{"id":"https://openalex.org/W4415318718","doi":"https://doi.org/10.1007/s10915-026-03337-1","title":"Parallel-in-Time Solution of Allen-Cahn Equations by Integrating Operator Learning into the Parareal Method","display_name":"Parallel-in-Time Solution of Allen-Cahn Equations by Integrating Operator Learning into the Parareal Method","publication_year":2026,"publication_date":"2026-06-02","ids":{"openalex":"https://openalex.org/W4415318718","doi":"https://doi.org/10.1007/s10915-026-03337-1"},"language":"en","primary_location":{"id":"doi:10.1007/s10915-026-03337-1","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10915-026-03337-1","pdf_url":null,"source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Scientific Computing","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2510.07672","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101350037","display_name":"Yuwei Geng","orcid":null},"institutions":[{"id":"https://openalex.org/I155781252","display_name":"University of South Carolina","ror":"https://ror.org/02b6qw903","country_code":"US","type":"education","lineage":["https://openalex.org/I155781252"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yuwei Geng","raw_affiliation_strings":["Department of Mathematics, University of South Carolina, Columbia, SC, 29208, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of South Carolina, Columbia, SC, 29208, USA","institution_ids":["https://openalex.org/I155781252"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5051882926","display_name":"Junqi Yin","orcid":"https://orcid.org/0000-0003-3843-5520"},"institutions":[{"id":"https://openalex.org/I1289243028","display_name":"Oak Ridge National Laboratory","ror":"https://ror.org/01qz5mb56","country_code":"US","type":"facility","lineage":["https://openalex.org/I1289243028","https://openalex.org/I1330989302","https://openalex.org/I39565521","https://openalex.org/I4210159294"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Junqi Yin","raw_affiliation_strings":["National Center for Computational Sciences, Oak Ridge National Laboratory, Oak Ridge, TN, 37831, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"National Center for Computational Sciences, Oak Ridge National Laboratory, Oak Ridge, TN, 37831, USA","institution_ids":["https://openalex.org/I1289243028"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5052883660","display_name":"Eric C. Cyr","orcid":"https://orcid.org/0000-0003-3833-9598"},"institutions":[{"id":"https://openalex.org/I192454743","display_name":"Sandia National Laboratories California","ror":"https://ror.org/058m7ey48","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I1330989302","https://openalex.org/I192454743","https://openalex.org/I198811213","https://openalex.org/I198811213","https://openalex.org/I4210104735"]},{"id":"https://openalex.org/I4210104735","display_name":"Sandia National Laboratories","ror":"https://ror.org/01apwpt12","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I198811213","https://openalex.org/I4210104735"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Eric C. Cyr","raw_affiliation_strings":["Computational Mathematics Department, Sandia National Laboratories, Albuquerque, NM, 87123, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computational Mathematics Department, Sandia National Laboratories, Albuquerque, NM, 87123, USA","institution_ids":["https://openalex.org/I4210104735","https://openalex.org/I192454743"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5046509521","display_name":"Guannan Zhang","orcid":"https://orcid.org/0000-0001-7256-150X"},"institutions":[{"id":"https://openalex.org/I1289243028","display_name":"Oak Ridge National Laboratory","ror":"https://ror.org/01qz5mb56","country_code":"US","type":"facility","lineage":["https://openalex.org/I1289243028","https://openalex.org/I1330989302","https://openalex.org/I39565521","https://openalex.org/I4210159294"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Guannan Zhang","raw_affiliation_strings":["Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, TN, 37831, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, TN, 37831, USA","institution_ids":["https://openalex.org/I1289243028"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100883984","display_name":"Lili Ju","orcid":null},"institutions":[{"id":"https://openalex.org/I155781252","display_name":"University of South Carolina","ror":"https://ror.org/02b6qw903","country_code":"US","type":"education","lineage":["https://openalex.org/I155781252"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Lili Ju","raw_affiliation_strings":["Department of Mathematics, University of South Carolina, Columbia, SC, 29208, USA"],"raw_orcid":"https://orcid.org/0000-0002-6520-582X","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of South Carolina, Columbia, SC, 29208, USA","institution_ids":["https://openalex.org/I155781252"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5100883984"],"corresponding_institution_ids":["https://openalex.org/I155781252"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00414416,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"108","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11087","display_name":"Solidification and crystal growth phenomena","score":0.8711000084877014,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11087","display_name":"Solidification and crystal growth phenomena","score":0.8711000084877014,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10049","display_name":"Magnetic properties of thin films","score":0.7792999744415283,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/speedup","display_name":"Speedup","score":0.6039000153541565},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5708000063896179},{"id":"https://openalex.org/keywords/consistency","display_name":"Consistency (knowledge bases)","score":0.5002999901771545},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.49799999594688416},{"id":"https://openalex.org/keywords/convolutional-neural-network","display_name":"Convolutional neural network","score":0.49300000071525574},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.46160000562667847},{"id":"https://openalex.org/keywords/deep-learning","display_name":"Deep learning","score":0.4462999999523163},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.41609999537467957}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6509000062942505},{"id":"https://openalex.org/C68339613","wikidata":"https://www.wikidata.org/wiki/Q1549489","display_name":"Speedup","level":2,"score":0.6039000153541565},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5708000063896179},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.5002999901771545},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.49799999594688416},{"id":"https://openalex.org/C81363708","wikidata":"https://www.wikidata.org/wiki/Q17084460","display_name":"Convolutional neural network","level":2,"score":0.49300000071525574},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.46160000562667847},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4505000114440918},{"id":"https://openalex.org/C108583219","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep learning","level":2,"score":0.4462999999523163},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.426800012588501},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.41609999537467957},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.39010000228881836},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3799000084400177},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.3517000079154968},{"id":"https://openalex.org/C104416048","wikidata":"https://www.wikidata.org/wiki/Q302518","display_name":"Propagator","level":2,"score":0.33390000462532043},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.3312000036239624},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.32440000772476196},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.2865999937057495},{"id":"https://openalex.org/C2984842247","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep neural networks","level":3,"score":0.28049999475479126},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.26739999651908875},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.25929999351501465},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.25270000100135803},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.2502000033855438}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s10915-026-03337-1","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10915-026-03337-1","pdf_url":null,"source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2510.07672","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2510.07672","pdf_url":"https://arxiv.org/pdf/2510.07672","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":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2510.07672","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2510.07672","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":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2510.07672","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2510.07672","pdf_url":"https://arxiv.org/pdf/2510.07672","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":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2661465621","display_name":null,"funder_award_id":"ERKJ443","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G3326141885","display_name":null,"funder_award_id":"DE-SC0025527","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G3586666612","display_name":null,"funder_award_id":"ERKJ388","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"}],"funders":[{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4415318718.pdf"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-06-04T06:14:18.571774","created_date":"2025-10-18T00:00:00"}