{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,29]],"date-time":"2025-10-29T13:50:10Z","timestamp":1761745810557,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2023,8,25]],"date-time":"2023-08-25T00:00:00Z","timestamp":1692921600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia","award":["PNURSP2023R404"],"award-info":[{"award-number":["PNURSP2023R404"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this work, an artificial neural network based on the Cuckoo search algorithm (CS-ANN) is implemented for squeezing flow problems. Three problems are considered: the squeezing flow, the MHD squeezing flow, and the flow of the third-grade fluid past a moving belt. First, the approximation for the said nonlinear differential equations is explained and the proposed problems are transformed into the L2 norms of minimization problems. Then, a well-known Cuckoo search algorithm is used to minimize the norms of each problem to get the best set of weights for artificial neural networks. The outcome of the proposed method is displayed through graphs. Two cases for each problem are discussed consisting of the solution, error, weights, and fitness function, respectively. The numerical results for the state variables are displayed in Tables. The error analysis in each case proves the accuracy of our implemented technique. The results are validated through graphs by comparing CS-ANN results with the gradient descent method.<\/jats:p>","DOI":"10.3390\/sym15091638","type":"journal-article","created":{"date-parts":[[2023,8,25]],"date-time":"2023-08-25T08:25:33Z","timestamp":1692951933000},"page":"1638","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A Cuckoo Search-Based Trained Artificial Neural Network for Symmetric Flow Problems"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4361-7786","authenticated-orcid":false,"given":"Asad","family":"Ullah","sequence":"first","affiliation":[{"name":"School of Finance and Economics, Jiangsu University, 301 Xuefu Road, Jingkou District, Zhenjiang 212013, China"},{"name":"Department of Mathematical Sciences, University of Lakki Marwat, Lakki Marwat 28420, Khyber Pakhtunkhwa, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tmader","family":"Alballa","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Sciences, Princess Nourah Bint Abdulrahman University, Riyadh 11671, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"family":"Waseem","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Jiangsu University, 301 Xuefu Road, Jingkou District, Zhenjiang 212013, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hamiden Abd El-Wahed","family":"Khalifa","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science and Arts, Qassim University, Al-Badaya 51951, Saudi Arabia"},{"name":"Department of Operations and Management Research, Faculty of Graduate Studies for Statistical Research, Cairo University, Giza 12613, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Haifa","family":"Alqahtani","sequence":"additional","affiliation":[{"name":"Department of Statistics and Business Analytics, United Arab Emirates University, Al Ain P.O. Box 15551, United Arab Emirates"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,8,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1007\/BF02430631","article-title":"On the integrability and perturbation of three-dimensional fluid flows with symmetry","volume":"4","author":"Wiggins","year":"1994","journal-title":"J. Nonlinear Sci."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"316","DOI":"10.1002\/andp.18752300213","article-title":"Versuche \u00fcber die scheinbare Adh\u00e4sion","volume":"230","author":"Stefan","year":"1875","journal-title":"Ann. Phys."},{"key":"ref_3","unstructured":"Nayfeh, A.H. (2008). Perturbation Methods, John Wiley & Sons."},{"key":"ref_4","unstructured":"Liao, S.J. (1992). The Proposed Homotopy Analysis Technique for the Solution of Nonlinear Problems. 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