{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T11:26:43Z","timestamp":1753874803120,"version":"3.41.2"},"reference-count":14,"publisher":"AIP Publishing","issue":"11","license":[{"start":{"date-parts":[[2025,3,21]],"date-time":"2025-03-21T00:00:00Z","timestamp":1742515200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100019180","name":"HORIZON EUROPE European Research Council","doi-asserted-by":"publisher","award":["101001290"],"award-info":[{"award-number":["101001290"]}],"id":[{"id":"10.13039\/100019180","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Spanish Ministry of Science","award":["MICIN\/AEI\/10.13039\/501100011033\/FEDER"],"award-info":[{"award-number":["MICIN\/AEI\/10.13039\/501100011033\/FEDER"]}]},{"name":"Spanish Ministry of Science","award":["PID2019-104604RB"],"award-info":[{"award-number":["PID2019-104604RB"]}]},{"name":"Spanish Ministry of Science","award":["PID2022-136784NB"],"award-info":[{"award-number":["PID2022-136784NB"]}]},{"name":"Asturias FICYT","award":["AYUD\/2021\/51185"],"award-info":[{"award-number":["AYUD\/2021\/51185"]}]},{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["EP\/L015978\/1"],"award-info":[{"award-number":["EP\/L015978\/1"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002428","name":"Austrian Science Fund","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100002428","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100006012","name":"Christian Doppler Research Association","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100006012","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2025,3,21]]},"abstract":"<jats:p>In operando techniques enable real-time measurement of intricate physical properties at the micro- and nano-scale under external stimuli, allowing the study of a wide range of materials and functionalities. In nanomagnetism, in operando techniques greatly benefit from precise three-dimensional (3D) magnetic field control, enabling access to complex magnetic states forming in systems where multiple energies are set to compete with each other. However, achieving such precision is challenging and uncommon, as specific applications impose constraints on the type and geometry of magnetic field sources, limiting their capabilities. Here, we introduce an approach that leverages machine learning algorithms to achieve precise 3D magnetic field control using a hexapole electromagnet that is composed of three independent, non-collinear dipole electromagnets. In our experimental setup, magnetic field sensors are placed at a distance from the sample position due to inherent constraints, leading to indirect field measurements that differ from the magnetic field experienced by the sample. We find that the existing relationship between the remote and sample frames of reference is non-linear, thus requiring a more complex calibration method. To address this, we employ a multi-layer perceptron neural network that processes multiple inputs from a dynamic magnetic field sequence, effectively capturing the time-dependent non-linear field response. The network achieves high calibration accuracy and demonstrates exceptional generalization to unseen magnetic field sequences. This study highlights the significant potential of machine learning in achieving high-precision control and calibration, crucial for in operando experiments where direct measurement at the point of interest is not possible.<\/jats:p>","DOI":"10.1063\/5.0249846","type":"journal-article","created":{"date-parts":[[2025,3,21]],"date-time":"2025-03-21T10:17:48Z","timestamp":1742552268000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":0,"title":["Remote-sensing based control of 3D magnetic fields using machine learning for <i>in operando<\/i> applications"],"prefix":"10.1063","volume":"137","author":[{"ORCID":"https:\/\/orcid.org\/0009-0005-7018-8031","authenticated-orcid":false,"given":"Miguel A.","family":"Cascales Sandoval","sequence":"first","affiliation":[{"name":"Institute of Applied Physics, TU Wien 1 , Wiedner Hauptstra\u00dfe 8-10, Vienna 1040,","place":["Austria"]}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4619-6550","authenticated-orcid":false,"given":"J.","family":"Jurczyk","sequence":"additional","affiliation":[{"name":"Institute of Applied Physics, TU Wien 1 , Wiedner Hauptstra\u00dfe 8-10, Vienna 1040,","place":["Austria"]}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2169-3008","authenticated-orcid":false,"given":"L.","family":"Skoric","sequence":"additional","affiliation":[{"name":"Cavendish Laboratory, University of Cambridge 2 , JJ Thomson Avenue, Cambridge CB3 0HE,","place":["United Kingdom"]}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5552-8836","authenticated-orcid":false,"given":"D.","family":"Sanz-Hern\u00e1ndez","sequence":"additional","affiliation":[{"name":"CNRS\/Thales: Laboratoire Albert Fert, CNRS, Thales, Universit\u00e9 Paris-Saclay 3 , 1 avenue Augustin Fresnel, 91767 Palaiseau,","place":["France"]}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0828-6889","authenticated-orcid":false,"given":"N.","family":"Leo","sequence":"additional","affiliation":[{"name":"Institute of Applied Physics, TU Wien 1 , Wiedner Hauptstra\u00dfe 8-10, Vienna 1040,","place":["Austria"]},{"name":"Department of Physics, Loughborough University 4 , Epinal Way, Loughborough LE11 3TU,","place":["United Kingdom"]}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8413-1950","authenticated-orcid":false,"given":"A.","family":"Kovacs","sequence":"additional","affiliation":[{"name":"Department for Integrated Sensor Systems, Danube University Krems 5 , Viktor Kaplan-Stra\u00dfe 2E, 2700 Wiener Neustadt,","place":["Austria"]}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0871-0520","authenticated-orcid":false,"given":"T.","family":"Schrefl","sequence":"additional","affiliation":[{"name":"Department for Integrated Sensor Systems, Danube University Krems 5 , Viktor Kaplan-Stra\u00dfe 2E, 2700 Wiener Neustadt,","place":["Austria"]},{"name":"Christian Doppler Laboratory for Magnet design through physics informed machine learning 6 , Viktor Kaplan-Stra\u00dfe 2E, 2700 Wiener Neustadt,","place":["Austria"]}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6600-7801","authenticated-orcid":false,"given":"A.","family":"Hierro-Rodr\u00edguez","sequence":"additional","affiliation":[{"name":"Departamento de F\u00edsica, Universidad de Oviedo 7 , Oviedo 33007,","place":["Spain"]},{"name":"CINN (CSIC-Universidad de Oviedo) 8 , El Entrego 33940,","place":["Spain"]},{"name":"SUPA, School of Physics and Astronomy, University of Glasgow 9 , Glasgow G12 8QQ,","place":["United Kingdom"]}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3862-8472","authenticated-orcid":false,"given":"A.","family":"Fern\u00e1ndez-Pacheco","sequence":"additional","affiliation":[{"name":"Institute of Applied Physics, TU Wien 1 , Wiedner Hauptstra\u00dfe 8-10, Vienna 1040,","place":["Austria"]}]}],"member":"317","published-online":{"date-parts":[[2025,3,21]]},"reference":[{"key":"2025032109561612400_c1","doi-asserted-by":"publisher","first-page":"25341","DOI":"10.1039\/D1TA04532F","article-title":"A critical discussion on the analysis of buried interfaces in Li solid-state batteries. Ex situ and in situ\/operando studies","volume":"9","year":"2021","journal-title":"J. Mater. Chem. A"},{"key":"2025032109561612400_c2","doi-asserted-by":"publisher","first-page":"100666","DOI":"10.1016\/j.checat.2023.100666","article-title":"Multi-technique operando methods and instruments for simultaneous assessment of thermal catalysis structure, performance, dynamics, and kinetics","volume":"3","year":"2023","journal-title":"Chem. 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Radiat."},{"key":"2025032109561612400_c5","doi-asserted-by":"publisher","first-page":"119593","DOI":"10.1016\/j.actamat.2023.119593","article-title":"Synchrotron x-ray operando study and multiphysics modelling of the solidification dynamics of intermetallic phases under electromagnetic pulses","volume":"265","year":"2024","journal-title":"Acta Mater."},{"key":"2025032109561612400_c6","doi-asserted-by":"publisher","first-page":"190","DOI":"10.1126\/science.1145799","article-title":"Magnetic domain-wall racetrack memory","volume":"320","year":"2008","journal-title":"Science"},{"key":"2025032109561612400_c7","doi-asserted-by":"publisher","first-page":"1454","DOI":"10.1016\/j.microrel.2011.07.001","article-title":"Design considerations and strategies for high-reliable STT-MRAM","volume":"51","year":"2011","journal-title":"Microelectron. Reliab."},{"key":"2025032109561612400_c8"},{"key":"2025032109561612400_c9","unstructured":"D.\n            Sanz Hern\u00e1ndez\n          , \u201cFabrication and characterization of three-dimensional magnetic nanostructures,\u201d Ph.D. thesis (Girton College, University of Cambridge, 2019)."},{"key":"2025032109561612400_c10","doi-asserted-by":"crossref","first-page":"043901","DOI":"10.1063\/5.0132250","article-title":"Probing 3D magnetic nanostructures by dark-field magneto-optical Kerr effect","volume":"133","year":"2023","journal-title":"J. Appl. Phys."},{"key":"2025032109561612400_c11","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1007\/s11004-009-9257-x","article-title":"Measurement of areas on a sphere using fibonacci and latitude\u2013longitude lattices","volume":"42","year":"2010","journal-title":"Math. 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