{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,27]],"date-time":"2026-05-27T11:09:35Z","timestamp":1779880175488,"version":"3.53.1"},"reference-count":35,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,5,15]],"date-time":"2026-05-15T00:00:00Z","timestamp":1778803200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002341","name":"Research Council of Finland","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100002341","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Engineering Applications of Artificial Intelligence"],"published-print":{"date-parts":[[2026,8]]},"DOI":"10.1016\/j.engappai.2026.115098","type":"journal-article","created":{"date-parts":[[2026,5,19]],"date-time":"2026-05-19T19:31:46Z","timestamp":1779219106000},"page":"115098","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"P2","title":["Surrogate modeling of inductance in axial active magnetic bearings using data-driven and physics-informed neural networks"],"prefix":"10.1016","volume":"178","author":[{"ORCID":"https:\/\/orcid.org\/0009-0009-1320-409X","authenticated-orcid":false,"given":"Jawad","family":"Tariq","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4902-1334","authenticated-orcid":false,"given":"Sadjad","family":"Madanzadeh","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0009-4407-7011","authenticated-orcid":false,"given":"Muhammad","family":"Numan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9923-3650","authenticated-orcid":false,"given":"Tuomo","family":"Lindh","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9766-0675","authenticated-orcid":false,"given":"Niko","family":"Nevaranta","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"issue":"3","key":"10.1016\/j.engappai.2026.115098_b1","doi-asserted-by":"crossref","first-page":"105","DOI":"10.4173\/mic.2024.3.3","article-title":"Optimizing PID controller design for rotor systems suspended by active magnetic bearings","volume":"45","author":"Abubakar","year":"2024","journal-title":"Model. Identif. Control"},{"issue":"5","key":"10.1016\/j.engappai.2026.115098_b2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/TMAG.2023.3247023","article-title":"Physics-informed neural networks for inverse electromagnetic problems","volume":"59","author":"Baldan","year":"2023","journal-title":"IEEE Trans. Magn."},{"issue":"11","key":"10.1016\/j.engappai.2026.115098_b3","doi-asserted-by":"crossref","first-page":"6454","DOI":"10.1109\/TIE.2014.2303785","article-title":"Using FE calculations and data-based system identification techniques to model the nonlinear behavior of PMSMs","volume":"61","author":"Bramerdorfer","year":"2014","journal-title":"IEEE Trans. Ind. Electron."},{"key":"10.1016\/j.engappai.2026.115098_b4","doi-asserted-by":"crossref","DOI":"10.1016\/j.ijsolstr.2025.113315","article-title":"Energy-based PINNs using the element integral approach and their enhancement for solid mechanics problems","volume":"313","author":"Chen","year":"2025","journal-title":"Int. J. Solids Struct."},{"issue":"3","key":"10.1016\/j.engappai.2026.115098_b5","doi-asserted-by":"crossref","first-page":"3771","DOI":"10.1109\/TTE.2022.3164644","article-title":"Data-driven electrical machines structural model using the vibration synthesis method","volume":"8","author":"Ciceo","year":"2022","journal-title":"IEEE Trans. Transp. Electrification"},{"key":"10.1016\/j.engappai.2026.115098_b6","series-title":"Physics-guided neural networks (pgnn): An application in lake temperature modeling","author":"Daw","year":"2017"},{"issue":"3","key":"10.1016\/j.engappai.2026.115098_b7","doi-asserted-by":"crossref","first-page":"1534","DOI":"10.3390\/ai5030074","article-title":"Understanding physics-informed neural networks: Techniques, applications, trends, and challenges","volume":"5","author":"Farea","year":"2024","journal-title":"AI"},{"issue":"6","key":"10.1016\/j.engappai.2026.115098_b8","doi-asserted-by":"crossref","first-page":"2946","DOI":"10.1109\/TIE.2013.2286777","article-title":"High-speed electrical machines: Technologies, trends, and developments","volume":"61","author":"Gerada","year":"2014","journal-title":"IEEE Trans. Ind. Electron."},{"key":"10.1016\/j.engappai.2026.115098_b9","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1016\/0893-6080(91)90009-T","article-title":"Approximation capabilities of multilayer feedforward networks","volume":"4","author":"Hornik","year":"1991","journal-title":"Neural Netw."},{"key":"10.1016\/j.engappai.2026.115098_b10","doi-asserted-by":"crossref","DOI":"10.1016\/j.engappai.2024.108302","article-title":"Physics-informed neural network for simulating magnetic field of coaxial magnetic gear","volume":"133","author":"Hou","year":"2024","journal-title":"Eng. Appl. Artif. Intell."},{"issue":"8","key":"10.1016\/j.engappai.2026.115098_b11","doi-asserted-by":"crossref","first-page":"11064","DOI":"10.1109\/TNNLS.2023.3247163","article-title":"Physics-informed neural networks with weighted losses by uncertainty evaluation for accurate and stable prediction of manufacturing systems","volume":"35","author":"Hua","year":"2023","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"issue":"6","key":"10.1016\/j.engappai.2026.115098_b12","doi-asserted-by":"crossref","first-page":"6892","DOI":"10.1109\/TIA.2021.3102463","article-title":"Design and modeling of 2 MW AMB rotor with three radial bearing-sensor planes","volume":"57","author":"Jastrzebski","year":"2021","journal-title":"IEEE Trans. Ind. Appl."},{"key":"10.1016\/j.engappai.2026.115098_b13","doi-asserted-by":"crossref","DOI":"10.1016\/j.engappai.2025.112112","article-title":"Machine learning-based estimation of sound transmission loss in single and double-layered rectangular functionally graded plates","volume":"161","author":"Jiang","year":"2025","journal-title":"Eng. Appl. Artif. Intell."},{"issue":"5","key":"10.1016\/j.engappai.2026.115098_b14","doi-asserted-by":"crossref","first-page":"5981","DOI":"10.1109\/TNNLS.2023.3310585","article-title":"Physics-informed neural networks for solving forward and inverse problems in complex beam systems","volume":"35","author":"Kapoor","year":"2023","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"issue":"6","key":"10.1016\/j.engappai.2026.115098_b15","doi-asserted-by":"crossref","first-page":"422","DOI":"10.1038\/s42254-021-00314-5","article-title":"Physics-informed machine learning","volume":"3","author":"Karniadakis","year":"2021","journal-title":"Nat. Rev. Phys."},{"key":"10.1016\/j.engappai.2026.115098_b16","series-title":"Adam: A method for stochastic optimization","author":"Kingma","year":"2014"},{"issue":"1","key":"10.1016\/j.engappai.2026.115098_b17","doi-asserted-by":"crossref","first-page":"310","DOI":"10.2478\/pead-2023-0021","article-title":"Rotor speed and load torque estimations of induction motors via LSTM network","volume":"8","author":"Kosten","year":"2023","journal-title":"Power Electron. Drives"},{"issue":"5","key":"10.1016\/j.engappai.2026.115098_b18","doi-asserted-by":"crossref","first-page":"987","DOI":"10.1109\/72.712178","article-title":"Artificial neural networks for solving ordinary and partial differential equations","volume":"9","author":"Lagaris","year":"1998","journal-title":"IEEE Trans. Neural Netw."},{"issue":"3","key":"10.1016\/j.engappai.2026.115098_b19","doi-asserted-by":"crossref","first-page":"194","DOI":"10.30941\/CESTEMS.2021.00023","article-title":"Modeling and hardware-in-the-loop system realization of electric machine drives \u2014 A review","volume":"5","author":"Lee","year":"2021","journal-title":"CES Trans. Electr. Mach. Syst."},{"issue":"15","key":"10.1016\/j.engappai.2026.115098_b20","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1016\/j.ifacol.2024.08.546","article-title":"Physics-Informed Neural Network for system identification of rotors","volume":"58","author":"Liu","year":"2024","journal-title":"IFAC-PapersOnLine"},{"key":"10.1016\/j.engappai.2026.115098_b21","series-title":"2023 IEEE 8th Southern Power Electronics Conference","first-page":"1","article-title":"Design optimization of an interior permanent magnet synchronous machine applying the PSO algorithm to a surrogate model based on artificial neural network","author":"Luna","year":"2023"},{"key":"10.1016\/j.engappai.2026.115098_b22","doi-asserted-by":"crossref","first-page":"S893","DOI":"10.1016\/S0098-1354(98)00174-4","article-title":"A hybrid neural network-first principles approach to batch unit optimisation","volume":"22","author":"Martinez","year":"1998","journal-title":"Comput. Chem. Eng."},{"issue":"7","key":"10.1016\/j.engappai.2026.115098_b23","doi-asserted-by":"crossref","first-page":"3357","DOI":"10.1109\/TNNLS.2021.3123968","article-title":"Physics-guided generative adversarial networks for sea subsurface temperature prediction","volume":"34","author":"Meng","year":"2021","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"10.1016\/j.engappai.2026.115098_b24","series-title":"Estimates on the generalization error of physics informed neural networks (PINNs) for approximating PDEs","author":"Mishra","year":"2023"},{"key":"10.1016\/j.engappai.2026.115098_b25","doi-asserted-by":"crossref","DOI":"10.1016\/j.engappai.2022.105546","article-title":"Data-driven multi-objective optimization with neural network-based sensitivity analysis for semiconductor devices","volume":"117","author":"Oh","year":"2023","journal-title":"Eng. Appl. Artif. Intell."},{"issue":"1","key":"10.1016\/j.engappai.2026.115098_b26","doi-asserted-by":"crossref","DOI":"10.3390\/s24010207","article-title":"Physics-informed neural networks for the condition monitoring of rotating shafts","volume":"24","author":"Parziale","year":"2024","journal-title":"Sensors"},{"key":"10.1016\/j.engappai.2026.115098_b27","doi-asserted-by":"crossref","DOI":"10.1016\/j.engappai.2023.106127","article-title":"Frequency-domain physical constrained neural network for nonlinear system dynamic prediction","volume":"122","author":"Qian","year":"2023","journal-title":"Eng. Appl. Artif. Intell."},{"key":"10.1016\/j.engappai.2026.115098_b28","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. Phys."},{"key":"10.1016\/j.engappai.2026.115098_b29","series-title":"2024 Energy Conversion Congress & Expo Europe","first-page":"1","article-title":"Replicating existing axial magnetic bearing controller with a neural network","author":"Rehtla","year":"2024"},{"key":"10.1016\/j.engappai.2026.115098_b30","series-title":"Proceedings of IEEE Workshop on Neural Networks for Signal Processing","first-page":"596","article-title":"Continuous-time nonlinear signal processing: a neural network based approach for gray box identification","author":"Rico-Martinez","year":"1994"},{"issue":"5","key":"10.1016\/j.engappai.2026.115098_b31","doi-asserted-by":"crossref","first-page":"2042","DOI":"10.4208\/cicp.OA-2020-0193","article-title":"On the convergence of physics informed neural networks for linear second-order elliptic and parabolic type PDEs","volume":"28","author":"Shin","year":"2020","journal-title":"Commun. Comput. Phys."},{"key":"10.1016\/j.engappai.2026.115098_b32","doi-asserted-by":"crossref","first-page":"220027","DOI":"10.1109\/ACCESS.2020.3042834","article-title":"Surrogate modeling of electrical machine torque using artificial neural networks","volume":"8","author":"Tahkola","year":"2020","journal-title":"IEEE Access"},{"key":"10.1016\/j.engappai.2026.115098_b33","doi-asserted-by":"crossref","first-page":"220027","DOI":"10.1109\/ACCESS.2020.3042834","article-title":"Surrogate modeling of electrical machine torque using artificial neural networks","volume":"8","author":"Tahkola","year":"2020","journal-title":"IEEE Access"},{"issue":"9","key":"10.1016\/j.engappai.2026.115098_b34","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/TMAG.2022.3180176","article-title":"Transient modeling of induction machine using artificial neural network surrogate models","volume":"58","author":"Tahkola","year":"2022","journal-title":"IEEE Trans. Magn."},{"issue":"9","key":"10.1016\/j.engappai.2026.115098_b35","doi-asserted-by":"crossref","first-page":"2016","DOI":"10.3390\/math11092016","article-title":"Enhancing computational accuracy in surrogate modeling for elastic\u2013plastic problems by coupling S-FEM and physics-informed deep learning","volume":"11","author":"Zhou","year":"2023","journal-title":"Mathematics"}],"container-title":["Engineering Applications of Artificial Intelligence"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0952197626013813?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0952197626013813?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,5,27]],"date-time":"2026-05-27T10:51:46Z","timestamp":1779879106000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0952197626013813"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,8]]},"references-count":35,"alternative-id":["S0952197626013813"],"URL":"https:\/\/doi.org\/10.1016\/j.engappai.2026.115098","relation":{},"ISSN":["0952-1976"],"issn-type":[{"value":"0952-1976","type":"print"}],"subject":[],"published":{"date-parts":[[2026,8]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Surrogate modeling of inductance in axial active magnetic bearings using data-driven and physics-informed neural networks","name":"articletitle","label":"Article Title"},{"value":"Engineering Applications of Artificial Intelligence","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.engappai.2026.115098","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 The Authors. Published by Elsevier Ltd.","name":"copyright","label":"Copyright"}],"article-number":"115098"}}