{"id":"https://openalex.org/W4320057647","doi":"https://doi.org/10.1109/ccis57298.2022.10016380","title":"Physics-guided Data Augmentation for Learning the Solution Operator of Linear Differential Equations","display_name":"Physics-guided Data Augmentation for Learning the Solution Operator of Linear Differential Equations","publication_year":2022,"publication_date":"2022-11-26","ids":{"openalex":"https://openalex.org/W4320057647","doi":"https://doi.org/10.1109/ccis57298.2022.10016380"},"language":"en","primary_location":{"id":"doi:10.1109/ccis57298.2022.10016380","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ccis57298.2022.10016380","pdf_url":null,"source":{"id":"https://openalex.org/S4363608348","display_name":"2022 IEEE 8th International Conference on Cloud Computing and Intelligent Systems (CCIS)","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":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2022 IEEE 8th International Conference on Cloud Computing and Intelligent Systems (CCIS)","raw_type":"proceedings-article"},"type":"article","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/A5100339233","display_name":"Ye Li","orcid":"https://orcid.org/0000-0002-5351-8546"},"institutions":[{"id":"https://openalex.org/I9842412","display_name":"Nanjing University of Aeronautics and Astronautics","ror":"https://ror.org/01scyh794","country_code":"CN","type":"education","lineage":["https://openalex.org/I9842412"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Ye Li","raw_affiliation_strings":["Nanjing University of Aeronautics and Astronautics,Nanjing,China,211106"],"affiliations":[{"raw_affiliation_string":"Nanjing University of Aeronautics and Astronautics,Nanjing,China,211106","institution_ids":["https://openalex.org/I9842412"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043295801","display_name":"Yiwen Pang","orcid":"https://orcid.org/0000-0003-2083-9260"},"institutions":[{"id":"https://openalex.org/I9842412","display_name":"Nanjing University of Aeronautics and Astronautics","ror":"https://ror.org/01scyh794","country_code":"CN","type":"education","lineage":["https://openalex.org/I9842412"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yiwen Pang","raw_affiliation_strings":["Nanjing University of Aeronautics and Astronautics,Nanjing,China,211106"],"affiliations":[{"raw_affiliation_string":"Nanjing University of Aeronautics and Astronautics,Nanjing,China,211106","institution_ids":["https://openalex.org/I9842412"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101767647","display_name":"Bin Shan","orcid":"https://orcid.org/0000-0002-0781-2760"},"institutions":[{"id":"https://openalex.org/I9842412","display_name":"Nanjing University of Aeronautics and Astronautics","ror":"https://ror.org/01scyh794","country_code":"CN","type":"education","lineage":["https://openalex.org/I9842412"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Bin Shan","raw_affiliation_strings":["Nanjing University of Aeronautics and Astronautics,Nanjing,China,211106"],"affiliations":[{"raw_affiliation_string":"Nanjing University of Aeronautics and Astronautics,Nanjing,China,211106","institution_ids":["https://openalex.org/I9842412"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5100339233"],"corresponding_institution_ids":["https://openalex.org/I9842412"],"apc_list":null,"apc_paid":null,"fwci":1.1647,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.77169811,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"543","last_page":"547"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9998999834060669,"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":0.9998999834060669,"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/T12560","display_name":"Nuclear Engineering Thermal-Hydraulics","score":0.9672999978065491,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"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/T11254","display_name":"Fluid Dynamics and Vibration Analysis","score":0.9469000101089478,"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/operator","display_name":"Operator (biology)","score":0.668023407459259},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.616169273853302},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.6098559498786926},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5125555992126465},{"id":"https://openalex.org/keywords/linearity","display_name":"Linearity","score":0.4885762631893158},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4759904146194458},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.45894140005111694},{"id":"https://openalex.org/keywords/differential-operator","display_name":"Differential operator","score":0.4547613561153412},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4069153666496277},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.33483242988586426},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.20386910438537598},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.19611799716949463},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.17649203538894653}],"concepts":[{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.668023407459259},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.616169273853302},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.6098559498786926},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5125555992126465},{"id":"https://openalex.org/C77170095","wikidata":"https://www.wikidata.org/wiki/Q1753188","display_name":"Linearity","level":2,"score":0.4885762631893158},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4759904146194458},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.45894140005111694},{"id":"https://openalex.org/C70915906","wikidata":"https://www.wikidata.org/wiki/Q1058681","display_name":"Differential operator","level":2,"score":0.4547613561153412},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4069153666496277},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.33483242988586426},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.20386910438537598},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.19611799716949463},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.17649203538894653},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/ccis57298.2022.10016380","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ccis57298.2022.10016380","pdf_url":null,"source":{"id":"https://openalex.org/S4363608348","display_name":"2022 IEEE 8th International Conference on Cloud Computing and Intelligent Systems (CCIS)","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":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2022 IEEE 8th International Conference on Cloud Computing and Intelligent Systems (CCIS)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":48,"referenced_works":["https://openalex.org/W569478347","https://openalex.org/W2139923370","https://openalex.org/W2735139999","https://openalex.org/W2749028154","https://openalex.org/W2760972773","https://openalex.org/W2785024182","https://openalex.org/W2891039272","https://openalex.org/W2899283552","https://openalex.org/W2919115771","https://openalex.org/W2922249543","https://openalex.org/W2936357167","https://openalex.org/W2949696172","https://openalex.org/W2954996726","https://openalex.org/W2979786244","https://openalex.org/W3022969843","https://openalex.org/W3092923133","https://openalex.org/W3145198368","https://openalex.org/W3163993681","https://openalex.org/W3164485545","https://openalex.org/W3199237569","https://openalex.org/W3201666041","https://openalex.org/W3209852456","https://openalex.org/W3214496267","https://openalex.org/W3216718982","https://openalex.org/W4221019179","https://openalex.org/W4221140777","https://openalex.org/W4226431136","https://openalex.org/W4286980132","https://openalex.org/W4298392935","https://openalex.org/W4308731656","https://openalex.org/W6694954494","https://openalex.org/W6748177122","https://openalex.org/W6758345809","https://openalex.org/W6759134542","https://openalex.org/W6760827199","https://openalex.org/W6761271948","https://openalex.org/W6767104088","https://openalex.org/W6773459916","https://openalex.org/W6774448971","https://openalex.org/W6784227514","https://openalex.org/W6800995735","https://openalex.org/W6801516442","https://openalex.org/W6803068854","https://openalex.org/W6804467878","https://openalex.org/W6809843401","https://openalex.org/W6811269282","https://openalex.org/W6929334658","https://openalex.org/W7002535191"],"related_works":["https://openalex.org/W2023858428","https://openalex.org/W2218509615","https://openalex.org/W2126963364","https://openalex.org/W3162204513","https://openalex.org/W2538259895","https://openalex.org/W2051287254","https://openalex.org/W1489573155","https://openalex.org/W2370937376","https://openalex.org/W2371138613","https://openalex.org/W4293868490"],"abstract_inverted_index":{"Neural":[0],"networks,":[1],"especially":[2],"the":[3,15,57,74,88,101,117],"recent":[4],"proposed":[5],"neural":[6,43,79],"operator":[7,17,44,80],"models,":[8],"are":[9,27],"increasingly":[10],"being":[11],"used":[12],"to":[13,22,72,123],"find":[14],"solution":[16],"of":[18,49,78,91,103,108],"differential":[19,92,110],"equations.":[20],"Compared":[21],"traditional":[23],"numerical":[24,59],"solvers,":[25],"they":[26],"much":[28],"faster":[29],"and":[30,76,97,120],"more":[31],"efficient":[32],"in":[33],"practical":[34],"applications.":[35],"However,":[36],"one":[37],"critical":[38],"issue":[39],"is":[40,84,121],"that":[41,113],"training":[42],"models":[45],"require":[46],"large":[47],"amount":[48],"ground":[50],"truth":[51],"data,":[52],"which":[53],"usually":[54],"comes":[55],"from":[56],"slow":[58],"solvers.":[60],"In":[61],"this":[62],"paper,":[63],"we":[64],"propose":[65],"a":[66,106],"physics-guided":[67],"data":[68,83],"augmentation":[69],"(PGDA)":[70],"method":[71],"improve":[73,116],"accuracy":[75],"generalization":[77],"models.":[81],"Training":[82],"augmented":[85],"naturally":[86],"through":[87],"physical":[89],"properties":[90],"equations":[93],"such":[94],"as":[95],"linearity":[96],"translation.":[98],"We":[99],"demonstrate":[100],"advantage":[102],"PGDA":[104,114],"on":[105],"variety":[107],"linear":[109],"equations,":[111],"showing":[112],"can":[115],"sample":[118],"complexity":[119],"robust":[122],"distributional":[124],"shift.":[125]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}