{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,21]],"date-time":"2026-03-21T03:21:28Z","timestamp":1774063288886,"version":"3.50.1"},"reference-count":18,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2022,3,1]],"date-time":"2022-03-01T00:00:00Z","timestamp":1646092800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["ChemEngineering"],"abstract":"<jats:p>Adsorption systems are characterized by challenging behavior to simulate any numerical method. A novel field of study emerged within the numerical method in the last two years: the physics-informed neural network (PINNs), the application of artificial intelligence to solve partial differential equations. This is a complete new standpoint for solving engineering first-principle models, which up to that date was not explored in the field of adsorption systems. Therefore, this work proposed the evaluation of PINN to address the numerical solutions of a fixed-bed column where a monoclonal antibody is purified. The PINNs solution is compared with a traditional numerical method. The results show the accuracy of the proposed PINNs when compared with the numerical method. This points towards the potential of this technique to address complex numerical problems found in chemical engineering.<\/jats:p>","DOI":"10.3390\/chemengineering6020021","type":"journal-article","created":{"date-parts":[[2022,3,1]],"date-time":"2022-03-01T08:17:03Z","timestamp":1646122623000},"page":"21","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":26,"title":["A First Approach towards Adsorption-Oriented Physics-Informed Neural Networks: Monoclonal Antibody Adsorption Performance on an Ion-Exchange Column as a Case Study"],"prefix":"10.3390","volume":"6","author":[{"given":"Vinicius V.","family":"Santana","sequence":"first","affiliation":[{"name":"Laboratory of Separation and Reaction Engineering, Associate Laboratory LSRE\/LCM Department of Chemical Engineering, Faculty of Engineering, University of Porto Rua Dr. Roberto Frias, 4200-465 Porto, Portugal"},{"name":"ALiCE\u2014Associate Laboratory in Chemical Engineering, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal"}]},{"given":"Marlon S.","family":"Gama","sequence":"additional","affiliation":[{"name":"Chemical Engineering Program\u2014PEQ\/COPPE, Universidade Federal do Rio de Janeiro (UFRJ), Cidade Universit\u00e1ria, Ilha do Fund\u00e3o, Rio de Janeiro 21949-900, Brazil"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6051-6039","authenticated-orcid":false,"given":"Jose M.","family":"Loureiro","sequence":"additional","affiliation":[{"name":"Laboratory of Separation and Reaction Engineering, Associate Laboratory LSRE\/LCM Department of Chemical Engineering, Faculty of Engineering, University of Porto Rua Dr. Roberto Frias, 4200-465 Porto, Portugal"},{"name":"ALiCE\u2014Associate Laboratory in Chemical Engineering, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0715-4761","authenticated-orcid":false,"given":"Al\u00edrio E.","family":"Rodrigues","sequence":"additional","affiliation":[{"name":"Laboratory of Separation and Reaction Engineering, Associate Laboratory LSRE\/LCM Department of Chemical Engineering, Faculty of Engineering, University of Porto Rua Dr. Roberto Frias, 4200-465 Porto, Portugal"},{"name":"ALiCE\u2014Associate Laboratory in Chemical Engineering, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4269-1420","authenticated-orcid":false,"given":"Ana M.","family":"Ribeiro","sequence":"additional","affiliation":[{"name":"Laboratory of Separation and Reaction Engineering, Associate Laboratory LSRE\/LCM Department of Chemical Engineering, Faculty of Engineering, University of Porto Rua Dr. Roberto Frias, 4200-465 Porto, Portugal"},{"name":"ALiCE\u2014Associate Laboratory in Chemical Engineering, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8108-1719","authenticated-orcid":false,"given":"Frederico W.","family":"Tavares","sequence":"additional","affiliation":[{"name":"Chemical Engineering Program\u2014PEQ\/COPPE, Universidade Federal do Rio de Janeiro (UFRJ), Cidade Universit\u00e1ria, Ilha do Fund\u00e3o, Rio de Janeiro 21949-900, Brazil"},{"name":"Chemical and Biochemical Engineering Processes (EPQB), School of Chemistry\u2014EQ\/UFRJ, Universidade Federal do Rio de Janeiro (UFRJ), Cidade Universit\u00e1ria, Ilha do Fund\u00e3o, Rio de Janeiro 21949-900, Brazil"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8238-2310","authenticated-orcid":false,"suffix":"Jr.","given":"Amaro G.","family":"Barreto","sequence":"additional","affiliation":[{"name":"Chemical and Biochemical Engineering Processes (EPQB), School of Chemistry\u2014EQ\/UFRJ, Universidade Federal do Rio de Janeiro (UFRJ), Cidade Universit\u00e1ria, Ilha do Fund\u00e3o, Rio de Janeiro 21949-900, Brazil"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0963-6449","authenticated-orcid":false,"given":"Idelfonso B. R.","family":"Nogueira","sequence":"additional","affiliation":[{"name":"Laboratory of Separation and Reaction Engineering, Associate Laboratory LSRE\/LCM Department of Chemical Engineering, Faculty of Engineering, University of Porto Rua Dr. Roberto Frias, 4200-465 Porto, Portugal"},{"name":"ALiCE\u2014Associate Laboratory in Chemical Engineering, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2022,3,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"686","DOI":"10.1016\/j.jcp.2018.10.045","article-title":"Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations","volume":"378","author":"Raissi","year":"2019","journal-title":"J. Comput. 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