simulation advances. Proposes that as SciML leverages ML capabilities, it will support rather than replace traditional CSE methods, and surveys key challenges, opportunities, and the special issue papers.","SCIENTIFIC MACHINE LEARNING: A SYMBIOSIS  \nBrendan Keith􀀀 1, Thomas O’Leary-Roseberry􀀀 2 ,  \nBenjamin Sanderse􀀀 3, Robert Scheichl􀀀 4 , and Bart van Bloemen Waanders􀀀 5  \n1 Brown University, Providence RI, USA  \n2 University of Texas at Austin, Austin TX, USA  \n3 Centrum Wiskunde & Informatica, Amsterdam, The Netherlands  \n4 Heidelberg University, Heidelberg, Germany  \n5 Sandia National Laboratories, Albuquerque NM, USA  \nAbstract . This editorial serves as a preface to the “Scientific Machine Learning”  \n(SciML) special issue of the AIMS Foundations of Data Science journal. In this piece, we contend that SciML exists in a symbiotic relationship with the fields of computational science and engineering (CSE) and machine learning  \n(ML) . We highlight the progress (and limitations) of CSE and reflect on the recent successes of ML. While ML creates significant possibilities for advancing simulation techniques, it lacks the mathematical guarantees that are typically found in CSE. We argue that as SciML develops and embraces the remarkable capabilities of ML, it will support, not replace, traditional methods of CSE. We then overview some existing challenges and opportunities in this interdisciplinary field and close by introducing the special issue papers.  \n1. Introduction. Mathematical modeling of physical phenomena has been a cornerstone of engineering and the natural sciences for centuries. The field of computational science and engineering (CSE) seeks to operationalize the resulting models through computer simulations based on numerical methods. Pursuing numerical methods has led to fundamental mathematical theories and advances in high-performance computing, creating a reliable paradigm for conducting physics-based computer simulations with rigorous mathematical guarantees. This paradigm has enabled major breakthroughs across disciplines by allowing scientists, engineers, and practitioners to investigate physical phenomena and make decisions about complex systems that would be impossible to achieve through theory and experimentation alone. As a result, CSE has been referred to as the “third pillar” of the scientific enterprise, alongside theory and experimentation [39, 43] .  \nThe tenets and impediments of traditional CSE. The key tenets of CSElie in exploiting two fundamental aspects of mathematical models: generalizability and interpretability [28] . Newton’s law of gravitation is an example of a simple mathematical model that is both generalizable (it generalizes from apples falling on Earth to planets orbiting the Sun) and interpretable (the gravitational force depends on the masses of the objects, their relative distance, and a universal constant) . Symplectic integrators [44] operationalize this planetary model (as well as far more complicated mathematical models), delivering accurately simulated orbital motions  \nii KEITH, O’LEARY-ROSEBERRY, SANDERSE, SCHEICHL AND VAN BLOEMEN WAANDERS  \nthat preserve key invariants of the true mechanics. As such, symplectic integrators are a prime example of a successful class of numerical methods: they preserve fundamental properties deriving from the original mathematical formulation while providing efficient execution and high-accuracy guarantees.  \nOver the past century, numerical methods from CSE have reformed prediction, decision-making, and design of complex physical and engineering systems, leading to major technological advances. However, significant challenges can persist even when such powerful tools are available. Indeed, direct simulation with state-of-the-art numerical methods can be infeasible in the following practical scenarios and for the following reasons:  \nOuter-loop and many-query problems. Tasks involving the design, optimization, uncertainty quantification, or control of complex physical systems require varying inputs and, thus, repeatedly evaluating model outputs. In these problems, the overall computational cost multiplies with the number of samples or iterati","cbCaihPKb1U3a2ZX","https://ap.wps.com/l/cbCaihPKb1U3a2ZX","pdf",337573,1,10,"English","en",105,"# Abstract\n# Introduction\n## Mathematical modeling and computational science and engineering\n# The tenets and impediments of traditional CSE\n## Generalizability and interpretability\n## Symplectic integrators and invariants\n## Practical limitations: outer-loop and many-query problems\n## Practical limitations: scales and physical complexity\n## Practical limitations: unknown models\n# The advent of machine learning (ML)\n## ML breakthroughs and scientific opportunities\n## Surrogates and learned models","[{\"question\":\"What relationship does the editorial claim exists between SciML, CSE, and ML?\",\"answer\":\"SciML is argued to have a symbiotic relationship with computational science and engineering (CSE) and machine learning (ML), combining CSE’s guarantees with ML’s capabilities.\"},{\"question\":\"Why does the editorial say ML cannot simply replace traditional CSE?\",\"answer\":\"ML is presented as powerful for advancing simulation techniques, but it typically lacks the mathematical guarantees associated with rigorous CSE methods.\"},{\"question\":\"What practical challenges in CSE are highlighted as motivations for SciML?\",\"answer\":\"The editorial highlights outer-loop and many-query costs, difficulties from multiple scales and physical complexity, and issues arising from unknown or empirically based governing models.\"}]","Scientific Machine Learning - A Symbiosis | PDF",1785674645,25,{"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},"scientific-machine-learning-a-symbiosis","",{"@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/scientific-machine-learning-a-symbiosis/117246/",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","2026-08-02",true,{"@type":65,"interactionType":66,"userInteractionCount":4},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What relationship does the editorial claim exists between SciML, CSE, and ML?","Question",{"text":75,"@type":76},"SciML is argued to have a symbiotic relationship with computational science and engineering (CSE) and machine learning (ML), combining CSE’s guarantees with ML’s capabilities.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"Why does the editorial say ML cannot simply replace traditional CSE?",{"text":80,"@type":76},"ML is presented as powerful for advancing simulation techniques, but it typically lacks the mathematical guarantees associated with rigorous CSE methods.",{"name":82,"@type":73,"acceptedAnswer":83},"What practical challenges in CSE are highlighted as motivations for SciML?",{"text":84,"@type":76},"The editorial highlights outer-loop and many-query costs, difficulties from multiple scales and physical complexity, and issues arising from unknown or empirically based governing models.","https://schema.org",{"og:url":52,"og:type":87,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":89,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,134],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":21,"doc_module":4,"doc_module_name":46,"category_name":132,"show_sort_weight":21,"slug":133},"Lifestyle","lifestyle",{"id":135,"doc_module":4,"doc_module_name":46,"category_name":136,"show_sort_weight":106,"slug":137},19,"General","general"]