{"id":"https://openalex.org/W3017301308","doi":"https://doi.org/10.48550/arxiv.2004.08151","title":"Accelerating Physics-Informed Neural Network Training with Prior Dictionaries","display_name":"Accelerating Physics-Informed Neural Network Training with Prior Dictionaries","publication_year":2020,"publication_date":"2020-04-17","ids":{"openalex":"https://openalex.org/W3017301308","doi":"https://doi.org/10.48550/arxiv.2004.08151","mag":"3017301308"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2004.08151","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2004.08151","pdf_url":"https://arxiv.org/pdf/2004.08151","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,"listed_in":[],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2004.08151","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101990146","display_name":"Wei Peng","orcid":"https://orcid.org/0000-0002-4994-8965","observed_orcids":["https://orcid.org/0000-0002-4994-8965"]},"institutions":[{"id":"https://openalex.org/I4210158522","display_name":"PLA Academy of Military Science","ror":"https://ror.org/05ct4s596","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210158522"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Peng, Wei","raw_affiliation_strings":["National Innovation Institute of Defense Technology , Chinese Academy of Military Science , 100071 , Beijing "],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"National Innovation Institute of Defense Technology , Chinese Academy of Military Science , 100071 , Beijing ","institution_ids":["https://openalex.org/I4210158522"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001113052","display_name":"Weien Zhou","orcid":"https://orcid.org/0000-0001-9833-679X","observed_orcids":["https://orcid.org/0000-0001-9833-679X"]},"institutions":[{"id":"https://openalex.org/I4210158522","display_name":"PLA Academy of Military Science","ror":"https://ror.org/05ct4s596","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210158522"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhou, Weien","raw_affiliation_strings":["National Innovation Institute of Defense Technology , Chinese Academy of Military Science , 100071 , Beijing "],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"National Innovation Institute of Defense Technology , Chinese Academy of Military Science , 100071 , Beijing ","institution_ids":["https://openalex.org/I4210158522"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057894212","display_name":"Jun Zhang","orcid":"https://orcid.org/0000-0002-3516-0392","observed_orcids":["https://orcid.org/0000-0002-3516-0392"]},"institutions":[{"id":"https://openalex.org/I4210158522","display_name":"PLA Academy of Military Science","ror":"https://ror.org/05ct4s596","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210158522"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhang, Jun","raw_affiliation_strings":["National Innovation Institute of Defense Technology , Chinese Academy of Military Science , 100071 , Beijing "],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"National Innovation Institute of Defense Technology , Chinese Academy of Military Science , 100071 , Beijing ","institution_ids":["https://openalex.org/I4210158522"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5089866078","display_name":"Wen Yao","orcid":"https://orcid.org/0000-0001-5224-9834","observed_orcids":["https://orcid.org/0000-0001-5224-9834","https://orcid.org/0000-0001-6730-1201","https://orcid.org/0009-0007-5260-4737","https://orcid.org/0000-0002-3726-7716"]},"institutions":[{"id":"https://openalex.org/I4210158522","display_name":"PLA Academy of Military Science","ror":"https://ror.org/05ct4s596","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210158522"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yao, Wen","raw_affiliation_strings":["National Innovation Institute of Defense Technology , Chinese Academy of Military Science , 100071 , Beijing "],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"National Innovation Institute of Defense Technology , Chinese Academy of Military Science , 100071 , Beijing ","institution_ids":["https://openalex.org/I4210158522"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I4210158522"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":26,"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":1.0,"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":1.0,"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/T10320","display_name":"Neural Networks and Applications","score":0.0,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/physics-informed-neural-networks","display_name":"physics-informed neural networks","score":1.0},{"id":"https://openalex.org/keywords/elliptic-equations","display_name":"elliptic equations","score":0.8370000123977661},{"id":"https://openalex.org/keywords/error-bounds","display_name":"error bounds","score":0.7799999713897705},{"id":"https://openalex.org/keywords/convergence-acceleration","display_name":"convergence acceleration","score":0.8629999756813049},{"id":"https://openalex.org/keywords/pde-solvers","display_name":"PDE solvers","score":0.8159999847412109},{"id":"https://openalex.org/keywords/power-of-representation","display_name":"power of representation","score":0.5009999871253967}],"concepts":[{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.717812716960907},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.714958906173706},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6213594079017639},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.570513129234314},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5657463073730469},{"id":"https://openalex.org/C2780451532","wikidata":"https://www.wikidata.org/wiki/Q759676","display_name":"Task (project management)","level":2,"score":0.5604755878448486},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.47536414861679077},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4706648588180542},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.4704282283782959},{"id":"https://openalex.org/C2777211547","wikidata":"https://www.wikidata.org/wiki/Q17141490","display_name":"Training (meteorology)","level":2,"score":0.4375249445438385},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4260568916797638},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.40588560700416565},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.38510093092918396},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.34950846433639526},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2564813792705536},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12378692626953125},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08908295631408691},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C153294291","wikidata":"https://www.wikidata.org/wiki/Q25261","display_name":"Meteorology","level":1,"score":0.0},{"id":"https://openalex.org/C187736073","wikidata":"https://www.wikidata.org/wiki/Q2920921","display_name":"Management","level":1,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2004.08151","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2004.08151","pdf_url":"https://arxiv.org/pdf/2004.08151","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,"listed_in":[],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2004.08151","doi":"https://doi.org/10.48550/arxiv.2004.08151","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2004.08151","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,"listed_in":[],"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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2004.08151","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2004.08151","pdf_url":"https://arxiv.org/pdf/2004.08151","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,"listed_in":[],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G2323976895","display_name":null,"funder_award_id":"51675525","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2404692483","display_name":null,"funder_award_id":"11725211","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W1912930600","https://openalex.org/W1996058586","https://openalex.org/W1996087276","https://openalex.org/W2031402837","https://openalex.org/W2046793177","https://openalex.org/W2098386213","https://openalex.org/W2109109045","https://openalex.org/W2338839614","https://openalex.org/W2534240011","https://openalex.org/W2534606940","https://openalex.org/W2772097715","https://openalex.org/W2899283552","https://openalex.org/W2903660960","https://openalex.org/W2948551291","https://openalex.org/W2957969499","https://openalex.org/W2964121744","https://openalex.org/W2975003945","https://openalex.org/W2994720379","https://openalex.org/W3197818647"],"related_works":["https://openalex.org/W4403335352","https://openalex.org/W4386044542","https://openalex.org/W4390872183","https://openalex.org/W4405235253","https://openalex.org/W4312309134","https://openalex.org/W4307473893","https://openalex.org/W4400076414","https://openalex.org/W3186083829","https://openalex.org/W4399317767","https://openalex.org/W4221153175"],"abstract_inverted_index":{"Physics-Informed":[0,43],"Neural":[1,44],"Networks":[2,45],"(PINNs)":[3],"can":[4,73,94,137],"be":[5,14,138],"regarded":[6],"as":[7],"general-purpose":[8],"PDE":[9],"solvers,":[10],"but":[11],"it":[12],"might":[13],"slow":[15],"to":[16,61,109],"train":[17],"PINNs":[18,110],"on":[19,56],"particular":[20],"problems,":[21],"and":[22,111,145],"there":[23],"is":[24,123],"no":[25],"theoretical":[26],"guarantee":[27],"of":[28,80,101,119,143],"corresponding":[29],"error":[30,106,132],"bounds.":[31],"In":[32,82,99],"this":[33],"manuscript,":[34],"we":[35,103],"propose":[36],"a":[37],"variant":[38],"called":[39],"Prior":[40],"Dictionary":[41],"based":[42],"(PD-PINNs).":[46],"Equipped":[47],"with":[48,87],"task-dependent":[49],"dictionaries,":[50],"PD-PINNs":[51,112],"enjoy":[52],"enhanced":[53],"representation":[54],"power":[55],"the":[57,69,78,105,130],"tasks,":[58],"which":[59],"helps":[60],"capture":[62],"features":[63],"provided":[64],"by":[65,134,140],"dictionaries":[66,93],"so":[67],"that":[68,125],"proposed":[70],"neural":[71,135],"networks":[72,136],"achieve":[74],"faster":[75],"convergence":[76,97],"in":[77],"process":[79],"training.":[81],"various":[83],"numerical":[84],"simulations,":[85],"compared":[86],"existing":[88],"PINN":[89],"methods,":[90],"combining":[91],"prior":[92],"significantly":[95],"enhance":[96],"speed.":[98],"terms":[100],"theory,":[102],"obtain":[104],"bounds":[107],"applicable":[108],"for":[113],"solving":[114],"elliptic":[115],"partial":[116],"differential":[117],"equations":[118],"second":[120],"order.":[121],"It":[122],"proved":[124],"under":[126],"certain":[127],"mild":[128],"conditions,":[129],"prediction":[131],"made":[133],"bounded":[139],"expected":[141],"loss":[142],"PDEs":[144],"boundary":[146],"conditions.":[147]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":11},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":2}],"updated_date":"2026-10-16T09:59:22.235173","created_date":"2020-04-24T00:00:00"}
