{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,4]],"date-time":"2026-04-04T18:06:24Z","timestamp":1775325984782,"version":"3.50.1"},"reference-count":53,"publisher":"Institute of Electrical and Electronics Engineers (IEEE)","issue":"12","license":[{"start":{"date-parts":[[2023,12,1]],"date-time":"2023-12-01T00:00:00Z","timestamp":1701388800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/ieeexplore.ieee.org\/Xplorehelp\/downloads\/license-information\/IEEE.html"},{"start":{"date-parts":[[2023,12,1]],"date-time":"2023-12-01T00:00:00Z","timestamp":1701388800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2023,12,1]],"date-time":"2023-12-01T00:00:00Z","timestamp":1701388800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"}],"funder":[{"DOI":"10.13039\/100000006","name":"Office of Naval Research","doi-asserted-by":"publisher","award":["N00014-18-1-2794"],"award-info":[{"award-number":["N00014-18-1-2794"]}],"id":[{"id":"10.13039\/100000006","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IEEE Trans. Pattern Anal. Mach. Intell."],"published-print":{"date-parts":[[2023,12]]},"DOI":"10.1109\/tpami.2023.3307688","type":"journal-article","created":{"date-parts":[[2023,8,23]],"date-time":"2023-08-23T17:57:42Z","timestamp":1692813462000},"page":"15588-15603","source":"Crossref","is-referenced-by-count":22,"title":["Self-Scalable Tanh (Stan): Multi-Scale Solutions for Physics-Informed Neural Networks"],"prefix":"10.1109","volume":"45","author":[{"ORCID":"https:\/\/orcid.org\/0009-0004-2159-4837","authenticated-orcid":false,"given":"Raghav","family":"Gnanasambandam","sequence":"first","affiliation":[{"name":"Industrial and Systems Engineering, Virginia Tech, Blacksburg, VA, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2643-3600","authenticated-orcid":false,"given":"Bo","family":"Shen","sequence":"additional","affiliation":[{"name":"Department of Mechanical and Industrial Engineering, New Jersey Institute of Technology, Newark, NJ, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6771-9034","authenticated-orcid":false,"given":"Jihoon","family":"Chung","sequence":"additional","affiliation":[{"name":"Industrial and Systems Engineering, Virginia Tech, Blacksburg, VA, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9929-8895","authenticated-orcid":false,"given":"Xubo","family":"Yue","sequence":"additional","affiliation":[{"name":"Department of Mechanical &amp; Industrial Engineering, Northeastern University, Boston, MA, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8827-502X","authenticated-orcid":false,"given":"Zhenyu","family":"Kong","sequence":"additional","affiliation":[{"name":"Industrial and Systems Engineering, Virginia Tech, Blacksburg, VA, USA"}]}],"member":"263","reference":[{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2019.112790"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1109\/ACCESS.2020.2970143"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1007\/s00466-019-01740-0"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1145\/3485128"},{"key":"ref53","doi-asserted-by":"publisher","DOI":"10.1038\/s41592-019-0686-2"},{"key":"ref52","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9290(89)90224-8"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1146\/annurev-fluid-010719-060214"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1146\/annurev-fluid-010518-040547"},{"key":"ref17","article-title":"Physics-informed neural networks for cardiac activation mapping","volume":"8","author":"sahli costabal","year":"2020","journal-title":"Frontiers in Physiology"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2019.112789"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1002\/0470013826"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1038\/s42254-021-00314-5"},{"key":"ref51","author":"meriam","year":"2020","journal-title":"Engineering Mechanics Dynamics"},{"key":"ref50","year":"2022"},{"key":"ref46","article-title":"Frequency principle: Fourier analysis sheds light on deep neural networks","author":"xu","year":"2019"},{"key":"ref45","first-page":"5301","article-title":"On the spectral bias of neural networks","author":"rahaman","year":"2019","journal-title":"Proc Int Conf Mach Learn"},{"key":"ref48","author":"belsley","year":"2005","journal-title":"Regression Diagnostics Identifying Influential Data and Sources of Collinearity"},{"key":"ref47","doi-asserted-by":"publisher","DOI":"10.1109\/EE.1948.6444503"},{"key":"ref42","doi-asserted-by":"publisher","DOI":"10.1016\/0893-6080(89)90020-8"},{"key":"ref41","first-page":"1","article-title":"Automatic differentiation in machine learning: A survey","volume":"18","author":"baydin","year":"2018","journal-title":"Journal of Marchine Learning Research"},{"key":"ref44","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2021.113938"},{"key":"ref43","first-page":"249","article-title":"Understanding the difficulty of training deep feedforward neural networks","author":"glorot","year":"2010","journal-title":"Proc 13th Int Conf Artif Intell Statist"},{"key":"ref49","doi-asserted-by":"publisher","DOI":"10.1142\/10984"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1109\/72.712178"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1007\/978-981-33-6108-9"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2018.10.045"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1080\/00207543.2021.1956675"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1007\/s10462-021-09967-1"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1038\/d41586-018-02174-z"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1186\/1475-925X-13-94"},{"key":"ref40","doi-asserted-by":"publisher","DOI":"10.1137\/0916069"},{"key":"ref35","first-page":"807","article-title":"Rectified linear units improve restricted boltzmann machines","author":"nair","year":"2010","journal-title":"Proc 27th Int Conf Mach Learn"},{"key":"ref34","author":"ranjan","year":"2020","journal-title":"Understanding deep learning Application in rare event prediction"},{"key":"ref37","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-77977-1_36"},{"key":"ref36","article-title":"Estimates on the generalization error of physics informed neural networks (PINNs) for approximating a class of inverse problems for PDEs","author":"mishra","year":"2020"},{"key":"ref31","article-title":"Searching for activation functions","author":"ramachandran","year":"2017"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-35289-8_3"},{"key":"ref33","first-page":"2672","article-title":"On the impact of the activation function on deep neural networks training","author":"hayou","year":"2019","journal-title":"Proc Int Conf Mach Learn"},{"key":"ref32","doi-asserted-by":"publisher","DOI":"10.1016\/j.neunet.2021.01.026"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.3390\/fi11040094"},{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1017\/jfm.2016.803"},{"key":"ref39","article-title":"Adam: A method for stochastic optimization","author":"kingma","year":"2014"},{"key":"ref38","article-title":"Is it time to swish? Comparing activation functions in solving the helmholtz equation using physics-informed neural networks","author":"al-safwan","year":"2021"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2019.109136"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2022.111722"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2021.10.036"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.2020.0334"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1115\/1.4050542"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2021.110768"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1137\/20M1318043"},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2020.113028"},{"key":"ref27","article-title":"Finite basis physics-informed neural networks (FBPINNs): A scalable domain decomposition approach for solving differential equations","author":"moseley","year":"2021"},{"key":"ref29","doi-asserted-by":"crossref","first-page":"2002","DOI":"10.4208\/cicp.OA-2020-0164","article-title":"Extended physics-informed neural networks (XPINNs): A generalized space-time domain decomposition based deep learning framework for nonlinear partial differential equations","volume":"28","author":"jagtap","year":"2020","journal-title":"Commun Comput Phys"}],"container-title":["IEEE Transactions on Pattern Analysis and Machine Intelligence"],"original-title":[],"link":[{"URL":"http:\/\/xplorestaging.ieee.org\/ielx7\/34\/10308548\/10227556.pdf?arnumber=10227556","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,5,27]],"date-time":"2025-05-27T17:15:43Z","timestamp":1748366143000},"score":1,"resource":{"primary":{"URL":"https:\/\/ieeexplore.ieee.org\/document\/10227556\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,12]]},"references-count":53,"journal-issue":{"issue":"12"},"URL":"https:\/\/doi.org\/10.1109\/tpami.2023.3307688","relation":{},"ISSN":["0162-8828","2160-9292","1939-3539"],"issn-type":[{"value":"0162-8828","type":"print"},{"value":"2160-9292","type":"electronic"},{"value":"1939-3539","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,12]]}}}