{"id":"https://openalex.org/W4405475749","doi":"https://doi.org/10.1137/23m1588196","title":"WAN Discretization of PDEs: Best Approximation, Stabilization, and Essential Boundary Conditions","display_name":"WAN Discretization of PDEs: Best Approximation, Stabilization, and Essential Boundary Conditions","publication_year":2024,"publication_date":"2024-12-17","ids":{"openalex":"https://openalex.org/W4405475749","doi":"https://doi.org/10.1137/23m1588196"},"language":"en","primary_location":{"id":"doi:10.1137/23m1588196","is_oa":false,"landing_page_url":"https://doi.org/10.1137/23m1588196","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Journal on Scientific Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://discovery.ucl.ac.uk/10203010/1/23m1588196.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5085907253","display_name":"Silvia Bertoluzza","orcid":"https://orcid.org/0000-0002-1354-7158"},"institutions":[{"id":"https://openalex.org/I4210137033","display_name":"Istituto di Matematica Applicata e Tecnologie Informatiche","ror":"https://ror.org/03m0n3c07","country_code":"IT","type":"education","lineage":["https://openalex.org/I4210137033","https://openalex.org/I4210155236"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Silvia Bertoluzza","raw_affiliation_strings":["Istituto di Matematica Applicata e Tecnologie Informatiche, CNR, 27100 Pavia, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Istituto di Matematica Applicata e Tecnologie Informatiche, CNR, 27100 Pavia, Italy","institution_ids":["https://openalex.org/I4210137033"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011409848","display_name":"Erik Burman","orcid":"https://orcid.org/0000-0003-4287-7241"},"institutions":[{"id":"https://openalex.org/I45129253","display_name":"University College London","ror":"https://ror.org/02jx3x895","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I45129253"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Erik Burman","raw_affiliation_strings":["Department of Mathematics, University College London, London, UK"],"raw_orcid":"https://orcid.org/0000-0003-4287-7241","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University College London, London, UK","institution_ids":["https://openalex.org/I45129253"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5090050766","display_name":"Cuiyu He","orcid":"https://orcid.org/0000-0003-1556-2682"},"institutions":[{"id":"https://openalex.org/I115475287","display_name":"Oklahoma State University","ror":"https://ror.org/01g9vbr38","country_code":"US","type":"education","lineage":["https://openalex.org/I115475287"]},{"id":"https://openalex.org/I165733156","display_name":"University of Georgia","ror":"https://ror.org/00te3t702","country_code":"US","type":"education","lineage":["https://openalex.org/I165733156"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Cuiyu He","raw_affiliation_strings":["Department of Mathematics, Oklahoma State University, Stillwater, OK 74078 USA, and Department of Mathematics, University of Georgia, Athens, GA 30602 USA"],"raw_orcid":"https://orcid.org/0000-0003-1556-2682","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Oklahoma State University, Stillwater, OK 74078 USA, and Department of Mathematics, University of Georgia, Athens, GA 30602 USA","institution_ids":["https://openalex.org/I165733156","https://openalex.org/I115475287"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5085907253"],"corresponding_institution_ids":["https://openalex.org/I4210137033"],"apc_list":null,"apc_paid":null,"fwci":1.0783,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.77292299,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":97,"max":98},"biblio":{"volume":"46","issue":"6","first_page":"C688","last_page":"C715"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9998000264167786,"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":0.9998000264167786,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9962999820709229,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9955999851226807,"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/mathematics","display_name":"Mathematics","score":0.8653440475463867},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.8244823217391968},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5964730978012085},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.5469602942466736},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.4791963994503021},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.43608421087265015},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.38090041279792786},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.32727304100990295}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8653440475463867},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.8244823217391968},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5964730978012085},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5469602942466736},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4791963994503021},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.43608421087265015},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.38090041279792786},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.32727304100990295}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/23m1588196","is_oa":false,"landing_page_url":"https://doi.org/10.1137/23m1588196","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Journal on Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:eprints.ucl.ac.uk.OAI2:10203010","is_oa":true,"landing_page_url":"https://discovery.ucl.ac.uk/id/eprint/10203010/","pdf_url":"https://discovery.ucl.ac.uk/10203010/1/23m1588196.pdf","source":{"id":"https://openalex.org/S4306400024","display_name":"UCL Discovery (University College London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I45129253","host_organization_name":"University College London","host_organization_lineage":["https://openalex.org/I45129253"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Scientific Computing , 46  (6)   C688-C715.   (2024)","raw_type":"Article"}],"best_oa_location":{"id":"pmh:oai:eprints.ucl.ac.uk.OAI2:10203010","is_oa":true,"landing_page_url":"https://discovery.ucl.ac.uk/id/eprint/10203010/","pdf_url":"https://discovery.ucl.ac.uk/10203010/1/23m1588196.pdf","source":{"id":"https://openalex.org/S4306400024","display_name":"UCL Discovery (University College London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I45129253","host_organization_name":"University College London","host_organization_lineage":["https://openalex.org/I45129253"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Scientific Computing , 46  (6)   C688-C715.   (2024)","raw_type":"Article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1705107144","display_name":"Integrated Simulation at the Exascale: coupling, synthesis and performance","funder_award_id":"EP/W007460/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G3241107012","display_name":null,"funder_award_id":"EP/V050400/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G3767543860","display_name":"Quantitative estimates of discretisation and modelling errors in variational data assimilation for incompressible flows","funder_award_id":"EP/T033126/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G4492184399","display_name":"Computational methods for inverse problems subject to wave equations in heterogeneous media","funder_award_id":"EP/V050400/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G7934575184","display_name":null,"funder_award_id":"EP/T033126/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4405475749.pdf","grobid_xml":"https://content.openalex.org/works/W4405475749.grobid-xml"},"referenced_works_count":20,"referenced_works":["https://openalex.org/W1601728065","https://openalex.org/W1970454553","https://openalex.org/W2043972301","https://openalex.org/W2342588342","https://openalex.org/W2899283552","https://openalex.org/W2912649832","https://openalex.org/W2963917324","https://openalex.org/W2964110066","https://openalex.org/W2969750612","https://openalex.org/W3007906701","https://openalex.org/W3011828542","https://openalex.org/W3025750359","https://openalex.org/W3040743533","https://openalex.org/W3044174989","https://openalex.org/W3082260983","https://openalex.org/W3083793324","https://openalex.org/W3217139884","https://openalex.org/W4220826888","https://openalex.org/W4224222807","https://openalex.org/W4226311057"],"related_works":["https://openalex.org/W2006251942","https://openalex.org/W2364741597","https://openalex.org/W1492103595","https://openalex.org/W1864774435","https://openalex.org/W946352265","https://openalex.org/W3020787026","https://openalex.org/W2334479858","https://openalex.org/W2793786119","https://openalex.org/W2196719869","https://openalex.org/W2133690079"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,56],"provide":[4],"a":[5,77],"theoretical":[6],"analysis":[7],"of":[8,32,71],"the":[9,28,33,50,58,62,68,72,92],"recently":[10],"introduced":[11],"weakly":[12],"adversarial":[13],"networks":[14],"(WAN)":[15],"method,":[16],"used":[17],"to":[18],"approximate":[19],"partial":[20],"differential":[21],"equations":[22],"in":[23],"high":[24],"dimensions.":[25],"We":[26,40,74],"address":[27],"existence":[29],"and":[30],"stability":[31],"solution,":[34],"as":[35,37],"well":[36],"approximation":[38],"bounds.":[39],"also":[41,75],"propose":[42],"two":[43],"new":[44],"stabilized":[45],"WAN-based":[46],"formulas":[47],"that":[48,66],"avoid":[49],"need":[51],"for":[52,61,82],"direct":[53],"normalization.":[54],"Furthermore,":[55],"analyze":[57],"method\u2019s":[59],"effectiveness":[60],"Dirichlet":[63],"boundary":[64],"problem":[65],"employs":[67],"implicit":[69],"representation":[70],"geometry.":[73],"devise":[76],"pseudotime":[78],"XNODE":[79],"neural":[80,95],"network":[81],"static":[83],"PDE":[84],"problems,":[85],"yielding":[86],"significantly":[87],"faster":[88],"convergence":[89],"results":[90],"than":[91],"classical":[93],"deep":[94],"networks.":[96]},"counts_by_year":[{"year":2025,"cited_by_count":4}],"updated_date":"2025-12-27T23:08:20.325037","created_date":"2025-10-10T00:00:00"}
