{"id":"https://openalex.org/W4286248447","doi":"https://doi.org/10.1109/icufn55119.2022.9829676","title":"Mitigating Coordinate Transformation for Solving Partial Differential Equations with Physic-Informed Neural Networks","display_name":"Mitigating Coordinate Transformation for Solving Partial Differential Equations with Physic-Informed Neural Networks","publication_year":2022,"publication_date":"2022-07-05","ids":{"openalex":"https://openalex.org/W4286248447","doi":"https://doi.org/10.1109/icufn55119.2022.9829676"},"language":"en","primary_location":{"id":"doi:10.1109/icufn55119.2022.9829676","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icufn55119.2022.9829676","pdf_url":null,"source":{"id":"https://openalex.org/S4363608515","display_name":"2022 Thirteenth International Conference on Ubiquitous and Future Networks (ICUFN)","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 Thirteenth International Conference on Ubiquitous and Future Networks (ICUFN)","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/A5046284028","display_name":"Hyo-Seok Hwang","orcid":"https://orcid.org/0000-0002-5908-0944"},"institutions":[{"id":"https://openalex.org/I197347611","display_name":"Korea University","ror":"https://ror.org/047dqcg40","country_code":"KR","type":"education","lineage":["https://openalex.org/I197347611"]}],"countries":["KR"],"is_corresponding":true,"raw_author_name":"Hyo-Seok Hwang","raw_affiliation_strings":["Korea University,School of Electrical Engineering,Seoul,Korea","School of Electrical Engineering, Korea University, Seoul, Korea"],"affiliations":[{"raw_affiliation_string":"Korea University,School of Electrical Engineering,Seoul,Korea","institution_ids":["https://openalex.org/I197347611"]},{"raw_affiliation_string":"School of Electrical Engineering, Korea University, Seoul, Korea","institution_ids":["https://openalex.org/I197347611"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101604588","display_name":"Suhan Son","orcid":"https://orcid.org/0000-0001-6365-4659"},"institutions":[{"id":"https://openalex.org/I197347611","display_name":"Korea University","ror":"https://ror.org/047dqcg40","country_code":"KR","type":"education","lineage":["https://openalex.org/I197347611"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Suhan Son","raw_affiliation_strings":["Korea University,School of Electrical Engineering,Seoul,Korea","School of Electrical Engineering, Korea University, Seoul, Korea"],"affiliations":[{"raw_affiliation_string":"Korea University,School of Electrical Engineering,Seoul,Korea","institution_ids":["https://openalex.org/I197347611"]},{"raw_affiliation_string":"School of Electrical Engineering, Korea University, Seoul, Korea","institution_ids":["https://openalex.org/I197347611"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008851484","display_name":"Yoojoong Kim","orcid":"https://orcid.org/0000-0002-6615-9116"},"institutions":[{"id":"https://openalex.org/I87111246","display_name":"Catholic University of Korea","ror":"https://ror.org/01fpnj063","country_code":"KR","type":"education","lineage":["https://openalex.org/I87111246"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Yoojoong Kim","raw_affiliation_strings":["The Catholic University of Korea,School of Computer Science and Information Engineering,Seoul,Korea","School of Computer Science and Information Engineering, The Catholic University of Korea, Seoul, Korea"],"affiliations":[{"raw_affiliation_string":"The Catholic University of Korea,School of Computer Science and Information Engineering,Seoul,Korea","institution_ids":["https://openalex.org/I87111246"]},{"raw_affiliation_string":"School of Computer Science and Information Engineering, The Catholic University of Korea, Seoul, Korea","institution_ids":["https://openalex.org/I87111246"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5069534195","display_name":"Junhee Seok","orcid":"https://orcid.org/0000-0002-6475-8457"},"institutions":[{"id":"https://openalex.org/I197347611","display_name":"Korea University","ror":"https://ror.org/047dqcg40","country_code":"KR","type":"education","lineage":["https://openalex.org/I197347611"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Junhee Seok","raw_affiliation_strings":["Korea University,School of Electrical Engineering,Seoul,Korea","School of Electrical Engineering, Korea University, Seoul, Korea"],"affiliations":[{"raw_affiliation_string":"Korea University,School of Electrical Engineering,Seoul,Korea","institution_ids":["https://openalex.org/I197347611"]},{"raw_affiliation_string":"School of Electrical Engineering, Korea University, Seoul, Korea","institution_ids":["https://openalex.org/I197347611"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5046284028"],"corresponding_institution_ids":["https://openalex.org/I197347611"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.11415094,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"382","last_page":"385"},"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":0.9733999967575073,"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/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.9697999954223633,"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/coordinate-system","display_name":"Coordinate system","score":0.9053601622581482},{"id":"https://openalex.org/keywords/cartesian-coordinate-system","display_name":"Cartesian coordinate system","score":0.7954485416412354},{"id":"https://openalex.org/keywords/coordinate-descent","display_name":"Coordinate descent","score":0.7578871250152588},{"id":"https://openalex.org/keywords/elliptic-coordinate-system","display_name":"Elliptic coordinate system","score":0.7116653919219971},{"id":"https://openalex.org/keywords/coordinate-space","display_name":"Coordinate space","score":0.6995238661766052},{"id":"https://openalex.org/keywords/ellipsoidal-coordinates","display_name":"Ellipsoidal coordinates","score":0.6328622102737427},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.5965157747268677},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5735393762588501},{"id":"https://openalex.org/keywords/transformation","display_name":"Transformation (genetics)","score":0.5290877819061279},{"id":"https://openalex.org/keywords/spherical-coordinate-system","display_name":"Spherical coordinate system","score":0.5018107891082764},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4620714783668518},{"id":"https://openalex.org/keywords/work","display_name":"Work (physics)","score":0.42970210313796997},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.37992286682128906},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3352392911911011},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.29961585998535156},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2036767303943634},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.17014718055725098},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.15934380888938904},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.120766282081604}],"concepts":[{"id":"https://openalex.org/C80551277","wikidata":"https://www.wikidata.org/wiki/Q11210","display_name":"Coordinate system","level":2,"score":0.9053601622581482},{"id":"https://openalex.org/C16038011","wikidata":"https://www.wikidata.org/wiki/Q62912","display_name":"Cartesian coordinate system","level":2,"score":0.7954485416412354},{"id":"https://openalex.org/C157553263","wikidata":"https://www.wikidata.org/wiki/Q5168004","display_name":"Coordinate descent","level":2,"score":0.7578871250152588},{"id":"https://openalex.org/C108172862","wikidata":"https://www.wikidata.org/wiki/Q1332432","display_name":"Elliptic coordinate system","level":3,"score":0.7116653919219971},{"id":"https://openalex.org/C162291796","wikidata":"https://www.wikidata.org/wiki/Q125977","display_name":"Coordinate space","level":2,"score":0.6995238661766052},{"id":"https://openalex.org/C68589394","wikidata":"https://www.wikidata.org/wiki/Q1332363","display_name":"Ellipsoidal coordinates","level":3,"score":0.6328622102737427},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5965157747268677},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5735393762588501},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.5290877819061279},{"id":"https://openalex.org/C126990412","wikidata":"https://www.wikidata.org/wiki/Q203218","display_name":"Spherical coordinate system","level":2,"score":0.5018107891082764},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4620714783668518},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.42970210313796997},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.37992286682128906},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3352392911911011},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.29961585998535156},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2036767303943634},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.17014718055725098},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.15934380888938904},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.120766282081604},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/icufn55119.2022.9829676","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icufn55119.2022.9829676","pdf_url":null,"source":{"id":"https://openalex.org/S4363608515","display_name":"2022 Thirteenth International Conference on Ubiquitous and Future Networks (ICUFN)","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 Thirteenth International Conference on Ubiquitous and Future Networks (ICUFN)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320671","display_name":"National Research Foundation","ror":"https://ror.org/05s0g1g46"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W2605147767","https://openalex.org/W2740776761","https://openalex.org/W2772097715","https://openalex.org/W2803629276","https://openalex.org/W2899283552","https://openalex.org/W2921773029","https://openalex.org/W2969381807","https://openalex.org/W2998366519","https://openalex.org/W3034372977","https://openalex.org/W3035842227","https://openalex.org/W3171202467","https://openalex.org/W6741374117","https://openalex.org/W6746731892","https://openalex.org/W6780261245"],"related_works":["https://openalex.org/W2363108177","https://openalex.org/W2372486955","https://openalex.org/W2350747896","https://openalex.org/W4286248447","https://openalex.org/W2386290424","https://openalex.org/W2027063296","https://openalex.org/W2366322774","https://openalex.org/W2148513345","https://openalex.org/W3042787614","https://openalex.org/W179025373"],"abstract_inverted_index":{"In":[0],"this":[1,82],"work,":[2],"we":[3],"investigate":[4],"some":[5],"coordinate":[6,32,38,51,63,70,74],"systems":[7,71],"to":[8,67,87,96],"solve":[9],"partial":[10],"differential":[11],"equations":[12],"(PDEs)":[13],"using":[14,22],"a":[15,37],"neural":[16,24],"network.":[17],"We":[18,45],"approximate":[19],"the":[20,31,61,68,77,84,97],"solution":[21],"physics-informed":[23],"networks":[25],"(PINNs)":[26],"both":[27],"before":[28],"and":[29,42],"after":[30],"transformation":[33],"for":[34],"two":[35],"cases:":[36],"system":[39,64],"with":[40,49],"periodicity":[41],"without":[43],"periodicity.":[44],"demonstrate":[46],"that":[47],"PINNs":[48,59,91],"Cartesian":[50,62],"shows":[52],"better":[53],"approximation":[54],"accuracy.":[55],"This":[56],"implies":[57],"in":[58],"training":[60,89],"is":[65,83],"superior":[66],"other":[69],"derived":[72],"by":[73,92],"transformation.":[75],"To":[76],"best":[78],"of":[79,90],"our":[80],"knowledge,":[81],"first":[85],"work":[86],"test":[88],"modifying":[93],"PDEs":[94],"according":[95],"boundary":[98],"shape.":[99]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}