[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-119074-en":3,"doc-seo-119074-105":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},119074,4398048950312,"Violet","https://ap-avatar.wpscdn.com/avatar/400002538284de19e3c?_k=1778320343897328908",8,"Research & Report","Optimized Multi􀀜delity Machine Learning for Quantum Chemistry","Machine learning enables rapid, accurate quantum chemistry predictions for properties such as excitation energies, but high accuracy typically requires large, expensive training sets. Prior strategies aim to reduce this cost, including 􀀁-ML, hierarchical-ML, and multi􀀜delity machine learning (MFML), where multiple models of different fidelities are combined via a sparse-grid-derived scheme. Here, an optimization procedure forms optimized MFML (o-MFML) by tuning combination hyperparameters on a holdout validation set. The method is benchmarked on atomization energies in QM7b and excitation energies for larger molecules, showing lower prediction error than MFML. Advantages also persist under weak data distributions and unclear fidelity hierarchies.","arXiv :2312 .05661v1 [physics .chem-ph] 9 Dec 2023  \nOptimized Multi􀀜delity Machine Learning for  \nQuantum Chemistry  \nVivin Vinod,† Ulrich Kleinekathöfer,‡ and Peter Zaspel􀀃 ,†  \n†School of Mathematics and Natural Science, University of Wuppertal, 42119 Wuppertal,  \nGermany  \n‡School of Science, Constructor University, Campus Ring 1, 28759 Bremen, Germany  \nE-mail: [zaspel@uni-wuppertal.de](zaspel@uni-wuppertal.de)  \nAbstract  \nMachine learning (ML) provides access to fast and accurate quantum chemistry (QC) calculations for various properties of interest such as excitation energies. It is often the case that high accuracy in prediction using an ML model, demands a large and costly training set. Various solutions and procedures have been presented to reduce this cost. These include methods such as 􀀁-ML, hierarchical-ML, and multi􀀜delity machine learning (MFML) . MFML combines various 􀀁-ML like sub-models for various 􀀜delities according to a 􀀜xed scheme derived from the sparse grid combination technique. In this work we implement an optimization procedure to combine multi􀀜delity models in a 􀀝exible scheme resulting in optimized MFML (o-MFML) that provides superior prediction capabilities. This hyper-parameter optimization is carried out on a holdout validation set of the property of interest. This work benchmarks the o-MFML method in predicting the atomization energies on the QM7b dataset, and again in the prediction of excitation energies for three molecules of growing size. The results indicate that oMFML is a strong methodological improvement over MFML and provides lower error of prediction. Even in cases of poor data distributions and lack of clear hierarchies among  \nthe 􀀜delities, which were previously identi􀀜ed as issues for multi􀀜delity methods, theo-MFML provides advantage to the prediction of quantum chemical properties.  \nKeywords: machine learning, multi􀀜delity machine learning, kernel ridge regression, electronic structure theory, basis sets, electron correlation, molecular modeling  \n1 Introduction  \nFast and accurate calculations of chemical properties have become increasingly accessible to the community of quantum chemistry (QC) in the recent years with the accelerated development of machine learning (ML) for QC 1􀀕4 . Various supervised and unsupervised learning approaches have seen widespread application in the 􀀜eld of QC. These applications include areas of material design and discovery 3 ,5􀀕12 excitation energies 2 , 13􀀕16, potential energy surfaces 17􀀕23, and even prediction of chemical reactions 24 and ML molecular dynamics for the simulation of infrared spectra 25 . The conventionally costly QC calculations are gradually being replaced with ML models or hybrids of ML and QC resulting in a drastic reduction of the compute cost associated with chemical design and discovery. The core principle of the various ML techniques is to reproduce some implicit mapping between the geometry of the molecules to some property of interest such as excitation energies, potential energy surfaces, or atomization energies. These are usually targeted at some level of theory which is relevant to the area of application.  \nThe general ML-QC pipeline for such applications begins with the generation of raw data consisting of the Cartesian geometries of the molecules of interest and the QC calculation property to be predicted at the level of theory (MP2, CCSD etc) that is deemed accurate for the application. The Cartesian coordinates are then transformed into some input feature format, called representations or molecular descriptors, that the ML models can map to the property of interest. In the recent past, much work has been dedicated to the development of such representations. These include molecule-wise descriptors such inverse  \ndistance representations and their extensions such as the Coulomb Matrix (CM)26􀀕29 ,29􀀕31 and Bag of Bonds 32􀀕34, or atom-wise descriptors such as Smooth Overlap of Atomic Positions (SOAP) 34 ,35 , SLAT","cbCairMX8AIdgMVs","https://ap.wps.com/l/cbCairMX8AIdgMVs","pdf",5420221,1,33,"English","en",105,"# Abstract\n# 1 Introduction","[{\"question\":\"What problem does optimized multi􀀜delity machine learning address in quantum chemistry?\",\"answer\":\"It targets the high cost of obtaining large, high-accuracy training sets required for machine-learning quantum chemistry predictions by improving how multi-fidelity models are combined.\"},{\"question\":\"How is o-MFML constructed in this work?\",\"answer\":\"o-MFML uses a flexible scheme to combine multi-fidelity models, with hyper-parameter optimization performed on a holdout validation set for the property of interest.\"},{\"question\":\"How is the proposed method evaluated?\",\"answer\":\"The method is benchmarked on atomization energies using the QM7b dataset and on excitation energies for three molecules with increasing size.\"}]","Optimized Multi􀀜delity Machine Learning for Quantum Chemistry | PDF",1785722193,83,{"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},"optimized-multidelity-machine-learning-for-quantum-chemistry","",{"@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/optimized-multidelity-machine-learning-for-quantum-chemistry/119074/",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","2026-08-03",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 problem does optimized multi􀀜delity machine learning address in quantum chemistry?","Question",{"text":75,"@type":76},"It targets the high cost of obtaining large, high-accuracy training sets required for machine-learning quantum chemistry predictions by improving how multi-fidelity models are combined.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How is o-MFML constructed in this work?",{"text":80,"@type":76},"o-MFML uses a flexible scheme to combine multi-fidelity models, with hyper-parameter optimization performed on a holdout validation set for the property of interest.",{"name":82,"@type":73,"acceptedAnswer":83},"How is the proposed method evaluated?",{"text":84,"@type":76},"The method is benchmarked on atomization energies using the QM7b dataset and on excitation energies for three molecules with increasing 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