{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:38:36Z","timestamp":1753882716568,"version":"3.41.2"},"reference-count":38,"publisher":"World Scientific Pub Co Pte Ltd","issue":"11","funder":[{"name":"This research was funded by the Fundamental Research Funds for the Central Universities."}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Patt. Recogn. Artif. Intell."],"published-print":{"date-parts":[[2024,9,15]]},"abstract":"<jats:p> The development of reduced-order models has been a pivotal advancement in the computational analysis of fluid dynamics, substantially simplifying the complexity and boosting the efficiency of simulations. The accuracy and practicality of these models largely depend on the reduction techniques applied and the inherent characteristics of the fluid dynamics systems they represent. In this paper, we introduce an innovative machine-learning framework for assessing model uncertainty in computationally intensive reduced-order models. By combining subspace construction methods with advanced Bayesian inference techniques, our approach effectively captures the posterior distribution of model parameters, thereby providing an accurate representation of uncertainty in aerodynamic performance predictions. We employ the NACA0012 airfoil as a case study to validate our method\u2019s ability to enhance the efficiency of reduced-order models and precisely measure the uncertainty inherent in predictions made by recurrent neural networks. It is important to note that our approach is influenced by specific constraints and variables that significantly impact the mean and variability of the predicted final lift coefficient distribution. Our findings indicate that setting the goodness of fit (R2) threshold above 0.985 markedly improves the correlation between Computational Fluid Dynamics (CFD) outcomes and model predictions, increasing from 72.2% to 97.9% as the interval amplification factor adjusts from 1.5 to 3. However, this adjustment causes a considerable expansion of the confidence interval, from 0.0737 to 0.1282, an increase of over 70%. Despite these challenges, our machine learning-based methodology provides essential insights into the further development of reduced-order modeling and uncertainty quantification in fluid dynamics. This highlights the need for ongoing research into the model parameters, especially in applications concerning aircraft control systems, to meet design specifications and ensure system reliability. <\/jats:p>","DOI":"10.1142\/s0218001424510182","type":"journal-article","created":{"date-parts":[[2024,6,8]],"date-time":"2024-06-08T04:48:01Z","timestamp":1717822081000},"source":"Crossref","is-referenced-by-count":0,"title":["Applying Machine Learning Techniques: Uncertainty Quantification in Nonlinear Dynamics Characters Predictions via Gated Recurrent Unit-Based Reduced-Order Models"],"prefix":"10.1142","volume":"38","author":[{"ORCID":"https:\/\/orcid.org\/0009-0008-3676-2484","authenticated-orcid":false,"given":"Xun","family":"Peng","sequence":"first","affiliation":[{"name":"School of Astronautics, Beihang University, Beijing 100191, P.\u00a0R.\u00a0China"},{"name":"National Key Laboratory of Aerospace Liquid Propulsion, Beijing 100091, P.\u00a0R.\u00a0China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1051-0819","authenticated-orcid":false,"given":"Hao","family":"Zhu","sequence":"additional","affiliation":[{"name":"School of Astronautics, Beihang University, Beijing 100191, P.\u00a0R.\u00a0China"},{"name":"National Key Laboratory of Aerospace Liquid Propulsion, Beijing 100091, P.\u00a0R.\u00a0China"}]},{"ORCID":"https:\/\/orcid.org\/0009-0006-9042-879X","authenticated-orcid":false,"given":"Dajun","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Astronautics, Beihang University, Beijing 100191, P.\u00a0R.\u00a0China"},{"name":"National Key Laboratory of Aerospace Liquid Propulsion, Beijing 100091, P.\u00a0R.\u00a0China"}]},{"ORCID":"https:\/\/orcid.org\/0009-0004-4846-8005","authenticated-orcid":false,"given":"Wenzhi","family":"Hao","sequence":"additional","affiliation":[{"name":"School of Astronautics, Beihang University, Beijing 100191, P.\u00a0R.\u00a0China"},{"name":"National Key Laboratory of Aerospace Liquid Propulsion, Beijing 100091, P.\u00a0R.\u00a0China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6022-1441","authenticated-orcid":false,"given":"Weizong","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Astronautics, Beihang University, Beijing 100191, P.\u00a0R.\u00a0China"},{"name":"National Key Laboratory of Aerospace Liquid Propulsion, Beijing 100091, P.\u00a0R.\u00a0China"},{"name":"Aircraft and Propulsion Laboratory, Ningbo Institute of Technology, Beihang University, Ningbo 315832, P.\u00a0R.\u00a0China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7909-4622","authenticated-orcid":false,"given":"Guobiao","family":"Cai","sequence":"additional","affiliation":[{"name":"School of Astronautics, Beihang University, Beijing 100191, P.\u00a0R.\u00a0China"},{"name":"National Key Laboratory of Aerospace Liquid Propulsion, Beijing 100091, P.\u00a0R.\u00a0China"}]}],"member":"219","published-online":{"date-parts":[[2024,7,25]]},"reference":[{"key":"S0218001424510182BIB001","doi-asserted-by":"publisher","DOI":"10.1115\/1.4028122"},{"key":"S0218001424510182BIB002","doi-asserted-by":"publisher","DOI":"10.1098\/rstl.1763.0053"},{"key":"S0218001424510182BIB003","doi-asserted-by":"publisher","DOI":"10.1146\/annurev.fl.25.010193.002543"},{"key":"S0218001424510182BIB004","volume-title":"Bayesian Theory","volume":"405","author":"Bernardo J. M.","year":"2009"},{"key":"S0218001424510182BIB005","unstructured":"C. M. Bishop,  Pattern Recognition and Machine Learning (Springer,  2006) pp. 645\u2013678."},{"key":"S0218001424510182BIB008","first-page":"14375","volume-title":"Proc. International Forum on Aeroelasticity and Structural Dynamics IFASD","author":"Dietz G.","year":"2003"},{"key":"S0218001424510182BIB009","doi-asserted-by":"publisher","DOI":"10.2514\/2.6864"},{"key":"S0218001424510182BIB010","doi-asserted-by":"publisher","DOI":"10.1201\/9780429258411"},{"key":"S0218001424510182BIB011","doi-asserted-by":"publisher","DOI":"10.2514\/3.25277"},{"key":"S0218001424510182BIB012","doi-asserted-by":"publisher","DOI":"10.2514\/1.J050471"},{"key":"S0218001424510182BIB013","doi-asserted-by":"publisher","DOI":"10.1016\/j.tust.2024.105724"},{"key":"S0218001424510182BIB014","doi-asserted-by":"publisher","DOI":"10.1016\/j.enggeo.2024.107458"},{"key":"S0218001424510182BIB015","doi-asserted-by":"publisher","DOI":"10.2514\/2.1754"},{"key":"S0218001424510182BIB016","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-019-04623-x"},{"key":"S0218001424510182BIB017","first-page":"1861","volume-title":"Int. Conf. Machine Learning, PMLR","author":"Hern\u00e1ndez-Lobato J. M.","year":"2015"},{"key":"S0218001424510182BIB018","doi-asserted-by":"publisher","DOI":"10.1162\/neco.1997.9.8.1735"},{"volume-title":"Modeling of Fluid Powered Actuators Using Auto Regressive with Exogenous Input Model","year":"2012","author":"Hossain Z.","key":"S0218001424510182BIB019"},{"key":"S0218001424510182BIB020","doi-asserted-by":"publisher","DOI":"10.3390\/electronics12204362"},{"key":"S0218001424510182BIB021","first-page":"1169","volume-title":"Uncertainty in Artificial Intelligence, PMLR","author":"Izmailov P.","year":"2020"},{"key":"S0218001424510182BIB022","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijepes.2014.03.060"},{"key":"S0218001424510182BIB023","doi-asserted-by":"publisher","DOI":"10.2514\/1.C031941"},{"key":"S0218001424510182BIB024","doi-asserted-by":"publisher","DOI":"10.1016\/j.ast.2015.12.006"},{"key":"S0218001424510182BIB025","doi-asserted-by":"publisher","DOI":"10.1061\/(ASCE)AS.1943-5525.0000932"},{"key":"S0218001424510182BIB026","doi-asserted-by":"publisher","DOI":"10.1016\/j.paerosci.2003.12.001"},{"key":"S0218001424510182BIB027","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112002007991"},{"key":"S0218001424510182BIB028","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfluidstructs.2014.02.016"},{"key":"S0218001424510182BIB029","doi-asserted-by":"publisher","DOI":"10.2514\/1.J052858"},{"volume-title":"43rd AIAA\/ASME\/ASCE\/AHS\/ASC Structures, Structural Dynamics, and Materials Conf.","author":"Marzocca P.","key":"S0218001424510182BIB030"},{"volume-title":"46th AIAA\/ASME\/ASCE\/AHS\/ASC Structures, Structural Dynamics and Materials Conf.","author":"Munteanu S.","key":"S0218001424510182BIB031"},{"key":"S0218001424510182BIB032","doi-asserted-by":"publisher","DOI":"10.1063\/5.0150288"},{"issue":"3","key":"S0218001424510182BIB033","first-page":"341","volume":"1","author":"Nouri M. J.","year":"2012","journal-title":"Int. J. Mech. Eng. Robotics Res."},{"key":"S0218001424510182BIB034","doi-asserted-by":"publisher","DOI":"10.1109\/ICMAE56000.2022.9852868"},{"key":"S0218001424510182BIB035","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112010001217"},{"key":"S0218001424510182BIB036","doi-asserted-by":"publisher","DOI":"10.2514\/1.9839"},{"key":"S0218001424510182BIB037","doi-asserted-by":"publisher","DOI":"10.2514\/2.1720"},{"key":"S0218001424510182BIB038","doi-asserted-by":"publisher","DOI":"10.2514\/2.1570"},{"key":"S0218001424510182BIB039","doi-asserted-by":"publisher","DOI":"10.1115\/1.2976449"},{"key":"S0218001424510182BIB040","doi-asserted-by":"publisher","DOI":"10.2514\/1.J050581"}],"container-title":["International Journal of Pattern Recognition and Artificial Intelligence"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218001424510182","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,2]],"date-time":"2024-09-02T03:40:54Z","timestamp":1725248454000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S0218001424510182"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,7,25]]},"references-count":38,"journal-issue":{"issue":"11","published-print":{"date-parts":[[2024,9,15]]}},"alternative-id":["10.1142\/S0218001424510182"],"URL":"https:\/\/doi.org\/10.1142\/s0218001424510182","relation":{},"ISSN":["0218-0014","1793-6381"],"issn-type":[{"type":"print","value":"0218-0014"},{"type":"electronic","value":"1793-6381"}],"subject":[],"published":{"date-parts":[[2024,7,25]]},"article-number":"2451018"}}