[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-124859-en":3,"doc-seo-124859-105":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},124859,549758252649,"Ivy","https://ap-avatar.wpscdn.com/avatar/8000253669c5317157?_k=1778319167496531819",8,"Research & Report","Robustness of Local Predictions in Atomistic Machine Learning Models","Machine learning models for molecules and materials often decompose a global target into local, atom-centered contributions, supporting linear-scaling simulations and interpretability of atomic environments. Although this local scheme is convenient, only the global quantity is rigorously defined, so local contributions may depend on training strategy or model architecture. The work introduces local prediction rigidity (LPR) to quantify robustness, studies LPR across toy and real chemical systems, and proposes strategies to enhance robustness, interpretability, and transferability.","This article is licensed under CC-BY 4.0   \n[pubs.acs.org/JCTC](pubs.acs.org/JCTC)  Article   \nRobustness of Local Predictions in Atomistic Machine Learning Models  \nPublished as part of Journal of Chemical Theory and Computation virtual special issue “Machine Learning and Statistical Mechanics: Shared Synergies for Next Generation of Chemical Theory and Computation”.  \nSanggyu Chong, Federico Grasselli, Chiheb Ben Mahmoud, Joe D. Morrow, Volker L. Deringer, and Michele Ceriotti*  \n Cite This: J. Chem. Theory Comput. 2023, 19, 8020−8031  \nRead Online  \n\n|  |  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- |\n| ACCESS   | Metrics & More |  |  Article Recommendations |  | *sı Supporting Information |\n\nABSTRACT: Machine learning (ML) models for molecules and materials commonly rely on a decomposition of the global target quantity into local, atom-centered contributions. This approach is convenient from a computational perspective, enabling large-scale MLdriven simulations with a linear-scaling cost and also allows for the identification and posthoc interpretation of contributions from individual chemical environments and motifs to complicated macroscopic properties. However, even though practical justifications exist for the local decomposition, only the global quantity is rigorously defined. Thus, when the atom-centered contributions are used, their sensitivity to the training strategy or the model architecture should be carefully considered. To this end, we introduce a quantitative metric, which we  \ncall the local prediction rigidity (LPR), that allows one to assess how robust the locally decomposed predictions of ML models are. We investigate the dependence of the LPR on the aspects of model training, particularly the composition of training data set, for a range of different problems from simple toy models to real chemical systems. We present strategies to systematically enhance the LPR, which can be used to improve the robustness, interpretability, and transferability of atomistic ML models.  \n1. INTRODUCTION  \nExtensive properties of matter, such as the total energy, arise from the collective interactions between atoms and can be rigorously defined only as global quantities that depend on the entire molecule or the condensed-phase structure. Nonetheless, the last decades have seen considerable efforts toward the construction of quantum-chemical methods that exploit the quantum-mechanical nearsightedness principle1 to perform a local decomposition of the global quantities.2−7 These methods either undertake a physically motivated local decomposition in the calculation of a global quantity8−11 or perform such decomposition for the purpose of analysis. 12−17 Despite the fact that the local quantities are not physical observables, such a decomposition allows one to break down the macroscopic observable for a complex structure into contributions from much simpler components, typically individual atoms and their  \ncornerstone of atomistic machine learning (ML).23−27 ML models can be trained to predict the contributions of the local environments to the global quantity of interest, which are then summed to ultimately yield the global prediction for a target system. Within the context of ML, this approach has two distinct advantages, the first of which is scalability. Local decomposition allows the models to be easily applied to systems of vastly different length scales (training on small cells and predicting for much larger ones),23,24 underpinning their widespread usage. This is especially the case for ML interatomic potentials,25,28−32 which allow accessing longer length and time scales in simulations with a linear-scaling cost. The second advantage is that contributions from a local, machine-learned decomposition of the global quantity can offer considerable heuristic power because one can then use the ML model to describe the complex behavior of chemical  \nDownloaded via UNIV DEGLI STUDI DI MODENA on July 1 1, 2024 at 09:18:3","cbCaikscVpPJAOg6","https://ap.wps.com/l/cbCaikscVpPJAOg6","pdf",5024631,1,12,"English","en",105,"# Abstract\n# 1. Introduction\n## Local decomposition of global quantities\n## Advantages and applications of atom-centered predictions","[{\"question\":\"What is the key idea behind local predictions in atomistic machine learning models?\",\"answer\":\"Local predictions decompose a global target quantity into atom-centered contributions, which are summed to obtain the global prediction for a system.\"},{\"question\":\"Why might local contributions be sensitive in practice?\",\"answer\":\"Because only the global quantity is rigorously defined, the atom-centered contributions can change with the training strategy or the model architecture.\"},{\"question\":\"How does the paper assess the robustness of locally decomposed predictions?\",\"answer\":\"It introduces a quantitative metric called local prediction rigidity (LPR) to measure how robust the locally decomposed predictions are across different training and problem settings.\"}]","Robustness of Local Predictions in Atomistic Machine Learning Models | PDF",1785895064,30,{"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},"robustness-of-local-predictions-in-atomistic-machine-learning-models","",{"@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/robustness-of-local-predictions-in-atomistic-machine-learning-models/124859/",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","2026-08-05",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 is the key idea behind local predictions in atomistic machine learning models?","Question",{"text":75,"@type":76},"Local predictions decompose a global target quantity into atom-centered contributions, which are summed to obtain the global prediction for a system.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"Why might local contributions be sensitive in practice?",{"text":80,"@type":76},"Because only the global quantity is rigorously defined, the atom-centered contributions can change with the training strategy or the model architecture.",{"name":82,"@type":73,"acceptedAnswer":83},"How does the paper assess the robustness of locally decomposed predictions?",{"text":84,"@type":76},"It introduces a quantitative metric called local prediction rigidity (LPR) to measure how robust the locally decomposed predictions are across different training and problem settings.","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},[93,97,101,105,110,115,120,122,127,130,134],{"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":29,"slug":121},"research-report",{"id":123,"doc_module":4,"doc_module_name":46,"category_name":124,"show_sort_weight":125,"slug":126},9,"Religion & Spirituality",20,"religion-spirituality",{"id":125,"doc_module":4,"doc_module_name":46,"category_name":128,"show_sort_weight":125,"slug":129},"World Cup","world-cup",{"id":131,"doc_module":4,"doc_module_name":46,"category_name":132,"show_sort_weight":131,"slug":133},10,"Lifestyle","lifestyle",{"id":135,"doc_module":4,"doc_module_name":46,"category_name":136,"show_sort_weight":106,"slug":137},19,"General","general"]