{"id":"https://openalex.org/W4403818920","doi":"https://doi.org/10.1137/24m1710693","title":"Neural Network Approaches for Variance Reduction in Fluctuation Formulas","display_name":"Neural Network Approaches for Variance Reduction in Fluctuation Formulas","publication_year":2026,"publication_date":"2026-03-05","ids":{"openalex":"https://openalex.org/W4403818920","doi":"https://doi.org/10.1137/24m1710693"},"language":"en","primary_location":{"id":"doi:10.1137/24m1710693","is_oa":false,"landing_page_url":"https://doi.org/10.1137/24m1710693","pdf_url":null,"source":{"id":"https://openalex.org/S2911293512","display_name":"SIAM/ASA Journal on Uncertainty Quantification","issn_l":"2166-2525","issn":["2166-2525"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM/ASA Journal on Uncertainty Quantification","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2410.00278","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5044857425","display_name":"Grigorios A. Pavliotis","orcid":"https://orcid.org/0000-0002-3468-9227"},"institutions":[{"id":"https://openalex.org/I47508984","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10","country_code":"GB","type":"education","lineage":["https://openalex.org/I47508984"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"G. A. Pavliotis","raw_affiliation_strings":["Department of Mathematics, Imperial College London, UK","Department of Mathematics [Imperial College London] (Imperial College London, 180 Queen's Gate, London SW7 2AZ, United Kingdom - United Kingdom)"],"raw_orcid":"https://orcid.org/0000-0002-3468-9227","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Imperial College London, UK","institution_ids":[]},{"raw_affiliation_string":"Department of Mathematics [Imperial College London] (Imperial College London, 180 Queen's Gate, London SW7 2AZ, United Kingdom - United Kingdom)","institution_ids":["https://openalex.org/I47508984"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5024361397","display_name":"Renato Spacek","orcid":"https://orcid.org/0009-0003-4392-3358"},"institutions":[{"id":"https://openalex.org/I4210128309","display_name":"CERMICS","ror":"https://ror.org/03wct8w46","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I142631665","https://openalex.org/I4210128309","https://openalex.org/I4210145102"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"R. Spacek","raw_affiliation_strings":["MATHERIALS team-project, Inria Paris, France and CERMICS, ENPC, Institut Polytechnique de Paris, Marne-la-Vall\u00e9e, France","CERMICS - Centre d'Enseignement et de Recherche en Math\u00e9matiques et Calcul Scientifique (6 et 8 avenue Blaise Pascal Cit\u00e9 Descartes - Champs sur Marne 77455 Marne la Vall\u00e9e Cedex 2 - France)","MATHERIALS - MATHematics for MatERIALS (Cit\u00e9 Descartes, 8 Av. Blaise Pascal 6 et, 77420 Champs-sur-Marne - France)"],"raw_orcid":"https://orcid.org/0009-0003-4392-3358","affiliations":[{"raw_affiliation_string":"MATHERIALS team-project, Inria Paris, France and CERMICS, ENPC, Institut Polytechnique de Paris, Marne-la-Vall\u00e9e, France","institution_ids":[]},{"raw_affiliation_string":"CERMICS - Centre d'Enseignement et de Recherche en Math\u00e9matiques et Calcul Scientifique (6 et 8 avenue Blaise Pascal Cit\u00e9 Descartes - Champs sur Marne 77455 Marne la Vall\u00e9e Cedex 2 - France)","institution_ids":["https://openalex.org/I4210128309"]},{"raw_affiliation_string":"MATHERIALS - MATHematics for MatERIALS (Cit\u00e9 Descartes, 8 Av. Blaise Pascal 6 et, 77420 Champs-sur-Marne - France)","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015347592","display_name":"Gabriel Stoltz","orcid":"https://orcid.org/0000-0002-2797-5938"},"institutions":[{"id":"https://openalex.org/I4210128309","display_name":"CERMICS","ror":"https://ror.org/03wct8w46","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I142631665","https://openalex.org/I4210128309","https://openalex.org/I4210145102"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"G. Stoltz","raw_affiliation_strings":["CERMICS, ENPC, Institut Polytechnique de Paris, Marne-la-Vall\u00e9e, France and MATHERIALS team-project, Inria Paris, France","CERMICS - Centre d'Enseignement et de Recherche en Math\u00e9matiques et Calcul Scientifique (6 et 8 avenue Blaise Pascal Cit\u00e9 Descartes - Champs sur Marne 77455 Marne la Vall\u00e9e Cedex 2 - France)","MATHERIALS - MATHematics for MatERIALS (Cit\u00e9 Descartes, 8 Av. Blaise Pascal 6 et, 77420 Champs-sur-Marne - France)"],"raw_orcid":"https://orcid.org/0000-0002-2797-5938","affiliations":[{"raw_affiliation_string":"CERMICS, ENPC, Institut Polytechnique de Paris, Marne-la-Vall\u00e9e, France and MATHERIALS team-project, Inria Paris, France","institution_ids":[]},{"raw_affiliation_string":"CERMICS - Centre d'Enseignement et de Recherche en Math\u00e9matiques et Calcul Scientifique (6 et 8 avenue Blaise Pascal Cit\u00e9 Descartes - Champs sur Marne 77455 Marne la Vall\u00e9e Cedex 2 - France)","institution_ids":["https://openalex.org/I4210128309"]},{"raw_affiliation_string":"MATHERIALS - MATHematics for MatERIALS (Cit\u00e9 Descartes, 8 Av. Blaise Pascal 6 et, 77420 Champs-sur-Marne - France)","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5029420841","display_name":"Urbain Vaes","orcid":"https://orcid.org/0000-0002-7629-7184"},"institutions":[{"id":"https://openalex.org/I4210128309","display_name":"CERMICS","ror":"https://ror.org/03wct8w46","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I142631665","https://openalex.org/I4210128309","https://openalex.org/I4210145102"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"U. Vaes","raw_affiliation_strings":["MATHERIALS team-project, Inria Paris, France and CERMICS, ENPC, Institut Polytechnique de Paris, Marne-la-Vall\u00e9e, France","MATHERIALS - MATHematics for MatERIALS (Cit\u00e9 Descartes, 8 Av. Blaise Pascal 6 et, 77420 Champs-sur-Marne - France)","CERMICS - Centre d'Enseignement et de Recherche en Math\u00e9matiques et Calcul Scientifique (6 et 8 avenue Blaise Pascal Cit\u00e9 Descartes - Champs sur Marne 77455 Marne la Vall\u00e9e Cedex 2 - France)"],"raw_orcid":"https://orcid.org/0000-0002-7629-7184","affiliations":[{"raw_affiliation_string":"MATHERIALS team-project, Inria Paris, France and CERMICS, ENPC, Institut Polytechnique de Paris, Marne-la-Vall\u00e9e, France","institution_ids":[]},{"raw_affiliation_string":"MATHERIALS - MATHematics for MatERIALS (Cit\u00e9 Descartes, 8 Av. Blaise Pascal 6 et, 77420 Champs-sur-Marne - France)","institution_ids":[]},{"raw_affiliation_string":"CERMICS - Centre d'Enseignement et de Recherche en Math\u00e9matiques et Calcul Scientifique (6 et 8 avenue Blaise Pascal Cit\u00e9 Descartes - Champs sur Marne 77455 Marne la Vall\u00e9e Cedex 2 - France)","institution_ids":["https://openalex.org/I4210128309"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00552369,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"14","issue":"1","first_page":"221","last_page":"255"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9988999962806702,"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":0.9988999962806702,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/control-variates","display_name":"Control variates","score":0.8931220769882202},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.7415210008621216},{"id":"https://openalex.org/keywords/variance-reduction","display_name":"Variance reduction","score":0.7396296262741089},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.7054977416992188},{"id":"https://openalex.org/keywords/poisson-distribution","display_name":"Poisson distribution","score":0.7045140266418457},{"id":"https://openalex.org/keywords/variance","display_name":"Variance (accounting)","score":0.6129630208015442},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.5913907289505005},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5866551399230957},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4899138808250427},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4849832057952881},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4568210244178772},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.436148464679718},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3713545799255371},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3359648287296295},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.297228068113327},{"id":"https://openalex.org/keywords/hybrid-monte-carlo","display_name":"Hybrid Monte Carlo","score":0.21043702960014343},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1635676622390747},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.11299854516983032},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11170724034309387}],"concepts":[{"id":"https://openalex.org/C121683094","wikidata":"https://www.wikidata.org/wiki/Q3554721","display_name":"Control variates","level":5,"score":0.8931220769882202},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.7415210008621216},{"id":"https://openalex.org/C62644790","wikidata":"https://www.wikidata.org/wiki/Q3454689","display_name":"Variance reduction","level":3,"score":0.7396296262741089},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.7054977416992188},{"id":"https://openalex.org/C100906024","wikidata":"https://www.wikidata.org/wiki/Q205692","display_name":"Poisson distribution","level":2,"score":0.7045140266418457},{"id":"https://openalex.org/C196083921","wikidata":"https://www.wikidata.org/wiki/Q7915758","display_name":"Variance (accounting)","level":2,"score":0.6129630208015442},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.5913907289505005},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5866551399230957},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4899138808250427},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4849832057952881},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4568210244178772},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.436148464679718},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3713545799255371},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3359648287296295},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.297228068113327},{"id":"https://openalex.org/C13153151","wikidata":"https://www.wikidata.org/wiki/Q1639846","display_name":"Hybrid Monte Carlo","level":4,"score":0.21043702960014343},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1635676622390747},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.11299854516983032},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11170724034309387},{"id":"https://openalex.org/C144133560","wikidata":"https://www.wikidata.org/wiki/Q4830453","display_name":"Business","level":0,"score":0.0},{"id":"https://openalex.org/C121955636","wikidata":"https://www.wikidata.org/wiki/Q4116214","display_name":"Accounting","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C111350023","wikidata":"https://www.wikidata.org/wiki/Q1191869","display_name":"Markov chain Monte Carlo","level":3,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/24m1710693","is_oa":false,"landing_page_url":"https://doi.org/10.1137/24m1710693","pdf_url":null,"source":{"id":"https://openalex.org/S2911293512","display_name":"SIAM/ASA Journal on Uncertainty Quantification","issn_l":"2166-2525","issn":["2166-2525"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM/ASA Journal on Uncertainty Quantification","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2410.00278","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2410.00278","pdf_url":"https://arxiv.org/pdf/2410.00278","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":null},{"id":"pmh:oai:HAL:hal-04765173v1","is_oa":true,"landing_page_url":"https://hal.science/hal-04765173v1/file/2410.00278v1.pdf","pdf_url":"https://hal.science/hal-04765173/document","source":null,"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2024","raw_type":"Preprints, Working Papers, ..."},{"id":"doi:10.48550/arxiv.2410.00278","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2410.00278","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2410.00278","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2410.00278","pdf_url":"https://arxiv.org/pdf/2410.00278","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":null},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1111137553","display_name":null,"funder_award_id":"EP/X038645","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G2176653565","display_name":"Complex Interfacial Flows: From the Nano- to the Macro-Scale","funder_award_id":"247031","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G2361257913","display_name":null,"funder_award_id":"810367","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G2798619229","display_name":null,"funder_award_id":"ANR-19-CE40-0010-01","funder_id":"https://openalex.org/F4320319993","funder_display_name":"Leverhulme Trust"},{"id":"https://openalex.org/G3124863526","display_name":"International Doctoral Training in Mathematical Sciences in Paris","funder_award_id":"945332","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G3173448015","display_name":null,"funder_award_id":"ANR-21-CE40-0006","funder_id":"https://openalex.org/F4320319993","funder_display_name":"Leverhulme Trust"},{"id":"https://openalex.org/G3754423395","display_name":null,"funder_award_id":"247031","funder_id":"https://openalex.org/F4320338335","funder_display_name":"H2020 European Research Council"},{"id":"https://openalex.org/G4712616550","display_name":"Simulation nonequilibrium stochastic dynamics","funder_award_id":"ANR-21-CE40-0006","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G4855017883","display_name":null,"funder_award_id":"19-CE40-0010-01","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G5669417410","display_name":null,"funder_award_id":"ANR-19-CE40-0010-01","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G5747723803","display_name":null,"funder_award_id":"SRF\\R1\\241055","funder_id":"https://openalex.org/F4320319993","funder_display_name":"Leverhulme Trust"},{"id":"https://openalex.org/G6617287496","display_name":null,"funder_award_id":"810367","funder_id":"https://openalex.org/F4320332999","funder_display_name":"Horizon 2020 Framework Programme"},{"id":"https://openalex.org/G7683707404","display_name":"Extreme-scale Mathematically-based Computational Chemistry","funder_award_id":"810367","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G8318455765","display_name":null,"funder_award_id":"ANR-19","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G8531439085","display_name":null,"funder_award_id":"810367","funder_id":"https://openalex.org/F4320319993","funder_display_name":"Leverhulme Trust"},{"id":"https://openalex.org/G8544760875","display_name":"Quantitative Analysis of Metastable Processes","funder_award_id":"ANR-19-CE40-0010","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G8780240426","display_name":"Interacting Particle systems for Sampling and Optimization: analysis, algorithms and application to statistical inference","funder_award_id":"ANR-23-CE40-0027","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G883294809","display_name":"International Doctoral Training in Mathematical Sciences in Paris","funder_award_id":"945332","funder_id":"https://openalex.org/F4320338337","funder_display_name":"H2020 Marie Sk\u0142odowska-Curie Actions"}],"funders":[{"id":"https://openalex.org/F4320319993","display_name":"Leverhulme Trust","ror":"https://ror.org/012mzw131"},{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320322892","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73"},{"id":"https://openalex.org/F4320332999","display_name":"Horizon 2020 Framework Programme","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"},{"id":"https://openalex.org/F4320338335","display_name":"H2020 European Research Council","ror":"https://ror.org/0472cxd90"},{"id":"https://openalex.org/F4320338337","display_name":"H2020 Marie Sk\u0142odowska-Curie Actions","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W2522892054","https://openalex.org/W4400814383","https://openalex.org/W2108446661","https://openalex.org/W423603040","https://openalex.org/W2171098928","https://openalex.org/W4376652717","https://openalex.org/W4386142202","https://openalex.org/W2063530260","https://openalex.org/W1977657887","https://openalex.org/W2141361312","https://openalex.org/W2103034645","https://openalex.org/W1987805535","https://openalex.org/W2094034395","https://openalex.org/W2157612169","https://openalex.org/W2401363764","https://openalex.org/W2905194182","https://openalex.org/W2119489903","https://openalex.org/W1979067774","https://openalex.org/W4238063566","https://openalex.org/W4245280614","https://openalex.org/W2062831541","https://openalex.org/W4283264355","https://openalex.org/W2964112122","https://openalex.org/W3216483750","https://openalex.org/W2035452300","https://openalex.org/W2963087995","https://openalex.org/W2962819986","https://openalex.org/W4323639449","https://openalex.org/W1572902284"],"related_works":["https://openalex.org/W3121013341","https://openalex.org/W4287392940","https://openalex.org/W2808706851","https://openalex.org/W1988863536","https://openalex.org/W65440759","https://openalex.org/W2905302290","https://openalex.org/W1997242758","https://openalex.org/W2169816622","https://openalex.org/W2298254442","https://openalex.org/W2169367269"],"abstract_inverted_index":{"We":[0,58],"propose":[1],"a":[2,69],"method":[3,99],"utilizing":[4],"physics-informed":[5],"neural":[6,45,73],"networks":[7,74],"(PINNs)":[8],"to":[9,39,75],"solve":[10,76],"Poisson":[11,41,78],"equations":[12],"that":[13],"serve":[14],"as":[15,28,90],"control":[16,92],"variates":[17],"in":[18],"the":[19,29,40,51,54,65,95,98],"computation":[20],"of":[21,53,64,97],"transport":[22],"coefficients":[23],"via":[24],"fluctuation":[25],"formulas,":[26],"such":[27],"Green--Kubo":[30],"and":[31,67],"generalized":[32],"Einstein-like":[33],"formulas.":[34],"By":[35],"leveraging":[36],"approximate":[37,81],"solutions":[38,82,107],"equation":[42],"constructed":[43],"through":[44],"networks,":[46],"our":[47],"approach":[48],"significantly":[49],"reduces":[50],"variance":[52],"estimator":[55],"at":[56],"hand.":[57],"provide":[59],"an":[60],"extensive":[61],"numerical":[62],"analysis":[63],"estimators":[66],"detail":[68],"methodology":[70],"for":[71,100],"training":[72],"these":[77],"equations.":[79],"The":[80],"are":[83,108],"then":[84],"incorporated":[85],"into":[86],"Monte":[87],"Carlo":[88],"simulations":[89],"effective":[91],"variates,":[93],"demonstrating":[94],"suitability":[96],"moderately":[101],"high-dimensional":[102],"problems":[103],"where":[104],"fully":[105],"deterministic":[106],"computationally":[109],"infeasible.":[110]},"counts_by_year":[],"updated_date":"2026-06-25T08:15:23.626066","created_date":"2025-10-10T00:00:00"}