{"id":"https://openalex.org/W3135635120","doi":"https://doi.org/10.1109/ipdpsw52791.2021.00106","title":"Parallel Machine Learning of Partial Differential Equations","display_name":"Parallel Machine Learning of Partial Differential Equations","publication_year":2021,"publication_date":"2021-06-01","ids":{"openalex":"https://openalex.org/W3135635120","doi":"https://doi.org/10.1109/ipdpsw52791.2021.00106","mag":"3135635120"},"language":"en","primary_location":{"id":"doi:10.1109/ipdpsw52791.2021.00106","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ipdpsw52791.2021.00106","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2021 IEEE International Parallel and Distributed Processing Symposium Workshops (IPDPSW)","raw_type":"proceedings-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2103.01869","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5040154582","display_name":"Amin Totounferoush","orcid":"https://orcid.org/0000-0003-1770-1711"},"institutions":[{"id":"https://openalex.org/I100066346","display_name":"University of Stuttgart","ror":"https://ror.org/04vnq7t77","country_code":"DE","type":"education","lineage":["https://openalex.org/I100066346"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Amin Totounferoush","raw_affiliation_strings":["Institute for Parallel and Distributed Systems, University of Stuttgart, Germany","University of Stuttgart,Institute for Parallel and Distributed Systems,Germany"],"affiliations":[{"raw_affiliation_string":"Institute for Parallel and Distributed Systems, University of Stuttgart, Germany","institution_ids":["https://openalex.org/I100066346"]},{"raw_affiliation_string":"University of Stuttgart,Institute for Parallel and Distributed Systems,Germany","institution_ids":["https://openalex.org/I100066346"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5024102896","display_name":"Neda Ebrahimi Pour","orcid":"https://orcid.org/0000-0002-8167-7456"},"institutions":[{"id":"https://openalex.org/I206895457","display_name":"University of Siegen","ror":"https://ror.org/02azyry73","country_code":"DE","type":"education","lineage":["https://openalex.org/I206895457"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Neda Ebrahimi Pour","raw_affiliation_strings":["Chair of Simulation Techniques and Scientific Computing, University of Siegen, Germany","University of Siegen,Chair of Simulation Techniques and Scientific Computing,Germany"],"affiliations":[{"raw_affiliation_string":"Chair of Simulation Techniques and Scientific Computing, University of Siegen, Germany","institution_ids":["https://openalex.org/I206895457"]},{"raw_affiliation_string":"University of Siegen,Chair of Simulation Techniques and Scientific Computing,Germany","institution_ids":["https://openalex.org/I206895457"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012579504","display_name":"Sabine Roller","orcid":"https://orcid.org/0000-0003-1483-8456"},"institutions":[{"id":"https://openalex.org/I206895457","display_name":"University of Siegen","ror":"https://ror.org/02azyry73","country_code":"DE","type":"education","lineage":["https://openalex.org/I206895457"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Sabine Roller","raw_affiliation_strings":["Chair of Simulation Techniques and Scientific Computing, University of Siegen, Germany","University of Siegen,Chair of Simulation Techniques and Scientific Computing,Germany"],"affiliations":[{"raw_affiliation_string":"Chair of Simulation Techniques and Scientific Computing, University of Siegen, Germany","institution_ids":["https://openalex.org/I206895457"]},{"raw_affiliation_string":"University of Siegen,Chair of Simulation Techniques and Scientific Computing,Germany","institution_ids":["https://openalex.org/I206895457"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5113995384","display_name":"Miriam Mehl","orcid":null},"institutions":[{"id":"https://openalex.org/I100066346","display_name":"University of Stuttgart","ror":"https://ror.org/04vnq7t77","country_code":"DE","type":"education","lineage":["https://openalex.org/I100066346"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Miriam Mehl","raw_affiliation_strings":["Institute for Parallel and Distributed Systems, University of Stuttgart, Germany","University of Stuttgart,Institute for Parallel and Distributed Systems,Germany"],"affiliations":[{"raw_affiliation_string":"Institute for Parallel and Distributed Systems, University of Stuttgart, Germany","institution_ids":["https://openalex.org/I100066346"]},{"raw_affiliation_string":"University of Stuttgart,Institute for Parallel and Distributed Systems,Germany","institution_ids":["https://openalex.org/I100066346"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5040154582"],"corresponding_institution_ids":["https://openalex.org/I100066346"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.04565836,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"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":0.9998999834060669,"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/T10466","display_name":"Meteorological Phenomena and Simulations","score":0.9944999814033508,"subfield":{"id":"https://openalex.org/subfields/1902","display_name":"Atmospheric Science"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9887999892234802,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/computer-science","display_name":"Computer science","score":0.7191654443740845},{"id":"https://openalex.org/keywords/scalability","display_name":"Scalability","score":0.6967349052429199},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.6477705836296082},{"id":"https://openalex.org/keywords/convolutional-neural-network","display_name":"Convolutional neural network","score":0.6246547102928162},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5667663812637329},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.5560480952262878},{"id":"https://openalex.org/keywords/multigrid-method","display_name":"Multigrid method","score":0.49060359597206116},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.47051113843917847},{"id":"https://openalex.org/keywords/euler-equations","display_name":"Euler equations","score":0.4580084979534149},{"id":"https://openalex.org/keywords/numerical-partial-differential-equations","display_name":"Numerical partial differential equations","score":0.43105342984199524},{"id":"https://openalex.org/keywords/interface","display_name":"Interface (matter)","score":0.42713162302970886},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.40958213806152344},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.40451571345329285},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3650476634502411},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.18767395615577698},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1006273627281189}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7191654443740845},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.6967349052429199},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.6477705836296082},{"id":"https://openalex.org/C81363708","wikidata":"https://www.wikidata.org/wiki/Q17084460","display_name":"Convolutional neural network","level":2,"score":0.6246547102928162},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5667663812637329},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.5560480952262878},{"id":"https://openalex.org/C137119250","wikidata":"https://www.wikidata.org/wiki/Q1413101","display_name":"Multigrid method","level":3,"score":0.49060359597206116},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.47051113843917847},{"id":"https://openalex.org/C38409319","wikidata":"https://www.wikidata.org/wiki/Q375175","display_name":"Euler equations","level":2,"score":0.4580084979534149},{"id":"https://openalex.org/C97826883","wikidata":"https://www.wikidata.org/wiki/Q7069659","display_name":"Numerical partial differential equations","level":3,"score":0.43105342984199524},{"id":"https://openalex.org/C113843644","wikidata":"https://www.wikidata.org/wiki/Q901882","display_name":"Interface (matter)","level":4,"score":0.42713162302970886},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.40958213806152344},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.40451571345329285},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3650476634502411},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.18767395615577698},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1006273627281189},{"id":"https://openalex.org/C129307140","wikidata":"https://www.wikidata.org/wiki/Q6795880","display_name":"Maximum bubble pressure method","level":3,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C157915830","wikidata":"https://www.wikidata.org/wiki/Q2928001","display_name":"Bubble","level":2,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/ipdpsw52791.2021.00106","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ipdpsw52791.2021.00106","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2021 IEEE International Parallel and Distributed Processing Symposium Workshops (IPDPSW)","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:2103.01869","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2103.01869","pdf_url":"https://arxiv.org/pdf/2103.01869","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"mag:3135635120","is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/2103.01869","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.2103.01869","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2103.01869","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":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2103.01869","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2103.01869","pdf_url":"https://arxiv.org/pdf/2103.01869","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5106512922","display_name":null,"funder_award_id":"Deutsche Forschungsgemeinschaft (DFG","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G8644345701","display_name":null,"funder_award_id":"EXC2075","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G8784604414","display_name":null,"funder_award_id":"390740016","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320334747","display_name":"Singapore Institute of Manufacturing Technology","ror":"https://ror.org/00f44np30"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3135635120.pdf","grobid_xml":"https://content.openalex.org/works/W3135635120.grobid-xml"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W344696635","https://openalex.org/W1522301498","https://openalex.org/W1583892864","https://openalex.org/W1980287119","https://openalex.org/W2156387975","https://openalex.org/W2557283755","https://openalex.org/W2767286248","https://openalex.org/W2788403524","https://openalex.org/W2899283552","https://openalex.org/W2925231804","https://openalex.org/W2972087877","https://openalex.org/W3105919389","https://openalex.org/W4205236375","https://openalex.org/W6611566204","https://openalex.org/W6631190155","https://openalex.org/W6682889407","https://openalex.org/W6746023985"],"related_works":["https://openalex.org/W3174261098","https://openalex.org/W2352652896","https://openalex.org/W1992203973","https://openalex.org/W1588420103","https://openalex.org/W1554597800","https://openalex.org/W2066885697","https://openalex.org/W1717255962","https://openalex.org/W2170379025","https://openalex.org/W2074605507","https://openalex.org/W2535500072","https://openalex.org/W78614349","https://openalex.org/W2384347289","https://openalex.org/W3008977290","https://openalex.org/W100789672","https://openalex.org/W2211376743","https://openalex.org/W1559513056","https://openalex.org/W72471495","https://openalex.org/W2777240992","https://openalex.org/W1538350742","https://openalex.org/W2050117522"],"abstract_inverted_index":{"In":[0,112],"this":[1],"work,":[2],"we":[3,114],"present":[4],"a":[5,100],"parallel":[6],"scheme":[7,16],"for":[8,47,61,93],"machine":[9],"learning":[10,67],"of":[11,22,68,77,83,90,104,119],"partial":[12],"differential":[13],"equations.":[14],"The":[15],"is":[17,35,45],"based":[18],"on":[19],"the":[20,23,66,69,75,78,81,84,105,109,120,125],"decomposition":[21],"training":[24,121],"data":[25,39,50],"corresponding":[26],"to":[27,37,59,73,124,134],"spatial":[28,62],"subdomains,":[29],"where":[30],"an":[31,116,129],"individual":[32],"neural":[33,55],"network":[34,56],"assigned":[36],"each":[38],"subset.":[40],"Message":[41],"Passing":[42],"Interface":[43],"(MPI)":[44],"used":[46],"parallelization":[48],"and":[49,80],"communication.":[51],"We":[52,64],"use":[53],"convolutional":[54],"layers":[57],"(CNN)":[58],"account":[60],"connectivity.":[63],"showcase":[65],"linearized":[70],"Euler":[71],"equations":[72,88],"assess":[74],"accuracy":[76],"predictions":[79],"efficiency":[82],"proposed":[85],"scheme.":[86],"These":[87],"are":[89],"particular":[91],"interest":[92],"aeroacoustic":[94],"problems.":[95],"A":[96],"first":[97],"investigation":[98],"demonstrated":[99],"very":[101],"good":[102],"agreement":[103],"predicted":[106],"results":[107],"with":[108],"simulation":[110],"results.":[111],"addition,":[113],"observe":[115],"excellent":[117],"reduction":[118],"time":[122],"compared":[123],"sequential":[126],"version,":[127],"providing":[128],"almost":[130],"perfect":[131],"scalability":[132],"up":[133],"64":[135],"CPU":[136],"cores.":[137]},"counts_by_year":[],"updated_date":"2026-03-12T08:34:05.389933","created_date":"2025-10-10T00:00:00"}