{"id":"https://openalex.org/W4412928992","doi":"https://doi.org/10.1063/5.0281713","title":"Phase-field physics-informed neural networks for multiphase flow simulations in axisymmetric coordinates with applications of bubble rising in multiple regimes","display_name":"Phase-field physics-informed neural networks for multiphase flow simulations in axisymmetric coordinates with applications of bubble rising in multiple regimes","publication_year":2025,"publication_date":"2025-08-01","ids":{"openalex":"https://openalex.org/W4412928992","doi":"https://doi.org/10.1063/5.0281713"},"language":"en","primary_location":{"id":"doi:10.1063/5.0281713","doi":"https://doi.org/10.1063/5.0281713","is_oa":false,"landing_page_url":"https://doi.org/10.1063/5.0281713","pdf_url":null,"source":{"id":"https://openalex.org/S22862804","display_name":"Physics of Fluids","issn_l":"1070-6631","issn":["1070-6631","1089-7666","1527-2435"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-d","jufo-1","ki-jl-1","norway-1","poland-100","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320257","host_organization_name":"American Institute of Physics","host_organization_lineage":["https://openalex.org/P4310320257"],"host_organization_lineage_names":["American Institute of Physics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physics of Fluids","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5016563009","display_name":"Chi-Chao Huang","orcid":"https://orcid.org/0009-0009-3552-692X","observed_orcids":["https://orcid.org/0009-0009-3552-692X"]},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210157653","display_name":"Institute of Mechanics","ror":"https://ror.org/057jnjd73","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210157653"]},{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chichao Huang","raw_affiliation_strings":["Key Laboratory for Mechanics in Fluid Solid Coupling Systems, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China","School of Future Technology, University of Chinese Academy of Sciences, Beijing 100049, China"],"raw_orcid":"https://orcid.org/0009-0009-3552-692X","affiliations":[{"raw_affiliation_string":"Key Laboratory for Mechanics in Fluid Solid Coupling Systems, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210157653"]},{"raw_affiliation_string":"School of Future Technology, University of Chinese Academy of Sciences, Beijing 100049, China","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5050386935","display_name":"Guanghang Wang","orcid":"https://orcid.org/0000-0002-0681-6153","observed_orcids":["https://orcid.org/0000-0002-0681-6153"]},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210157653","display_name":"Institute of Mechanics","ror":"https://ror.org/057jnjd73","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210157653"]},{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Guanghang Wang","raw_affiliation_strings":["Key Laboratory for Mechanics in Fluid Solid Coupling Systems, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China","School of Future Technology, University of Chinese Academy of Sciences, Beijing 100049, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Key Laboratory for Mechanics in Fluid Solid Coupling Systems, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210157653"]},{"raw_affiliation_string":"School of Future Technology, University of Chinese Academy of Sciences, Beijing 100049, China","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048839933","display_name":"Jingzhu Wang","orcid":"https://orcid.org/0000-0003-3032-4068","observed_orcids":["https://orcid.org/0000-0003-3032-4068"]},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210157653","display_name":"Institute of Mechanics","ror":"https://ror.org/057jnjd73","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210157653"]},{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jingzhu Wang","raw_affiliation_strings":["Guangdong Aerospace Research Academy, Guangzhou 511458, People's Republic of China","Key Laboratory for Mechanics in Fluid Solid Coupling Systems, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China","School of Engineering Science, University of Chinese Academy of Sciences, Beijing 100049, China"],"raw_orcid":"https://orcid.org/0000-0003-3032-4068","affiliations":[{"raw_affiliation_string":"Guangdong Aerospace Research Academy, Guangzhou 511458, People's Republic of China","institution_ids":[]},{"raw_affiliation_string":"Key Laboratory for Mechanics in Fluid Solid Coupling Systems, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210157653"]},{"raw_affiliation_string":"School of Engineering Science, University of Chinese Academy of Sciences, Beijing 100049, China","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5031801103","display_name":"Rundi Qiu","orcid":"https://orcid.org/0009-0005-9236-1691","observed_orcids":["https://orcid.org/0009-0005-9236-1691"]},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210157653","display_name":"Institute of Mechanics","ror":"https://ror.org/057jnjd73","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210157653"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Rundi Qiu","raw_affiliation_strings":["Key Laboratory for Mechanics in Fluid Solid Coupling Systems, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China"],"raw_orcid":"https://orcid.org/0009-0005-9236-1691","affiliations":[{"raw_affiliation_string":"Key Laboratory for Mechanics in Fluid Solid Coupling Systems, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210157653"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100397326","display_name":"Yiwei Wang","orcid":"https://orcid.org/0000-0003-2803-5048","observed_orcids":["https://orcid.org/0000-0003-2803-5048","https://orcid.org/0000-0002-1267-9669"]},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210157653","display_name":"Institute of Mechanics","ror":"https://ror.org/057jnjd73","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210157653"]},{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yiwei Wang","raw_affiliation_strings":["Key Laboratory for Mechanics in Fluid Solid Coupling Systems, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China","School of Engineering Science, University of Chinese Academy of Sciences, Beijing 100049, China","School of Future Technology, University of Chinese Academy of Sciences, Beijing 100049, China"],"raw_orcid":"https://orcid.org/0000-0003-2803-5048","affiliations":[{"raw_affiliation_string":"Key Laboratory for Mechanics in Fluid Solid Coupling Systems, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210157653"]},{"raw_affiliation_string":"School of Engineering Science, University of Chinese Academy of Sciences, Beijing 100049, China","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]},{"raw_affiliation_string":"School of Future Technology, University of Chinese Academy of Sciences, Beijing 100049, China","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.8959,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.71275121,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":97},"biblio":{"volume":"37","issue":"8","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":0.8622999787330627,"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":0.8622999787330627,"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/T11382","display_name":"Fluid Dynamics and Heat Transfer","score":0.13279999792575836,"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"}},{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.0005000000237487257,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/physics-informed-neural-networks","display_name":"physics-informed neural networks","score":0.8989999890327454},{"id":"https://openalex.org/keywords/phase-field-model","display_name":"phase-field model","score":0.8809999823570251},{"id":"https://openalex.org/keywords/multiphase-flow","display_name":"multiphase flow","score":0.9390000104904175},{"id":"https://openalex.org/keywords/bubble-rise","display_name":"bubble rise","score":0.9539999961853027},{"id":"https://openalex.org/keywords/weighted-sampling","display_name":"weighted sampling","score":0.7149999737739563},{"id":"https://openalex.org/keywords/interfacial-dynamics","display_name":"interfacial dynamics","score":0.4620000123977661},{"id":"https://openalex.org/keywords/reynolds-number","display_name":"Reynolds number","score":0.765999972820282},{"id":"https://openalex.org/keywords/bond-number","display_name":"Bond number","score":0.8100000023841858},{"id":"https://openalex.org/keywords/rising-velocity","display_name":"rising velocity","score":0.8489999771118164}],"concepts":[{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.9429793953895569},{"id":"https://openalex.org/C33026886","wikidata":"https://www.wikidata.org/wiki/Q593950","display_name":"Rotational symmetry","level":2,"score":0.7274971604347229},{"id":"https://openalex.org/C157915830","wikidata":"https://www.wikidata.org/wiki/Q2928001","display_name":"Bubble","level":2,"score":0.6915911436080933},{"id":"https://openalex.org/C2779379648","wikidata":"https://www.wikidata.org/wiki/Q1559665","display_name":"Multiphase flow","level":2,"score":0.5933531522750854},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.5358024835586548},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.533229410648346},{"id":"https://openalex.org/C144308804","wikidata":"https://www.wikidata.org/wiki/Q232997","display_name":"Two-phase flow","level":3,"score":0.5200017094612122},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.4903907775878906},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.4651886522769928},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4087648391723633},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.0},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1063/5.0281713","doi":"https://doi.org/10.1063/5.0281713","is_oa":false,"landing_page_url":"https://doi.org/10.1063/5.0281713","pdf_url":null,"source":{"id":"https://openalex.org/S22862804","display_name":"Physics of Fluids","issn_l":"1070-6631","issn":["1070-6631","1089-7666","1527-2435"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-d","jufo-1","ki-jl-1","norway-1","poland-100","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320257","host_organization_name":"American Institute of Physics","host_organization_lineage":["https://openalex.org/P4310320257"],"host_organization_lineage_names":["American Institute of Physics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physics of Fluids","raw_type":"journal-article"},{"id":"pmh:oai:/dspace.imech.ac.cn:311007/103736","doi":null,"is_oa":false,"landing_page_url":"http://dspace.imech.ac.cn/handle/311007/103736","pdf_url":null,"source":{"id":"https://openalex.org/S4306400463","display_name":"\u4e2d\u56fd\u79d1\u5b66\u9662\u529b\u5b66\u7814\u7a76\u6240","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"\u671f\u520a\u8bba\u6587"},{"id":"pmh:oai:/dspace.imech.ac.cn:311007/103737","doi":null,"is_oa":false,"landing_page_url":"http://dspace.imech.ac.cn/handle/311007/103737","pdf_url":null,"source":{"id":"https://openalex.org/S4306400463","display_name":"\u4e2d\u56fd\u79d1\u5b66\u9662\u529b\u5b66\u7814\u7a76\u6240","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"\u671f\u520a\u8bba\u6587"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G3281306182","display_name":null,"funder_award_id":"52441101","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3321013484","display_name":null,"funder_award_id":"12293003","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4085799365","display_name":null,"funder_award_id":"U22B6010","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6141858082","display_name":null,"funder_award_id":"12272382","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6531065145","display_name":null,"funder_award_id":"12293000","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7038522709","display_name":null,"funder_award_id":"12293004","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7880049001","display_name":null,"funder_award_id":"2022019","funder_id":"https://openalex.org/F4320322847","funder_display_name":"Youth Innovation Promotion Association of the Chinese Academy of Sciences"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322847","display_name":"Youth Innovation Promotion Association of the Chinese Academy of Sciences","ror":"https://ror.org/031141b54"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":43,"referenced_works":["https://openalex.org/W1533861849","https://openalex.org/W1966311985","https://openalex.org/W1967527699","https://openalex.org/W1973265201","https://openalex.org/W1998343934","https://openalex.org/W2025941945","https://openalex.org/W2045545335","https://openalex.org/W2080325082","https://openalex.org/W2080922987","https://openalex.org/W2086681684","https://openalex.org/W2092886188","https://openalex.org/W2102583759","https://openalex.org/W2104152474","https://openalex.org/W2250555791","https://openalex.org/W2767286248","https://openalex.org/W2899283552","https://openalex.org/W2908510526","https://openalex.org/W2973886134","https://openalex.org/W2998366519","https://openalex.org/W3010839048","https://openalex.org/W3011806874","https://openalex.org/W3015865829","https://openalex.org/W3028009715","https://openalex.org/W3094381768","https://openalex.org/W3098546160","https://openalex.org/W3112199937","https://openalex.org/W3118861991","https://openalex.org/W3126053712","https://openalex.org/W3133755477","https://openalex.org/W3153200540","https://openalex.org/W3153315752","https://openalex.org/W3156609952","https://openalex.org/W3200673624","https://openalex.org/W4224314625","https://openalex.org/W4385561992","https://openalex.org/W4390204351","https://openalex.org/W4390674397","https://openalex.org/W4400243771","https://openalex.org/W4400878180","https://openalex.org/W4402585080","https://openalex.org/W4402938027","https://openalex.org/W4405103258","https://openalex.org/W4408362723"],"related_works":["https://openalex.org/W7077045432","https://openalex.org/W7163544386","https://openalex.org/W4400243771","https://openalex.org/W4390086779","https://openalex.org/W4402585080","https://openalex.org/W7167695660","https://openalex.org/W7213519263","https://openalex.org/W4224314625","https://openalex.org/W7203855753","https://openalex.org/W7125246036"],"abstract_inverted_index":{"While":[0],"physics-informed":[1],"neural":[2],"networks":[3],"are":[4,51,92],"becoming":[5],"a":[6,29],"promising":[7],"approach":[8],"for":[9,37],"multiphase":[10,39],"flow":[11,40],"simulations,":[12],"the":[13,72,75,98,124,132],"transition":[14],"from":[15],"two-dimensional":[16],"to":[17,53,134],"three-dimensional":[18],"applications":[19],"is":[20,59],"primarily":[21],"hindered":[22],"by":[23],"computational":[24],"inefficiency.":[25],"This":[26],"study":[27],"presents":[28],"phase-field":[30],"Physics-Informed":[31],"Neural":[32],"Networks":[33],"(PF-PINNs)":[34],"specifically":[35],"designed":[36],"axisymmetric":[38,47,129],"dynamics.":[41],"Adaptive":[42],"time":[43],"marching":[44],"strategy":[45,50],"and":[46,89,110,119,131],"weighted":[48],"sampling":[49],"introduced":[52],"ensure":[54],"training":[55],"convergence.":[56],"The":[57,113],"framework":[58],"validated":[60],"through":[61],"bubble":[62,137],"rising":[63,87],"simulations":[64],"in":[65,116,128,139],"infinite":[66],"fluid":[67],"domain.":[68],"Results":[69],"show":[70],"that":[71],"shape":[73],"of":[74,101,126],"interface":[76],"coincides":[77],"well":[78],"with":[79,104],"numerical":[80],"validation.":[81],"Dynamic":[82],"behaviors,":[83],"including":[84],"centroid":[85],"trajectories,":[86],"velocity":[88,90],"fields":[91],"precisely":[93],"captured.":[94],"We":[95],"also":[96],"evaluate":[97],"applicable":[99],"range":[100],"this":[102],"method":[103],"cases":[105],"over":[106],"different":[107,136,140],"Reynolds":[108],"numbers":[109],"Bond":[111],"numbers.":[112],"prediction":[114],"succeeds":[115],"Re=[10,":[117],"200]":[118],"Bo=[10,":[120],"200],":[121],"which":[122],"demonstrates":[123],"generality":[125],"PF-PINNs":[127],"coordinate":[130],"ability":[133],"capture":[135],"dynamics":[138],"regimes.":[141]},"counts_by_year":[{"year":2026,"cited_by_count":3}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2025-10-10T00:00:00"}
