[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-126445-en":3,"doc-seo-126445-105":31,"detail-sidebar-cat-0-en-105":85},{"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},126445,8796095027276,"Valentina","https://avatar.qwps.com/avatar/d3BzX2FwX3Rlc3RfMjUxMTI2XzAxODA=",8,"Research & Report","Resolving the body-order paradox of machine learning interatomic potentials - Research article","Machine learning interatomic potentials (MLIPs) are often viewed as sums of body-ordered contributions, either explicitly through neighbor density correlation descriptors or implicitly through nonlinear functions of low body-order terms. The effective body-orderedness of MLIPs remains unclear: how energies decompose into body-ordered parts, and how this influences accuracy and learning dynamics. This work analyzes many-body expansion constraints at the atomic limit, trains curated MLIPs on hydrogen-cluster datasets, and examines convergence of body-order trends and model generalizability.","RESEARCH ARTICLE | FEBRUARY 13 2026  \nResolving the body-order paradox of machine learning interatomic potentials  \nSpecial Collection: Festschrift in honor of Christoph Dellago: Exploring Paths and Barriers in Statistical Mechanics  \nSanggyu Chong 􀀧  ; Tong Jiang  ; Michelangelo Domina  ; Filippo Bigi  ; Federico Grasselli  ; Joonho Lee  ; Michele Ceriotti   \nJ. Chem. Phys. 164, 064121 (2026)  \n[https://doi.org/10.1063/5.0303302](https://doi.org/10.1063/5.0303302)  \n􀀭  \nView Online  \n􀀱  \nExport Citation  \nThe Journal  \nof Chemical Physics  \nARTICLE  \n[pubs.aip.org/aip/jcp](pubs.aip.org/aip/jcp)  \nResolving the body-order paradox of machine learning interatomic potentials  \n\n| Cite as: J. Chem. Phys. 164, 064121 (2026); doi: 10. 1063/5.0303302 Submitted: 20 September 2025 • Accepted: 20 January 2026 •\u003Cbr>Published Online: 13 February 2026 |  |  |  |\n| --- | --- | --- | --- |\n| Sanggyu Chong,1, a)  Tong Jiang,2  Michelangelo Domina,1  Filippo Bigi,1  Federico Grasselli,1, b)  Joonho Lee,2  and Michele Ceriotti1  |  |  |  |\n| AFFILIATIONS\u003Cbr>1 Laboratory of Computational Science and Modeling, Institute of Materials, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland\u003Cbr>2 Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts 02138, USA\u003Cbr>Note: This paper is part of the Special Topic Festschrift in Honor of Christoph Dellago: Exploring Paths and Barriersin Statistical Mechanics.\u003Cbr>a)Author to whom correspondence should be addressed: sanggyu.chong@epfl.ch\u003Cbr>b)Present address: Dipartimento di Scienze Fisiche, Informatiche e Matematiche, Università degli Studi di Modena e Reggio Emilia, 41125 Modena, Italy. |  |  |  |\n| ABSTRACT\u003Cbr>In many cases, the predictions of machine learning interatomic potentials (MLIPs) can be interpreted as a sum of body-ordered contributions, which is explicit when the model is directly built on neighbor density correlation descriptors and is implicit when the model captures the correlations through the non-linear functions of low body-order terms. In both cases, the “effective body-orderedness” of MLIPs remains largely unexplained: how do the models decompose the total energy into body-ordered contributions, and how does their body-orderedness affect the accuracy and learning behavior? In answering these questions, we first discuss the complexities in imposing the many-body expansion on ab initio calculations at the atomic limit. Next, we train a curated set of MLIPs on datasets of hydrogen clusters and reveal the inherent tendency of the ML models to deduce their own, effective body-order trends, which are dependent on the model type and dataset makeup. Finally, we present different trends in the convergence of the body-orders and generalizability of the models, providing useful insights into the development of future MLIPs.\u003Cbr>© 2026 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license ([https://creativecommons.org/licenses/by/4.0/](https://creativecommons.org/licenses/by/4.0/)). [https://doi.org/10.1063/5.0303302](https://doi.org/10.1063/5.0303302) |  |  |  |\n\nI. INTRODUCTION  \nThe many-body expansion (MBE) expresses the global observable of a chemical system as a sum of contributions from interactions at different body-orders, where the “bodies” are taken to be atoms, molecules, or larger fragments in the system. The MBE enables the interpretation of complex interactions in terms of simpler bodyordered contributions and can provide reasonable approximations to the global quantity, especially when the contributions decay rapidly with the number of bodies involved. The MBE has given rise to many local or fragment-based quantum chemistry methods1–9 that offer favorable scaling for large systems, as well as force fields that can be used for atomic scale simulations at large length and timescales.10–12  \nMachine learning interatomic potentials (MLIPs)13–17 enable ab initio-qua","cbCaillqSOq9mnXs","https://ap.wps.com/l/cbCaillqSOq9mnXs","pdf",5650927,9,1,13,"English","en",105,"# Abstract\n# Introduction\n## Many-body expansion as a reference\n## Locality ansatz and body-ordered correlations in MLIPs\n## The body-order paradox and motivation\n# Methods and training approach (hydrogen-cluster MLIPs)\n# Analysis of inferred body-order trends\n# Convergence and generalizability insights\n# Conclusions and outlook","[{\"question\":\"What does the paper find about convergence and generalizability?\",\"answer\":\"Different MLIP model types and dataset compositions lead to distinct effective body-order trends, and these variations correlate with different convergence behaviors of body orders and the generalizability of the models.\"}]","Resolving the body-order paradox of machine learning interatomic potentials - Research article | PDF",1785905095,33,{"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":80,"head_meta":82,"extra_data":84,"updated_unix":29},"resolving-the-body-order-paradox-of-machine-learning-interatomic-potentials-research-article","",{"@graph":37,"@context":79},[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/resolving-the-body-order-paradox-of-machine-learning-interatomic-potentials-research-article/126445/",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],{"name":74,"@type":75,"acceptedAnswer":76},"What does the paper find about convergence and generalizability?","Question",{"text":77,"@type":78},"Different MLIP model types and dataset compositions lead to distinct effective body-order trends, and these variations correlate with different convergence behaviors of body orders and the generalizability of the models.","Answer","https://schema.org",{"og:url":53,"og:type":81,"og:title":13,"og:site_name":60,"og:description":14},"article",{"robots":83,"canonical":53},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":86},[87,91,95,99,104,109,114,117,121,124,128],{"id":21,"doc_module":4,"doc_module_name":47,"category_name":88,"show_sort_weight":89,"slug":90},"Story & Novel",90,"story-novel",{"id":48,"doc_module":4,"doc_module_name":47,"category_name":92,"show_sort_weight":93,"slug":94},"Literature",80,"literature",{"id":54,"doc_module":4,"doc_module_name":47,"category_name":96,"show_sort_weight":97,"slug":98},"Exam",70,"exam",{"id":100,"doc_module":4,"doc_module_name":47,"category_name":101,"show_sort_weight":102,"slug":103},5,"Comic",60,"comic",{"id":105,"doc_module":4,"doc_module_name":47,"category_name":106,"show_sort_weight":107,"slug":108},6,"Technology",50,"technology",{"id":110,"doc_module":4,"doc_module_name":47,"category_name":111,"show_sort_weight":112,"slug":113},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":47,"category_name":12,"show_sort_weight":115,"slug":116},30,"research-report",{"id":20,"doc_module":4,"doc_module_name":47,"category_name":118,"show_sort_weight":119,"slug":120},"Religion & Spirituality",20,"religion-spirituality",{"id":119,"doc_module":4,"doc_module_name":47,"category_name":122,"show_sort_weight":119,"slug":123},"World Cup","world-cup",{"id":125,"doc_module":4,"doc_module_name":47,"category_name":126,"show_sort_weight":125,"slug":127},10,"Lifestyle","lifestyle",{"id":129,"doc_module":4,"doc_module_name":47,"category_name":130,"show_sort_weight":100,"slug":131},19,"General","general"]