{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,2]],"date-time":"2026-03-02T10:25:03Z","timestamp":1772447103668,"version":"3.50.1"},"reference-count":59,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2022,1,21]],"date-time":"2022-01-21T00:00:00Z","timestamp":1642723200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"FEDER funds through the COMPETE 2020 Programme and National Funds through FCT (Portuguese Foundation for Science and Technology)","award":["UID-B\/05256\/2020, UID-P\/05256\/2020, MIT-EXPL\/TDI\/0038\/2019"],"award-info":[{"award-number":["UID-B\/05256\/2020, UID-P\/05256\/2020, MIT-EXPL\/TDI\/0038\/2019"]}]},{"name":"University of Minho cluster","award":["NORTE-07-0162-FEDER-000086"],"award-info":[{"award-number":["NORTE-07-0162-FEDER-000086"]}]},{"name":"Minho Advanced Computing Center","award":["CPCA A2 6052 2020"],"award-info":[{"award-number":["CPCA A2 6052 2020"]}]},{"name":"Consorzio Interuniversitario dell'Italia Nord Est per il Calcolo Automatico (CINECA)","award":["HPC-EUROPA3 (INFRAIA-2016-1-730897)"],"award-info":[{"award-number":["HPC-EUROPA3 (INFRAIA-2016-1-730897)"]}]},{"name":"PRACE - Partnership for Advanced Computing in Europe","award":["icei-prace-2020-0009"],"award-info":[{"award-number":["icei-prace-2020-0009"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Polymers"],"abstract":"<jats:p>This study presents a framework based on Machine Learning (ML) models to predict the drag coefficient of a spherical particle translating in viscoelastic fluids. For the purpose of training and testing the ML models, two datasets were generated using direct numerical simulations (DNSs) for the viscoelastic unbounded flow of Oldroyd-B (OB-set containing 12,120 data points) and Giesekus (GI-set containing 4950 data points) fluids past a spherical particle. The kinematic input features were selected to be Reynolds number, 0&lt;Re\u226450, Weissenberg number, 0\u2264Wi\u226410, polymeric retardation ratio, 0&lt;\u03b6&lt;1, and shear thinning mobility parameter, 0&lt;\u03b1&lt;1. The ML models, specifically Random Forest (RF), Deep Neural Network (DNN) and Extreme Gradient Boosting (XGBoost), were all trained, validated, and tested, and their best architecture was obtained using a 10-Fold cross-validation method. All the ML models presented remarkable accuracy on these datasets; however the XGBoost model resulted in the highest R2 and the lowest root mean square error (RMSE) and mean absolute percentage error (MAPE) measures. Additionally, a blind dataset was generated using DNSs, where the input feature coverage was outside the scope of the training set or interpolated within the training sets. The ML models were tested against this blind dataset, to further assess their generalization capability. The DNN model achieved the highest R2 and the lowest RMSE and MAPE measures when inferred on this blind dataset. Finally, we developed a meta-model using stacking technique to ensemble RF, XGBoost and DNN models and output a prediction based on the individual learner\u2019s predictions and a DNN meta-regressor. The meta-model consistently outperformed the individual models on all datasets.<\/jats:p>","DOI":"10.3390\/polym14030430","type":"journal-article","created":{"date-parts":[[2022,1,23]],"date-time":"2022-01-23T20:34:40Z","timestamp":1642970080000},"page":"430","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":30,"title":["A Meta-Model to Predict the Drag Coefficient of a Particle Translating in Viscoelastic Fluids: A Machine Learning Approach"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6543-1691","authenticated-orcid":false,"given":"Salah A.","family":"Faroughi","sequence":"first","affiliation":[{"name":"Geo-Intelligence Laboratory, Ingram School of Engineering, Texas State University, San Marcos, TX 78666, USA"}]},{"given":"Ana I.","family":"Roriz","sequence":"additional","affiliation":[{"name":"Department of Polymer Engineering, Institute for Polymers and Composites (IPC), Campus of Azur\u00e9m, Engineering School of the University of Minho, 4800-058 Guimar\u00e3es, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0340-3556","authenticated-orcid":false,"given":"C\u00e9lio","family":"Fernandes","sequence":"additional","affiliation":[{"name":"Geo-Intelligence Laboratory, Ingram School of Engineering, Texas State University, San Marcos, TX 78666, USA"},{"name":"Department of Polymer Engineering, Institute for Polymers and Composites (IPC), Campus of Azur\u00e9m, Engineering School of the University of Minho, 4800-058 Guimar\u00e3es, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2022,1,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Chhabra, R.P. 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