{"id":"https://openalex.org/W4416749947","doi":"https://doi.org/10.1109/access.2025.3638011","title":"Neural Networks Under Hamiltonian Constraints: A Comprehensive Review on Structural Evolution and Applications","display_name":"Neural Networks Under Hamiltonian Constraints: A Comprehensive Review on Structural Evolution and Applications","publication_year":2025,"publication_date":"2025-01-01","ids":{"openalex":"https://openalex.org/W4416749947","doi":"https://doi.org/10.1109/access.2025.3638011"},"language":"en","primary_location":{"id":"doi:10.1109/access.2025.3638011","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2025.3638011","pdf_url":null,"source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.1109/access.2025.3638011","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Zhiyi Zhang","orcid":"https://orcid.org/0009-0007-1143-4524"},"institutions":[{"id":"https://openalex.org/I22046295","display_name":"Inner Mongolia Normal University","ror":"https://ror.org/0497ase59","country_code":"CN","type":"education","lineage":["https://openalex.org/I22046295"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhiyi Zhang","raw_affiliation_strings":["College of Computer Science and Technology, Inner Mongolia Normal University, Hohhot, China"],"raw_orcid":"https://orcid.org/0009-0007-1143-4524","affiliations":[{"raw_affiliation_string":"College of Computer Science and Technology, Inner Mongolia Normal University, Hohhot, China","institution_ids":["https://openalex.org/I22046295"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018906028","display_name":"Shuangcheng Bai","orcid":"https://orcid.org/0000-0001-7335-8589"},"institutions":[{"id":"https://openalex.org/I22046295","display_name":"Inner Mongolia Normal University","ror":"https://ror.org/0497ase59","country_code":"CN","type":"education","lineage":["https://openalex.org/I22046295"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shuangcheng Bai","raw_affiliation_strings":["College of Artificial Intelligence, Inner Mongolia Normal University, Hohhot, China"],"raw_orcid":"https://orcid.org/0000-0001-7335-8589","affiliations":[{"raw_affiliation_string":"College of Artificial Intelligence, Inner Mongolia Normal University, Hohhot, China","institution_ids":["https://openalex.org/I22046295"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101578572","display_name":"Yongqi Liang","orcid":"https://orcid.org/0000-0002-9900-1657"},"institutions":[{"id":"https://openalex.org/I22046295","display_name":"Inner Mongolia Normal University","ror":"https://ror.org/0497ase59","country_code":"CN","type":"education","lineage":["https://openalex.org/I22046295"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yongqi Liang","raw_affiliation_strings":["College of Computer Science and Technology, Inner Mongolia Normal University, Hohhot, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Computer Science and Technology, Inner Mongolia Normal University, Hohhot, China","institution_ids":["https://openalex.org/I22046295"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5084389739","display_name":"Zhengyi Bao","orcid":"https://orcid.org/0000-0001-7206-188X"},"institutions":[{"id":"https://openalex.org/I22046295","display_name":"Inner Mongolia Normal University","ror":"https://ror.org/0497ase59","country_code":"CN","type":"education","lineage":["https://openalex.org/I22046295"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhengyi Bao","raw_affiliation_strings":["College of Artificial Intelligence, Inner Mongolia Normal University, Hohhot, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Artificial Intelligence, Inner Mongolia Normal University, Hohhot, China","institution_ids":["https://openalex.org/I22046295"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I22046295"],"apc_list":{"value":1850,"currency":"USD","value_usd":1850},"apc_paid":{"value":1850,"currency":"USD","value_usd":1850},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.25605938,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"13","issue":null,"first_page":"208017","last_page":"208033"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.47589999437332153,"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"}},"topics":[{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.47589999437332153,"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"}},{"id":"https://openalex.org/T11948","display_name":"Machine Learning in Materials Science","score":0.21539999544620514,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11804","display_name":"Quantum many-body systems","score":0.1315000057220459,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.6682000160217285},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.552299976348877},{"id":"https://openalex.org/keywords/conservation-of-energy","display_name":"Conservation of energy","score":0.5275999903678894},{"id":"https://openalex.org/keywords/leverage","display_name":"Leverage (statistics)","score":0.5267999768257141},{"id":"https://openalex.org/keywords/hamiltonian-mechanics","display_name":"Hamiltonian mechanics","score":0.5088000297546387},{"id":"https://openalex.org/keywords/energy-conservation","display_name":"Energy conservation","score":0.45820000767707825}],"concepts":[{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.6682000160217285},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6669999957084656},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.552299976348877},{"id":"https://openalex.org/C52957995","wikidata":"https://www.wikidata.org/wiki/Q11382","display_name":"Conservation of energy","level":2,"score":0.5275999903678894},{"id":"https://openalex.org/C153083717","wikidata":"https://www.wikidata.org/wiki/Q6535263","display_name":"Leverage (statistics)","level":2,"score":0.5267999768257141},{"id":"https://openalex.org/C136864674","wikidata":"https://www.wikidata.org/wiki/Q477921","display_name":"Hamiltonian mechanics","level":3,"score":0.5088000297546387},{"id":"https://openalex.org/C520301825","wikidata":"https://www.wikidata.org/wiki/Q380170","display_name":"Energy conservation","level":2,"score":0.45820000767707825},{"id":"https://openalex.org/C3445786","wikidata":"https://www.wikidata.org/wiki/Q205805","display_name":"Conservation law","level":2,"score":0.4390000104904175},{"id":"https://openalex.org/C121770821","wikidata":"https://www.wikidata.org/wiki/Q2072471","display_name":"Hamiltonian system","level":2,"score":0.4223000109195709},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.41589999198913574},{"id":"https://openalex.org/C39890363","wikidata":"https://www.wikidata.org/wiki/Q36108","display_name":"Generative grammar","level":2,"score":0.3228999972343445},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.31119999289512634},{"id":"https://openalex.org/C2742236","wikidata":"https://www.wikidata.org/wiki/Q924713","display_name":"Efficient energy use","level":2,"score":0.30169999599456787},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.29670000076293945},{"id":"https://openalex.org/C116672817","wikidata":"https://www.wikidata.org/wiki/Q1454986","display_name":"Physical system","level":2,"score":0.26669999957084656},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.2581000030040741}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/access.2025.3638011","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2025.3638011","pdf_url":null,"source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:c9e3cf18bdbc4279b2b64a0fe38c7077","is_oa":true,"landing_page_url":"https://doaj.org/article/c9e3cf18bdbc4279b2b64a0fe38c7077","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Access, Vol 13, Pp 208017-208033 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1109/access.2025.3638011","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2025.3638011","pdf_url":null,"source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3815877718","display_name":null,"funder_award_id":"20XYY027","funder_id":"https://openalex.org/F4320335869","funder_display_name":"National Social Science Fund of China"},{"id":"https://openalex.org/G4074283696","display_name":null,"funder_award_id":"NMGIRT2414","funder_id":"https://openalex.org/F4320327830","funder_display_name":"Research Program of Science and Technology at Universities of Inner Mongolia Autonomous Region"}],"funders":[{"id":"https://openalex.org/F4320327830","display_name":"Research Program of Science and Technology at Universities of Inner Mongolia Autonomous Region","ror":null},{"id":"https://openalex.org/F4320335869","display_name":"National Social Science Fund of China","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Traditional":[0],"algorithms":[1],"and":[2,16,46,66,74,92,110,120,138,150,158,180],"neural":[3,37,77,95,129,166],"networks":[4,78,130,167],"often":[5],"suffer":[6],"from":[7],"energy":[8,45,104,136],"drift":[9],"in":[10,29,57,125,134],"long-term":[11],"predictions":[12],"when":[13],"modeling":[14],"simple":[15],"fundamental":[17,63],"natural":[18],"laws,":[19],"primarily":[20],"due":[21],"to":[22,54,146,154],"the":[23,42,72,118,162],"lack":[24],"of":[25,44,50,76,112,122,164],"inductive":[26],"biases":[27],"rooted":[28],"physical":[30,140],"structures.":[31],"By":[32],"incorporating":[33],"Hamiltonian":[34,51,81,88,94,165],"mechanics":[35],"into":[36],"networks,":[38,96],"these":[39,123],"models":[40,124,171],"leverage":[41],"conservation":[43,105,137],"other":[47],"desirable":[48],"properties":[49],"systems,":[52],"leading":[53],"improved":[55],"performance":[56,157],"tasks":[58,179],"such":[59],"as":[60],"trajectory":[61],"prediction,":[62],"law":[64],"learning,":[65],"image":[67],"recognition.":[68],"This":[69],"study":[70],"reviews":[71],"development":[73],"applications":[75],"constructed":[79],"with":[80,168],"mechanics.":[82],"We":[83],"analyze":[84],"two":[85],"main":[86],"categories:":[87],"Neural":[89],"Networks":[90],"(HNNs)":[91],"generative":[93],"focusing":[97],"on":[98],"their":[99],"architectural":[100],"designs,":[101],"data":[102],"representations,":[103],"capabilities,":[106],"loss":[107],"function":[108],"formulations,":[109],"choices":[111],"numerical":[113],"integrators.":[114],"Furthermore,":[115],"we":[116],"assess":[117],"advantages":[119],"challenges":[121],"real-world":[126],"applications.":[127],"Hamiltonian-based":[128],"demonstrate":[131],"significant":[132],"potential":[133],"preserving":[135],"enhancing":[139],"consistency.":[141],"Future":[142],"research":[143],"should":[144],"aim":[145],"optimize":[147],"network":[148],"architectures":[149],"parameter":[151],"update":[152],"mechanisms":[153],"improve":[155],"both":[156],"interpretability.":[159],"Additionally,":[160],"exploring":[161],"integration":[163],"large":[169],"language":[170],"may":[172],"offer":[173],"novel":[174],"insights":[175],"for":[176],"tackling":[177],"complex":[178],"achieving":[181],"more":[182],"efficient":[183],"learning.":[184]},"counts_by_year":[],"updated_date":"2025-12-19T00:32:22.182498","created_date":"2025-11-28T00:00:00"}