[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-123653-en":3,"doc-seo-123653-105":30,"detail-sidebar-cat-0-en-105":92},{"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},123653,962075006959,"Anda","https://ap-avatar.wpscdn.com/avatar/e0002397efbe92a78e?_k=1776741047341049297",8,"Research & Report","A Two-Step Machine Learning Method for Predicting the Formation Energy of Ternary Compounds - Article","Predicting the chemical stability of yet-to-be-discovered materials depends on accurate formation energies, but conventional ab initio workflows are computationally expensive and slow. The proposed approach introduces a two-step machine learning pipeline tailored to ternary compounds: a classifier first estimates the reliability of heuristically computed formation energies to expand the training set, followed by a regression model that predicts formation energy. The regression outcomes align with current state-of-the-art prediction models, and experiments include a centered Adam optimizer variant.","computation  \nArticle  \nA Two-Step Machine Learning Method for Predicting the Formation Energy of Ternary Compounds  \nVaradarajan Rengaraj 1, Sebastian Jost 2, Franz Bethke 2, Christian Plessl 3,4, Hossein Mirhosseini 1, *, Andrea Walther 2 and Thomas D. Kühne 1,4,5  \nCitation: Rengaraj, V.; Jost, S.; Bethke, F.; Plessl, C.; Mirhosseini, H.; Walther, A.; Kühne, T.D. A Two-Step Machine Learning Method for Predicting the Formation Energy of Ternary Compounds. Computation 2023, 11, 95. [https://doi.org/10.3390/](https://doi.org/10.3390/)[ ](https://doi.org/10.3390/)computation11050095  \nAcademic Editor: Aleksey E. Kuznetsov  \nReceived: 27 March 2023  \nRevised: 24 April 2023  \nAccepted: 5 May 2023  \nPublished: 9 May 2023  \nCopyright: © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license ([https://](https://)[ ](https://)[creativecommons.org/licenses/by/](creativecommons.org/licenses/by/)[ ](creativecommons.org/licenses/by/)[4.0/](4.0/)) .  \n1 Dynamics of Condensed Matter, Chair of Theoretical Chemistry, University of Paderborn, Warburger Str. 100, 33098 Paderborn, Germany; tdkuehne@mail.uni-paderborn.de (T.D.K.)  \n2 Department of Mathematics, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099 Berlin, Germany; [bastivonjost@gmail.com](bastivonjost@gmail.com) (S.J.); [franz.bethke@hu-berlin.de](franz.bethke@hu-berlin.de) (F.B.); [andrea.walther@math.hu-berlin.de](andrea.walther@math.hu-berlin.de) (A.W.)  \n3 Department of Computer Science, University of Paderborn, Warburger Str. 100, 33098 Paderborn, Germany  \n4 Paderborn Center for Parallel Computing (PC2), University of Paderborn, Warburger Str. 100,  \n33098 Paderborn, Germany  \n5 Center for Sustainable Systems Design, University of Paderborn, Warburger Str. 100,  \n33098 Paderborn, Germany  \n* Correspondence: mirhosse@mail.uni-paderborn.de  \nAbstract: Predicting the chemical stability of yet-to-be-discovered materials is an important aspect of the discovery and development of virtual materials. The conventional approach for computing the enthalpy of formation based on ab initio methods is time consuming and computationally demanding. In this regard, alternative machine learning approaches are proposed to predict the formation energies of different classes of materials with decent accuracy. In this paper, one such machine learning approach, a novel two-step method that predicts the formation energy of ternary compounds, is presented. In the first step, with a classifier, we determine the accuracy of heuristically calculated formation energies in order to increase the size of the training dataset for the second step. The second step is a regression model that predicts the formation energy of the ternary compounds. The first step leads to at least a 100% increase in the size of the dataset with respect to the data available in the Materials Project database. The results from the regression model match those from the existing state-of-the-art prediction models. In addition, we propose a slightly modified version of the Adam optimizer, namely centered Adam, and report the results from testing the centered Adam optimizer.  \nKeywords: machine learning; neural network; enthalpy of formation; thermodynamic stability  \n1. Introduction  \nA key step in the data-driven materials discovery process is predicting the enthalpy of formation (the formation energy) for compounds that have not been synthesized yet [1] . Knowledge about the formation energy of a compound helps determine whether the compound is thermodynamically stable against competing phases. The phase stability can be determined using convex hull analysis [2] . In a compositional phase diagram, a convex hull is constructed by connecting the lowest formation energies. Compounds that lie on the convex hull are thermodynamically stable, and the ones above the hull are metastable or unstable [3] . In","cbCail9dJ0YFEDos","https://ap.wps.com/l/cbCail9dJ0YFEDos","pdf",795869,1,15,"English","en",105,"# Introduction\n## Formation energy and thermodynamic stability\n## Limitations of DFT-based formation energy calculations\n## Machine learning approaches and prior work","[{\"question\":\"What problem does the two-step method address?\",\"answer\":\"It addresses the high computational cost of calculating formation energies for unsynthesized ternary compounds using ab initio methods, by leveraging machine learning to predict formation energy more efficiently.\"},{\"question\":\"How does the method work in two steps?\",\"answer\":\"First, a classifier evaluates the accuracy of heuristically calculated formation energies to enlarge the training dataset. Second, a regression model predicts the formation energy of ternary compounds using the expanded dataset.\"},{\"question\":\"What results are reported regarding performance and optimization?\",\"answer\":\"The regression model’s predictions match existing state-of-the-art methods. The study also evaluates a modified Adam optimizer called centered Adam and reports the corresponding test results.\"}]","A Two-Step Machine Learning Method for Predicting the Formation Energy of Ternary Compounds - Article | PDF",1785817854,38,{"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":87,"head_meta":89,"extra_data":91,"updated_unix":28},"a-two-step-machine-learning-method-for-predicting-the-formation-energy-of-ternary-compounds-article","",{"@graph":36,"@context":86},[37,54,69],{"@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/a-two-step-machine-learning-method-for-predicting-the-formation-energy-of-ternary-compounds-article/123653/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":63,"encodingFormat":61,"isAccessibleForFree":64,"interactionStatistic":65},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-05","2026-08-04",true,{"@type":66,"interactionType":67,"userInteractionCount":20},"InteractionCounter",{"@type":68},"ViewAction",{"@type":70,"mainEntity":71},"FAQPage",[72,78,82],{"name":73,"@type":74,"acceptedAnswer":75},"What problem does the two-step method address?","Question",{"text":76,"@type":77},"It addresses the high computational cost of calculating formation energies for unsynthesized ternary compounds using ab initio methods, by leveraging machine learning to predict formation energy more efficiently.","Answer",{"name":79,"@type":74,"acceptedAnswer":80},"How does the method work in two steps?",{"text":81,"@type":77},"First, a classifier evaluates the accuracy of heuristically calculated formation energies to enlarge the training dataset. Second, a regression model predicts the formation energy of ternary compounds using the expanded dataset.",{"name":83,"@type":74,"acceptedAnswer":84},"What results are reported regarding performance and optimization?",{"text":85,"@type":77},"The regression model’s predictions match existing state-of-the-art methods. 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