{"id":"https://openalex.org/W4394616145","doi":"https://doi.org/10.1007/s12145-024-01294-7","title":"Physics-informed loss functions for vertical total electron content forecast","display_name":"Physics-informed loss functions for vertical total electron content forecast","publication_year":2024,"publication_date":"2024-04-09","ids":{"openalex":"https://openalex.org/W4394616145","doi":"https://doi.org/10.1007/s12145-024-01294-7"},"language":"en","primary_location":{"id":"doi:10.1007/s12145-024-01294-7","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s12145-024-01294-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s12145-024-01294-7.pdf","source":{"id":"https://openalex.org/S198914822","display_name":"Earth Science Informatics","issn_l":"1865-0473","issn":["1865-0473","1865-0481"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Earth Science Informatics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s12145-024-01294-7.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5075875665","display_name":"Eric Nana Asamoah","orcid":null},"institutions":[{"id":"https://openalex.org/I142910587","display_name":"University of Salento","ror":"https://ror.org/03fc1k060","country_code":"IT","type":"education","lineage":["https://openalex.org/I142910587"]},{"id":"https://openalex.org/I29078338","display_name":"Istituto Nazionale di Geofisica e Vulcanologia","ror":"https://ror.org/00qps9a02","country_code":"IT","type":"facility","lineage":["https://openalex.org/I29078338"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Eric Nana Asamoah","raw_affiliation_strings":["Department of Engineering for Innovation, University of Salento, Via per Monteroni, Lecce, 73100, Puglia, Italy","Environmental Department, Upper Atmosphere Physics and Radiopropagation Unit, Istituto Nazionale di Geofisica e Vulcanologia, Via di Vigna Murata 605, Rome, 00142, Lazio, Italy"],"affiliations":[{"raw_affiliation_string":"Department of Engineering for Innovation, University of Salento, Via per Monteroni, Lecce, 73100, Puglia, Italy","institution_ids":["https://openalex.org/I142910587"]},{"raw_affiliation_string":"Environmental Department, Upper Atmosphere Physics and Radiopropagation Unit, Istituto Nazionale di Geofisica e Vulcanologia, Via di Vigna Murata 605, Rome, 00142, Lazio, Italy","institution_ids":["https://openalex.org/I29078338"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077589329","display_name":"Massimo Cafaro","orcid":"https://orcid.org/0000-0003-1118-7109"},"institutions":[{"id":"https://openalex.org/I142910587","display_name":"University of Salento","ror":"https://ror.org/03fc1k060","country_code":"IT","type":"education","lineage":["https://openalex.org/I142910587"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Massimo Cafaro","raw_affiliation_strings":["Department of Engineering for Innovation, University of Salento, Via per Monteroni, Lecce, 73100, Puglia, Italy"],"affiliations":[{"raw_affiliation_string":"Department of Engineering for Innovation, University of Salento, Via per Monteroni, Lecce, 73100, Puglia, Italy","institution_ids":["https://openalex.org/I142910587"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079559754","display_name":"Italo Epicoco","orcid":"https://orcid.org/0000-0002-6408-1335"},"institutions":[{"id":"https://openalex.org/I142910587","display_name":"University of Salento","ror":"https://ror.org/03fc1k060","country_code":"IT","type":"education","lineage":["https://openalex.org/I142910587"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Italo Epicoco","raw_affiliation_strings":["Department of Engineering for Innovation, University of Salento, Via per Monteroni, Lecce, 73100, Puglia, Italy"],"affiliations":[{"raw_affiliation_string":"Department of Engineering for Innovation, University of Salento, Via per Monteroni, Lecce, 73100, Puglia, Italy","institution_ids":["https://openalex.org/I142910587"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5068142358","display_name":"Giorgiana De Franceschi","orcid":"https://orcid.org/0000-0002-3943-6798"},"institutions":[{"id":"https://openalex.org/I29078338","display_name":"Istituto Nazionale di Geofisica e Vulcanologia","ror":"https://ror.org/00qps9a02","country_code":"IT","type":"facility","lineage":["https://openalex.org/I29078338"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Giorgiana De Franceschi","raw_affiliation_strings":["Environmental Department, Upper Atmosphere Physics and Radiopropagation Unit, Istituto Nazionale di Geofisica e Vulcanologia, Via di Vigna Murata 605, Rome, 00142, Lazio, Italy"],"affiliations":[{"raw_affiliation_string":"Environmental Department, Upper Atmosphere Physics and Radiopropagation Unit, Istituto Nazionale di Geofisica e Vulcanologia, Via di Vigna Murata 605, Rome, 00142, Lazio, Italy","institution_ids":["https://openalex.org/I29078338"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5025301498","display_name":"Claudio Cesaroni","orcid":"https://orcid.org/0000-0003-2268-4389"},"institutions":[{"id":"https://openalex.org/I29078338","display_name":"Istituto Nazionale di Geofisica e Vulcanologia","ror":"https://ror.org/00qps9a02","country_code":"IT","type":"facility","lineage":["https://openalex.org/I29078338"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Claudio Cesaroni","raw_affiliation_strings":["Environmental Department, Upper Atmosphere Physics and Radiopropagation Unit, Istituto Nazionale di Geofisica e Vulcanologia, Via di Vigna Murata 605, Rome, 00142, Lazio, Italy"],"affiliations":[{"raw_affiliation_string":"Environmental Department, Upper Atmosphere Physics and Radiopropagation Unit, Istituto Nazionale di Geofisica e Vulcanologia, Via di Vigna Murata 605, Rome, 00142, Lazio, Italy","institution_ids":["https://openalex.org/I29078338"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5075875665"],"corresponding_institution_ids":["https://openalex.org/I142910587","https://openalex.org/I29078338"],"apc_list":{"value":2690,"currency":"EUR","value_usd":3390},"apc_paid":{"value":2690,"currency":"EUR","value_usd":3390},"fwci":0.3549,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.63049772,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":97,"max":99},"biblio":{"volume":"17","issue":"3","first_page":"2569","last_page":"2586"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10159","display_name":"Ionosphere and magnetosphere dynamics","score":0.9692999720573425,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"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/T10159","display_name":"Ionosphere and magnetosphere dynamics","score":0.9692999720573425,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"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/T11854","display_name":"Laser-induced spectroscopy and plasma","score":0.9682999849319458,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/T10688","display_name":"Image and Signal Denoising Methods","score":0.9656000137329102,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/content","display_name":"Content (measure theory)","score":0.5334753394126892},{"id":"https://openalex.org/keywords/electron","display_name":"Electron","score":0.5166521668434143},{"id":"https://openalex.org/keywords/ontology","display_name":"Ontology","score":0.45054683089256287},{"id":"https://openalex.org/keywords/total-electron-content","display_name":"Total electron content","score":0.42011162638664246},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3308684527873993},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3270265758037567},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.20125660300254822},{"id":"https://openalex.org/keywords/geophysics","display_name":"Geophysics","score":0.16573044657707214},{"id":"https://openalex.org/keywords/nuclear-physics","display_name":"Nuclear physics","score":0.14050692319869995},{"id":"https://openalex.org/keywords/epistemology","display_name":"Epistemology","score":0.12282949686050415},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.1030806303024292},{"id":"https://openalex.org/keywords/ionosphere","display_name":"Ionosphere","score":0.08988937735557556},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08925902843475342}],"concepts":[{"id":"https://openalex.org/C2778152352","wikidata":"https://www.wikidata.org/wiki/Q5165061","display_name":"Content (measure theory)","level":2,"score":0.5334753394126892},{"id":"https://openalex.org/C147120987","wikidata":"https://www.wikidata.org/wiki/Q2225","display_name":"Electron","level":2,"score":0.5166521668434143},{"id":"https://openalex.org/C25810664","wikidata":"https://www.wikidata.org/wiki/Q44325","display_name":"Ontology","level":2,"score":0.45054683089256287},{"id":"https://openalex.org/C165391973","wikidata":"https://www.wikidata.org/wiki/Q844304","display_name":"Total electron content","level":4,"score":0.42011162638664246},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3308684527873993},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3270265758037567},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.20125660300254822},{"id":"https://openalex.org/C8058405","wikidata":"https://www.wikidata.org/wiki/Q46255","display_name":"Geophysics","level":1,"score":0.16573044657707214},{"id":"https://openalex.org/C185544564","wikidata":"https://www.wikidata.org/wiki/Q81197","display_name":"Nuclear physics","level":1,"score":0.14050692319869995},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.12282949686050415},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.1030806303024292},{"id":"https://openalex.org/C116403925","wikidata":"https://www.wikidata.org/wiki/Q162219","display_name":"Ionosphere","level":2,"score":0.08988937735557556},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08925902843475342},{"id":"https://openalex.org/C176379880","wikidata":"https://www.wikidata.org/wiki/Q18031939","display_name":"TEC","level":3,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s12145-024-01294-7","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s12145-024-01294-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s12145-024-01294-7.pdf","source":{"id":"https://openalex.org/S198914822","display_name":"Earth Science Informatics","issn_l":"1865-0473","issn":["1865-0473","1865-0481"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Earth Science Informatics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s12145-024-01294-7","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s12145-024-01294-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s12145-024-01294-7.pdf","source":{"id":"https://openalex.org/S198914822","display_name":"Earth Science Informatics","issn_l":"1865-0473","issn":["1865-0473","1865-0481"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Earth Science Informatics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4394616145.pdf"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W1889491664","https://openalex.org/W1995341919","https://openalex.org/W1997349402","https://openalex.org/W2007940437","https://openalex.org/W2029116031","https://openalex.org/W2040870580","https://openalex.org/W2085101070","https://openalex.org/W2102636708","https://openalex.org/W2135447106","https://openalex.org/W2147800946","https://openalex.org/W2151554678","https://openalex.org/W2194300422","https://openalex.org/W2395409059","https://openalex.org/W2765415009","https://openalex.org/W2963484873","https://openalex.org/W3000320953","https://openalex.org/W3009289413","https://openalex.org/W3033830765","https://openalex.org/W3171696226","https://openalex.org/W3182706339","https://openalex.org/W3196170282","https://openalex.org/W3200350000","https://openalex.org/W3201603229","https://openalex.org/W3207764986","https://openalex.org/W4249736682","https://openalex.org/W4285283281","https://openalex.org/W4286209456","https://openalex.org/W4300789312","https://openalex.org/W4378070286"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2935759653","https://openalex.org/W3105167352","https://openalex.org/W54078636","https://openalex.org/W2954470139","https://openalex.org/W1501425562","https://openalex.org/W2902782467","https://openalex.org/W3084825885","https://openalex.org/W4391427275","https://openalex.org/W4398607867"],"abstract_inverted_index":{"Abstract":[0],"We":[1,268],"design":[2,176],"physics-informed":[3,34,179,287,495],"loss":[4,35,180,288,302,311,387,442,449,469,496],"functions":[5,289],"for":[6,102,344,501],"training":[7,106],"Artificial":[8],"Neural":[9],"Network":[10],"(ANN)":[11],"models":[12,31,105],"to":[13,24,87,115,125,280,299,391,400,434,446,475],"forecast":[14],"the":[15,40,103,116,127,133,136,155,175,178,184,190,215,223,229,232,238,257,262,272,295,300,309,316,319,329,345,385,392,401,432,440,447,467,476,480,484,491,502,506],"ionospheric":[16,507],"vertical":[17],"Total":[18],"Electron":[19],"Content":[20],"(vTEC)":[21],"from":[22,83],"1":[23,353],"24":[25],"hours":[26],"in":[27,113,174,271,315,328],"advance.":[28],"The":[29,78,381],"ANN":[30,104,234,296,317,382,481],"exploit":[32],"our":[33,286,487],"functions,":[36],"data":[37],"provided":[38],"by":[39,109,408,437],"Global":[41],"Navigation":[42],"Satellite":[43],"Systems":[44],"(GNSS)":[45],"receiver":[46],"installed":[47],"at":[48,119,278,282],"Tsukuba":[49],"(36.06":[50],"$$^{o}$$":[51,61],"<mml:math":[52,62,142,196,247,359,371,418,456],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[53,63,143,197,248,360,372,419,457],"<mml:msup>":[54,64,249,361,373],"<mml:mrow/>":[55,65],"<mml:mi>o</mml:mi>":[56,66],"</mml:msup>":[57,67,254,366,378],"</mml:math>":[58,68,152,212,255,367,379,430,462],"N,":[59],"140.05":[60],"E),":[69],"Japan,":[70],"and":[71,75,154,214,218,261,332,341,348,389],"external":[72,100],"drivers":[73,101],"(solar":[74],"geomagnetic":[76],"indices).":[77],"time":[79,493],"series":[80],"used":[81,314],"span":[82],"January":[84],"1,":[85],"2006,":[86],"December":[88],"31,":[89],"2018,":[90],"i.e.,":[91],"a":[92,161,291,396,410,472,494],"full":[93],"solar":[94,191],"cycle.":[95],"A":[96],"proper":[97],"set":[98,163],"of":[99,135,164,177,222,231,242,285,294,479,486,504],"are":[107,183],"selected":[108],"ranking":[110],"their":[111],"importance":[112],"relation":[114],"vTEC":[117],"dynamics":[118],"different":[120],"forecasting":[121,326,477,505],"horizons.":[122],"They":[123,182],"result":[124],"be":[126],"10.7":[128],"cm":[129],"Solar":[130],"Flux":[131],"(F10.7),":[132],"magnitude":[134],"Interplanetary":[137],"Magnetic":[138],"Field":[139],"(IMF)":[140],"$$\\boldsymbol{B}_{\\boldsymbol{T}}$$":[141],"<mml:msub>":[144,203],"<mml:mrow>":[145,148,198,199,204,207,250,362,374,420,421,425,458],"<mml:mi>B</mml:mi>":[146,205],"</mml:mrow>":[147,150,201,206,209,211,252,364,376,423,428,429,461],"<mml:mi>T</mml:mi>":[149,208],"</mml:msub>":[151,210],",":[153,213,431],"Auroral":[156],"Electrojet":[157],"(AE)":[158],"index.":[159],"Moreover,":[160],"second":[162],"indices":[165],"among":[166],"those":[167],"available":[168],"has":[169,498],"been":[170,499],"considered":[171],"as":[172,444],"constraints":[173],"functions.":[181],"Disturbance":[185],"Storm":[186],"Time":[187],"(Dst)":[188],"index,":[189],"wind":[192],"speed":[193],"$$\\boldsymbol{v},":[194],"\\boldsymbol{B}_{\\boldsymbol{T}}$$":[195],"<mml:mi>v</mml:mi>":[200],"<mml:mo>,</mml:mo>":[202],"B":[216,219],"y":[217],"z":[220],"components":[221],"interplanetary":[224],"magnetic":[225],"field.":[226],"To":[227,483],"assess":[228],"performance":[230,293],"resulting":[233],"models,":[235],"we":[236],"use":[237],"statistical":[239,473],"parameter":[240],"coefficient":[241],"determination":[243],"(":[244],"$$\\boldsymbol{R}^{{\\textbf":[245],"{2}}}$$":[246,370],"<mml:mi>R</mml:mi>":[251],"<mml:mn>2</mml:mn>":[253,377],"),":[256,463],"standard":[258,301,448],"deviation":[259],"(SD),":[260],"Wilcoxon":[263,402],"non-parametric":[264],"signed":[265,403],"ranked":[266,404],"test.":[267,405],"show":[269],"that,":[270],"testing":[273],"period":[274],"analyzed":[275],"(from":[276],"2017-09-13,":[277],"04:40:00,":[279],"2018-12-31,":[281],"23:55:00),":[283],"one":[284],"provides":[290],"better":[292],"with":[297,439],"regard":[298],"function":[303,312,388,443,450,470,497],"commonly":[304],"adopted.":[305],"In":[306,406],"particular,":[307],"when":[308],"new":[310,386,441,468],"is":[313,322,336,451,490],"model,":[318,383],"average":[320],"SD":[321,335],"minimized":[323],"across":[324],"all":[325],"horizons":[327],"training,":[330,346],"validation":[331,347],"test":[333,349,393],"datasets.":[334],"0.2560":[337],"TECU,":[338],"0.3183":[339],"TECU":[340,343,354],"0.4240":[342],"dataset":[350],"respectively,":[351],"where":[352],"=":[355],"$${\\textbf":[356],"{10}}^{{\\textbf":[357],"{16}}}$$":[358],"<mml:mn>10</mml:mn>":[363],"<mml:mn>16</mml:mn>":[365],"electrons/":[368],"$$\\boldsymbol{m}^{{\\textbf":[369],"<mml:mi>m</mml:mi>":[375],".":[380],"incorporating":[384],"applied":[390],"dataset,":[394],"shows":[395],"significant":[397],"improvement":[398,474],"according":[399],"fact":[407],"selecting":[409],"significance":[411],"level":[412],"$$\\boldsymbol{\\alpha":[413],"}~":[414],"\\mathbf":[415],"{=":[416],"0.05}$$":[417],"<mml:mi>\u03b1</mml:mi>":[422,460],"<mml:mspace/>":[424],"<mml:mo>=</mml:mo>":[426],"<mml:mn>0.05</mml:mn>":[427],"probability":[433],"obtain":[435],"results":[436],"chance":[438],"compared":[445],"0.01504":[452],"(i.e.,":[453],"$$&lt;\\alpha":[454],"$$":[455],"<mml:mo>&lt;</mml:mo>":[459],"which":[464],"implies":[465],"that":[466],"gives":[471],"capability":[478],"model.":[482],"best":[485],"knowledge,":[488],"this":[489],"first":[492],"designed":[500],"task":[503],"vTEC.":[508]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2025-12-19T19:40:27.379048","created_date":"2025-10-10T00:00:00"}
