{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T10:22:47Z","timestamp":1770978167829,"version":"3.50.1"},"reference-count":49,"publisher":"MDPI AG","issue":"13","license":[{"start":{"date-parts":[[2022,6,24]],"date-time":"2022-06-24T00:00:00Z","timestamp":1656028800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"PDE Models for Nanotechnology","award":["Y660"],"award-info":[{"award-number":["Y660"]}]},{"name":"PDE Models for Nanotechnology","award":["390833453"],"award-info":[{"award-number":["390833453"]}]},{"name":"Alexander von Humbold Foundation","award":["Y660"],"award-info":[{"award-number":["Y660"]}]},{"name":"Alexander von Humbold Foundation","award":["390833453"],"award-info":[{"award-number":["390833453"]}]},{"name":"Cluster of Excellence PhoenixD","award":["Y660"],"award-info":[{"award-number":["Y660"]}]},{"name":"Cluster of Excellence PhoenixD","award":["390833453"],"award-info":[{"award-number":["390833453"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Silicon nanowire field-effect transistors are promising devices used to detect minute amounts of different biological species. We introduce the theoretical and computational aspects of forward and backward modeling of biosensitive sensors. Firstly, we introduce a forward system of partial differential equations to model the electrical behavior, and secondly, a backward Bayesian Markov-chain Monte-Carlo method is used to identify the unknown parameters such as the concentration of target molecules. Furthermore, we introduce a machine learning algorithm according to multilayer feed-forward neural networks. The trained model makes it possible to predict the sensor behavior based on the given parameters.<\/jats:p>","DOI":"10.3390\/s22134785","type":"journal-article","created":{"date-parts":[[2022,6,26]],"date-time":"2022-06-26T22:50:23Z","timestamp":1656283823000},"page":"4785","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["Rational Design of Field-Effect Sensors Using Partial Differential Equations, Bayesian Inversion, and Artificial Neural Networks"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2374-0557","authenticated-orcid":false,"given":"Amirreza","family":"Khodadadian","sequence":"first","affiliation":[{"name":"Institute of Applied Mathematics, Leibniz University Hannover, Welfengarten 1, 30167 Hannover, Germany"}]},{"given":"Maryam","family":"Parvizi","sequence":"additional","affiliation":[{"name":"Institute of Applied Mathematics, Leibniz University Hannover, Welfengarten 1, 30167 Hannover, Germany"},{"name":"Cluster of Excellence PhoenixD (Photonics, Optics, and Engineering-Innovation Across Disciplines), Leibniz University Hannover, 30167 Hannover, Germany"}]},{"given":"Mohammad","family":"Teshnehlab","sequence":"additional","affiliation":[{"name":"Faculty of Electrical Engineering, K. N. Toosi University of Technology, Tehran 19697, Iran"}]},{"given":"Clemens","family":"Heitzinger","sequence":"additional","affiliation":[{"name":"Institute of Analysis and Scientific Computing, TU Wien, Wiedner Hauptstrasse 8\u201310, 1040 Vienna, Austria"},{"name":"Center for Artificial Intelligence and Machine Learning (CAIML), TU Wien, 1040 Vienna, Austria"}]}],"member":"1968","published-online":{"date-parts":[[2022,6,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"111527","DOI":"10.1016\/j.bios.2019.111527","article-title":"A new method for selective functionalization of silicon nanowire sensors and Bayesian inversion for its parameters","volume":"142","author":"Mirsian","year":"2019","journal-title":"Biosens. 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