{"id":"https://openalex.org/W7162112560","doi":"https://doi.org/10.48550/arxiv.2605.22115","title":"Physics-Informed Neural Networks with Attention Feature Expansion for Monge-Amp\u00e8re Equations","display_name":"Physics-Informed Neural Networks with Attention Feature Expansion for Monge-Amp\u00e8re Equations","publication_year":2026,"publication_date":"2026-05-21","ids":{"openalex":"https://openalex.org/W7162112560","doi":"https://doi.org/10.48550/arxiv.2605.22115"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.22115","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.22115","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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.2605.22115","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5136768974","display_name":"Anxiao Yu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yu, Anxiao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040707822","display_name":"Bangmin Wu","orcid":"https://orcid.org/0009-0001-1798-5868"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wu, Bangmin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5136735813","display_name":"Zhengbang Zha","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zha, Zhengbang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5136744471","display_name":"Xinlong Feng","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Feng, Xinlong","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5047277085","display_name":"Dongwoo Sheen","orcid":"https://orcid.org/0000-0001-6857-7883"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sheen, Dongwoo","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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9793999791145325,"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":0.9793999791145325,"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/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.0031999999191612005,"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"}},{"id":"https://openalex.org/T12794","display_name":"Adaptive Dynamic Programming Control","score":0.0012000000569969416,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/feature","display_name":"Feature (linguistics)","score":0.7044000029563904},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.651199996471405},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.6312999725341797},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5949000120162964},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.5292999744415283},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.521399974822998},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.44929999113082886},{"id":"https://openalex.org/keywords/image-processing","display_name":"Image processing","score":0.3824999928474426}],"concepts":[{"id":"https://openalex.org/C2776401178","wikidata":"https://www.wikidata.org/wiki/Q12050496","display_name":"Feature (linguistics)","level":2,"score":0.7044000029563904},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.651199996471405},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.6312999725341797},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5949000120162964},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5936999917030334},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.5292999744415283},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5242999792098999},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.521399974822998},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.44929999113082886},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.39649999141693115},{"id":"https://openalex.org/C9417928","wikidata":"https://www.wikidata.org/wiki/Q1070689","display_name":"Image processing","level":3,"score":0.3824999928474426},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.3668999969959259},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.3343999981880188},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3312999904155731},{"id":"https://openalex.org/C812465","wikidata":"https://www.wikidata.org/wiki/Q5058375","display_name":"Cellular neural network","level":3,"score":0.328000009059906},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3190000057220459},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.2955000102519989},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.2903999984264374},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.2897000014781952},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.2840999960899353},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2632000148296356},{"id":"https://openalex.org/C52622490","wikidata":"https://www.wikidata.org/wiki/Q1026626","display_name":"Feature extraction","level":2,"score":0.2596000134944916},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.2547000050544739}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.22115","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.22115","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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.2605.22115","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.22115","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"The":[0,97],"Monge-Amp\u00e8re":[1],"equation":[2,11],"is":[3,43,78,100],"a":[4,22,69],"fundamental":[5],"fully":[6],"nonlinear":[7,48],"elliptic":[8],"partial":[9],"differential":[10],"that":[12],"finds":[13],"extensive":[14],"applications":[15],"across":[16],"multiple":[17],"disciplines.":[18],"This":[19],"study":[20],"proposes":[21],"novel":[23],"physics-informed":[24],"neural":[25,54],"network":[26],"integrated":[27],"with":[28,64,75],"attention":[29,39],"feature":[30,41,49],"expansion":[31],"(PINN-AFE)":[32],"for":[33],"its":[34],"numerical":[35,85],"solution.":[36],"A":[37],"multi-head":[38],"enhanced":[40],"pool":[42],"constructed":[44],"to":[45,58,80,103],"enable":[46],"adaptive":[47],"representation,":[50],"and":[51,90,109,117],"input":[52],"convex":[53],"networks":[55],"are":[56],"adopted":[57],"impose":[59],"strict":[60],"convexity":[61],"of":[62,93],"solutions":[63],"rigorous":[65],"theoretical":[66],"guarantees.":[67],"Meanwhile,":[68],"dynamically":[70],"weighted":[71],"loss":[72],"function":[73],"combined":[74],"hybrid":[76],"optimization":[77],"formulated":[79],"accelerate":[81],"training":[82],"convergence.":[83],"Comprehensive":[84],"experiments":[86],"validate":[87],"the":[88,94],"accuracy":[89],"computational":[91],"efficiency":[92],"developed":[95],"framework.":[96],"PINN-AFE":[98],"paradigm":[99],"further":[101],"extended":[102],"image":[104,115,119],"processing":[105],"tasks,":[106],"delivering":[107],"high-quality":[108],"physically":[110],"consistent":[111],"results":[112],"in":[113],"both":[114],"enhancement":[116],"medical":[118],"registration":[120],"scenarios.":[121]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-05-23T00:00:00"}