{"id":"https://openalex.org/W7162395247","doi":"https://doi.org/10.48550/arxiv.2605.25640","title":"3D Magnetic Field Reconstruction and Mapping with Physics-Informed Neural Networks","display_name":"3D Magnetic Field Reconstruction and Mapping with Physics-Informed Neural Networks","publication_year":2026,"publication_date":"2026-05-25","ids":{"openalex":"https://openalex.org/W7162395247","doi":"https://doi.org/10.48550/arxiv.2605.25640"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.25640","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.25640","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2605.25640","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5137067317","display_name":"Haohan Yu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yu, Haohan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5136999947","display_name":"Zhanxu Hao","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hao, Zhanxu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5137010352","display_name":"Bingzhi Li","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Li, Bingzhi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067175393","display_name":"Zejia Lu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lu, Zejia","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5137068517","display_name":"Xiang Chen","orcid":"https://orcid.org/0000-0003-4977-2717"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chen, Xiang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5137067343","display_name":"Liang Li","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Li, Liang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11993","display_name":"Atomic and Subatomic Physics Research","score":0.3977999985218048,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11993","display_name":"Atomic and Subatomic Physics Research","score":0.3977999985218048,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12692","display_name":"Magnetic Field Sensors Techniques","score":0.20010000467300415,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.0544000007212162,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5401999950408936},{"id":"https://openalex.org/keywords/consistency","display_name":"Consistency (knowledge bases)","score":0.5163000226020813},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.5016000270843506},{"id":"https://openalex.org/keywords/truncation","display_name":"Truncation (statistics)","score":0.5012999773025513},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.4526999890804291},{"id":"https://openalex.org/keywords/magnetic-field","display_name":"Magnetic field","score":0.3953000009059906},{"id":"https://openalex.org/keywords/data-validation","display_name":"Data validation","score":0.3903000056743622},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.3758000135421753},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.36489999294281006},{"id":"https://openalex.org/keywords/singular-value-decomposition","display_name":"Singular value decomposition","score":0.352400004863739}],"concepts":[{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5401999950408936},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5360999703407288},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.5163000226020813},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.5016000270843506},{"id":"https://openalex.org/C106195933","wikidata":"https://www.wikidata.org/wiki/Q7847935","display_name":"Truncation (statistics)","level":2,"score":0.5012999773025513},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4699999988079071},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.4526999890804291},{"id":"https://openalex.org/C115260700","wikidata":"https://www.wikidata.org/wiki/Q11408","display_name":"Magnetic field","level":2,"score":0.3953000009059906},{"id":"https://openalex.org/C92446256","wikidata":"https://www.wikidata.org/wiki/Q3306762","display_name":"Data validation","level":2,"score":0.3903000056743622},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.3758000135421753},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.36489999294281006},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3547999858856201},{"id":"https://openalex.org/C22789450","wikidata":"https://www.wikidata.org/wiki/Q420904","display_name":"Singular value decomposition","level":2,"score":0.352400004863739},{"id":"https://openalex.org/C30403606","wikidata":"https://www.wikidata.org/wiki/Q2981904","display_name":"Electromagnetic coil","level":2,"score":0.350600004196167},{"id":"https://openalex.org/C19619285","wikidata":"https://www.wikidata.org/wiki/Q196372","display_name":"Observational error","level":2,"score":0.3393000066280365},{"id":"https://openalex.org/C70958404","wikidata":"https://www.wikidata.org/wiki/Q7512728","display_name":"Signal reconstruction","level":4,"score":0.32749998569488525},{"id":"https://openalex.org/C104942944","wikidata":"https://www.wikidata.org/wiki/Q3434686","display_name":"Truncation error","level":2,"score":0.3147999942302704},{"id":"https://openalex.org/C3768446","wikidata":"https://www.wikidata.org/wiki/Q877100","display_name":"Spherical harmonics","level":2,"score":0.31209999322891235},{"id":"https://openalex.org/C165838908","wikidata":"https://www.wikidata.org/wiki/Q736777","display_name":"Calibration","level":2,"score":0.3050999939441681},{"id":"https://openalex.org/C37649242","wikidata":"https://www.wikidata.org/wiki/Q932268","display_name":"System of measurement","level":2,"score":0.2953000068664551},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.2930999994277954},{"id":"https://openalex.org/C80023036","wikidata":"https://www.wikidata.org/wiki/Q5147531","display_name":"Collocation (remote sensing)","level":2,"score":0.2890999913215637},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.28630000352859497},{"id":"https://openalex.org/C127934551","wikidata":"https://www.wikidata.org/wiki/Q1148098","display_name":"Harmonic","level":2,"score":0.28209999203681946},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.27570000290870667},{"id":"https://openalex.org/C141379421","wikidata":"https://www.wikidata.org/wiki/Q6094427","display_name":"Iterative reconstruction","level":2,"score":0.27459999918937683},{"id":"https://openalex.org/C293773","wikidata":"https://www.wikidata.org/wiki/Q7608015","display_name":"Step detection","level":3,"score":0.2689000070095062},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.26589998602867126},{"id":"https://openalex.org/C202799725","wikidata":"https://www.wikidata.org/wiki/Q272035","display_name":"Accuracy and precision","level":2,"score":0.26260000467300415},{"id":"https://openalex.org/C138827492","wikidata":"https://www.wikidata.org/wiki/Q6661985","display_name":"Data processing","level":2,"score":0.2624000012874603},{"id":"https://openalex.org/C137209882","wikidata":"https://www.wikidata.org/wiki/Q1403517","display_name":"Measurement uncertainty","level":2,"score":0.25459998846054077}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.25640","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.25640","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2605.25640","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.25640","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/9","display_name":"Industry, innovation and infrastructure","score":0.5624356269836426}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Accurate":[0],"reconstruction":[1,99,120],"of":[2,78,101],"magnetic":[3,45],"fields":[4],"in":[5,14,145],"inaccessible":[6],"regions":[7],"is":[8,75,153],"vital":[9],"for":[10,42,140],"many":[11],"high-precision":[12,43,138],"experiments":[13],"physics.":[15],"Traditional":[16],"methods,":[17],"such":[18],"as":[19],"spherical":[20],"harmonic":[21],"expansion,":[22],"often":[23],"suffer":[24],"from":[25],"truncation":[26],"errors":[27],"that":[28],"limit":[29],"their":[30],"precision.":[31],"This":[32,132],"study":[33],"proposes":[34],"an":[35],"advanced":[36],"Physics-Informed":[37],"Neural":[38],"Network":[39],"(PINN)":[40],"framework":[41],"3D":[44],"field":[46,141],"mapping.":[47],"Unlike":[48],"conventional":[49],"data-driven":[50],"models,":[51],"the":[52,60,69,76,126],"proposed":[53],"PINN":[54,108],"integrates":[55],"Maxwell's":[56],"equations":[57],"directly":[58],"into":[59],"loss":[61],"function,":[62],"enforcing":[63],"divergence-free":[64],"and":[65,143],"curl-free":[66],"conditions":[67],"across":[68],"entire":[70],"domain.":[71],"A":[72],"key":[73],"innovation":[74],"inclusion":[77],"explicit":[79],"physics-residual":[80],"losses":[81],"at":[82],"measurement":[83,144],"locations,":[84],"ensuring":[85],"rigorous":[86],"physical":[87],"consistency":[88],"beyond":[89],"random":[90],"collocation":[91],"sampling.":[92],"Validation":[93],"using":[94,113],"simulated":[95],"data":[96],"achieves":[97],"a":[98,103,114,136],"accuracy":[100],"$10^{-4}$,":[102],"tenfold":[104],"improvement":[105],"over":[106],"existing":[107],"benchmarks.":[109],"Furthermore,":[110],"experimental":[111,147],"validation":[112],"custom":[115],"coil":[116],"assembly":[117],"demonstrates":[118],"robust":[119],"with":[121],"sub-percent":[122],"relative":[123],"accuracy,":[124],"reaching":[125],"$10^{-3}$":[127],"level":[128],"under":[129],"ambient":[130],"conditions.":[131],"AI-driven":[133],"methodology":[134],"provides":[135],"robust,":[137],"solution":[139],"monitoring":[142],"complex":[146],"environments":[148],"where":[149],"direct":[150],"sensor":[151],"placement":[152],"restricted.":[154]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-05-27T00:00:00"}