{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,26]],"date-time":"2026-02-26T20:31:59Z","timestamp":1772137919046,"version":"3.50.1"},"reference-count":37,"publisher":"IOP Publishing","issue":"4","license":[{"start":{"date-parts":[[2024,10,7]],"date-time":"2024-10-07T00:00:00Z","timestamp":1728259200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2024,10,7]],"date-time":"2024-10-07T00:00:00Z","timestamp":1728259200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/iopscience.iop.org\/info\/page\/text-and-data-mining"}],"funder":[{"name":"National Science Foundation","award":["DMS-2153376"],"award-info":[{"award-number":["DMS-2153376"]}]},{"DOI":"10.13039\/100000893","name":"Simons Foundation","doi-asserted-by":"crossref","award":["711776"],"award-info":[{"award-number":["711776"]}],"id":[{"id":"10.13039\/100000893","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["iopscience.iop.org"],"crossmark-restriction":false},"short-container-title":["Mach. 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Initial numerical tests, involving perturbations of model parameters and interface locations, demonstrate that the PNPic deep learning solver can generate highly accurate numerical solutions.<\/jats:p>","DOI":"10.1088\/2632-2153\/ad7e7a","type":"journal-article","created":{"date-parts":[[2024,9,23]],"date-time":"2024-09-23T18:58:20Z","timestamp":1727117900000},"page":"045001","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["A PNP ion channel deep learning solver with local neural network and finite element input data"],"prefix":"10.1088","volume":"5","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5130-6884","authenticated-orcid":true,"given":"Hwi","family":"Lee","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0008-6503-315X","authenticated-orcid":false,"given":"Zhen","family":"Chao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0007-9289-1179","authenticated-orcid":false,"given":"Harris","family":"Cobb","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1543-7371","authenticated-orcid":true,"given":"Yingjie","family":"Liu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7072-6275","authenticated-orcid":true,"given":"Dexuan","family":"Xie","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"266","published-online":{"date-parts":[[2024,10,7]]},"reference":[{"key":"mlstad7e7abib1","author":"Hille","year":"2001","edition":"3rd edn"},{"key":"mlstad7e7abib2","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pcbi.1000277","article-title":"Poisson-Nernst-Planck models of nonequilibrium ion electrodiffusion through a protegrin transmembrane pore","volume":"5","author":"Bolintineanu","year":"2009","journal-title":"PLoS Comput. 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