{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,22]],"date-time":"2026-01-22T05:39:09Z","timestamp":1769060349446,"version":"3.49.0"},"reference-count":38,"publisher":"IOP Publishing","issue":"3","license":[{"start":{"date-parts":[[2024,9,11]],"date-time":"2024-09-11T00:00:00Z","timestamp":1726012800000},"content-version":"vor","delay-in-days":10,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2024,9,11]],"date-time":"2024-09-11T00:00:00Z","timestamp":1726012800000},"content-version":"tdm","delay-in-days":10,"URL":"https:\/\/iopscience.iop.org\/info\/page\/text-and-data-mining"}],"content-domain":{"domain":["iopscience.iop.org"],"crossmark-restriction":false},"short-container-title":["Mach. Learn.: Sci. Technol."],"published-print":{"date-parts":[[2024,9,1]]},"abstract":"Abstract<\/jats:title>\n Currently, mainstream methods for multi-fidelity data fusion have achieved great success in many fields, but they generally suffer from poor scalability. Therefore, this paper proposes a \n \n \n \n \n C<\/mml:mi>\n 3<\/mml:mn>\n 2<\/mml:mn>\n <\/mml:msubsup>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula> combination modeling method for complex multi-fidelity data fusion, devoted to solving the modeling problems with three types of multi-fidelity data fusion, and explores a general solution for any n<\/jats:italic> types of multi-fidelity data fusion. Different from the traditional direct modeling method\u2014Multi-Fidelity Deep Neural Network (MFDNN)\u2014the \n \n \n \n \n C<\/mml:mi>\n 3<\/mml:mn>\n 2<\/mml:mn>\n <\/mml:msubsup>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula> method is an indirect modeling method. The experimental results on three representative benchmark functions and the prediction tasks of SG6043 airfoil aerodynamic performance show that \n \n \n \n \n C<\/mml:mi>\n 3<\/mml:mn>\n 2<\/mml:mn>\n <\/mml:msubsup>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula> combination modeling has the following advantages: (1) It can quickly establish the mapping relationship between high, medium, and low fidelity data. (2) It can effectively solve the data imbalance problem in multi-fidelity modeling. (3) Compared with MFDNN, it has stronger noise resistance and higher prediction accuracy. Additionally, this paper discusses the scalability problem of the \n \n \n \n \n C<\/mml:mi>\n n<\/mml:mi>\n 2<\/mml:mn>\n <\/mml:msubsup>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula> method when n<\/jats:italic>\u2009=\u20094 and n<\/jats:italic>\u2009=\u20095, providing a reference for further research on the combined modeling method.<\/jats:p>","DOI":"10.1088\/2632-2153\/ad718f","type":"journal-article","created":{"date-parts":[[2024,8,22]],"date-time":"2024-08-22T20:03:55Z","timestamp":1724357035000},"page":"035071","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":4,"title":["A combined modeling method for complex multi-fidelity data fusion"],"prefix":"10.1088","volume":"5","author":[{"ORCID":"https:\/\/orcid.org\/0009-0008-2917-2961","authenticated-orcid":true,"given":"Lei","family":"Tang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0008-4173-5659","authenticated-orcid":true,"given":"Feng","family":"Liu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2030-8355","authenticated-orcid":false,"given":"Anping","family":"Wu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6376-6324","authenticated-orcid":false,"given":"Yubo","family":"Li","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wanqiu","family":"Jiang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8299-2992","authenticated-orcid":false,"given":"Qingfeng","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4081-7897","authenticated-orcid":false,"given":"Jun","family":"Huang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"266","published-online":{"date-parts":[[2024,9,11]]},"reference":[{"key":"mlstad718fbib1","doi-asserted-by":"publisher","DOI":"10.1063\/5.0140545","article-title":"Fast aerodynamics prediction of laminar airfoils based on deep attention network","volume":"35","author":"Zuo","year":"2023","journal-title":"Phys. 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