{"id":"https://openalex.org/W4310911406","doi":"https://doi.org/10.1137/21m1463768","title":"Projection Methods for Neural Field Equations","display_name":"Projection Methods for Neural Field Equations","publication_year":2023,"publication_date":"2023-03-13","ids":{"openalex":"https://openalex.org/W4310911406","doi":"https://doi.org/10.1137/21m1463768"},"language":"en","primary_location":{"id":"doi:10.1137/21m1463768","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1463768","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://research.vu.nl/en/publications/fb5beee4-a90d-45cf-9499-277c1543e450","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5046360782","display_name":"Daniele Avitabile","orcid":"https://orcid.org/0000-0003-3714-7973"},"institutions":[{"id":"https://openalex.org/I865915315","display_name":"Vrije Universiteit Amsterdam","ror":"https://ror.org/008xxew50","country_code":"NL","type":"education","lineage":["https://openalex.org/I865915315"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"Daniele Avitabile","raw_affiliation_strings":["Vrije Universiteit Amsterdam, Department of Mathematics, Faculteit der Exacte Wetenschappen, De Boelelaan 1081a, 1081 HV Amsterdam, The Netherlands, and MathNeuro Team, Inria Centre at Universit\u00e9 C\u00f4te d\u2019Azur, 2004 route des Lucioles-Bo\u00eete Postale 93 06902, Sophia Antipolis Cedex, France"],"raw_orcid":"https://orcid.org/0000-0003-3714-7973","affiliations":[{"raw_affiliation_string":"Vrije Universiteit Amsterdam, Department of Mathematics, Faculteit der Exacte Wetenschappen, De Boelelaan 1081a, 1081 HV Amsterdam, The Netherlands, and MathNeuro Team, Inria Centre at Universit\u00e9 C\u00f4te d\u2019Azur, 2004 route des Lucioles-Bo\u00eete Postale 93 06902, Sophia Antipolis Cedex, France","institution_ids":["https://openalex.org/I865915315"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5046360782"],"corresponding_institution_ids":["https://openalex.org/I865915315"],"apc_list":null,"apc_paid":null,"fwci":0.6452,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.63046875,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"61","issue":"2","first_page":"562","last_page":"591"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9994999766349792,"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":0.9994999766349792,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9955000281333923,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.98089998960495,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.6897594332695007},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6440054178237915},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.6291704773902893},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6078095436096191},{"id":"https://openalex.org/keywords/projector","display_name":"Projector","score":0.5628547668457031},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4620271325111389},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.43922582268714905},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.43652045726776123},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.37140220403671265},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.28949034214019775},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2654735743999481},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2615097165107727},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09785613417625427}],"concepts":[{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.6897594332695007},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6440054178237915},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.6291704773902893},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6078095436096191},{"id":"https://openalex.org/C2776865275","wikidata":"https://www.wikidata.org/wiki/Q311666","display_name":"Projector","level":2,"score":0.5628547668457031},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4620271325111389},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.43922582268714905},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.43652045726776123},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.37140220403671265},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.28949034214019775},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2654735743999481},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2615097165107727},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09785613417625427},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/21m1463768","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1463768","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:research.vu.nl:openaire_cris_publications/fb5beee4-a90d-45cf-9499-277c1543e450","is_oa":true,"landing_page_url":"https://research.vu.nl/en/publications/fb5beee4-a90d-45cf-9499-277c1543e450","pdf_url":null,"source":{"id":"https://openalex.org/S4306401107","display_name":"VU Research Portal","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I865915315","host_organization_name":"Vrije Universiteit Amsterdam","host_organization_lineage":["https://openalex.org/I865915315"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Avitabile, D 2023, 'PROJECTION METHODS FOR NEURAL FIELD EQUATIONS', SIAM Journal on Numerical Analysis, vol. 61, no. 2, pp. 562-591. https://doi.org/10.1137/21M1463768","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:research.vu.nl:openaire/fb5beee4-a90d-45cf-9499-277c1543e450","is_oa":true,"landing_page_url":"https://hdl.handle.net/1871.1/fb5beee4-a90d-45cf-9499-277c1543e450","pdf_url":null,"source":{"id":"https://openalex.org/S4306401107","display_name":"VU Research Portal","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I865915315","host_organization_name":"Vrije Universiteit Amsterdam","host_organization_lineage":["https://openalex.org/I865915315"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Avitabile, D 2023, 'PROJECTION METHODS FOR NEURAL FIELD EQUATIONS', SIAM Journal on Numerical Analysis, vol. 61, no. 2, pp. 562-591. https://doi.org/10.1137/21M1463768","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":{"id":"pmh:oai:research.vu.nl:openaire_cris_publications/fb5beee4-a90d-45cf-9499-277c1543e450","is_oa":true,"landing_page_url":"https://research.vu.nl/en/publications/fb5beee4-a90d-45cf-9499-277c1543e450","pdf_url":null,"source":{"id":"https://openalex.org/S4306401107","display_name":"VU Research Portal","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I865915315","host_organization_name":"Vrije Universiteit Amsterdam","host_organization_lineage":["https://openalex.org/I865915315"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Avitabile, D 2023, 'PROJECTION METHODS FOR NEURAL FIELD EQUATIONS', SIAM Journal on Numerical Analysis, vol. 61, no. 2, pp. 562-591. https://doi.org/10.1137/21M1463768","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":47,"referenced_works":["https://openalex.org/W316919195","https://openalex.org/W595079961","https://openalex.org/W1152352997","https://openalex.org/W1963638114","https://openalex.org/W1965386465","https://openalex.org/W1978142553","https://openalex.org/W1981115560","https://openalex.org/W1992476998","https://openalex.org/W1998527589","https://openalex.org/W2004571039","https://openalex.org/W2004917186","https://openalex.org/W2006819273","https://openalex.org/W2015102866","https://openalex.org/W2029374903","https://openalex.org/W2032407678","https://openalex.org/W2033022456","https://openalex.org/W2034617954","https://openalex.org/W2036156558","https://openalex.org/W2052040160","https://openalex.org/W2070069190","https://openalex.org/W2106645998","https://openalex.org/W2114363860","https://openalex.org/W2117971770","https://openalex.org/W2129207384","https://openalex.org/W2130694104","https://openalex.org/W2152876587","https://openalex.org/W2154653671","https://openalex.org/W2156526409","https://openalex.org/W2494076123","https://openalex.org/W2594732619","https://openalex.org/W2754238062","https://openalex.org/W2889389256","https://openalex.org/W2889910924","https://openalex.org/W2897659848","https://openalex.org/W2914881533","https://openalex.org/W2962910210","https://openalex.org/W2963234875","https://openalex.org/W3006543920","https://openalex.org/W3012213320","https://openalex.org/W3044654986","https://openalex.org/W3080914972","https://openalex.org/W3099747905","https://openalex.org/W3101755145","https://openalex.org/W4233214253","https://openalex.org/W4247375400","https://openalex.org/W4294836170","https://openalex.org/W4318598293"],"related_works":["https://openalex.org/W2366989203","https://openalex.org/W1492103595","https://openalex.org/W2364741597","https://openalex.org/W2013995543","https://openalex.org/W1864774435","https://openalex.org/W946352265","https://openalex.org/W3020787026","https://openalex.org/W2055696851","https://openalex.org/W2037688108","https://openalex.org/W4238937692"],"abstract_inverted_index":{"Neural":[0,25],"field":[1,97],"models":[2],"are":[3,15,27,140],"nonlinear":[4],"integro-differential":[5],"equations":[6,73],"for":[7,53,62,70,81,94,135,212],"the":[8,75,87,105,109,117,136,152,155,168,180,185,221],"evolution":[9],"of":[10,34,90,108,119,154,191,214],"neuronal":[11,20],"activity,":[12],"and":[13,56,121,147,182,200,203,209,231],"they":[14],"a":[16,58,91,95,101,144,171],"prototypical":[17],"large-scale,":[18],"coarse-grained":[19],"model":[21],"in":[22,32,37,127,170],"continuum":[23],"cortices.":[24],"fields":[26,55],"often":[28],"simulated":[29],"heuristically":[30],"and,":[31],"spite":[33],"their":[35,40],"popularity":[36],"mathematical":[38],"neuroscience,":[39],"numerical":[41],"analysis":[42],"is":[43,79,98,124],"not":[44],"yet":[45],"fully":[46],"established.":[47],"We":[48,65,84,188],"introduce":[49,224],"generic":[50],"projection":[51,92,110,193],"methods":[52],"neural":[54,96],"derive":[57,217],"priori":[59],"error":[60,169,218],"bounds":[61,219],"these":[63],"schemes.":[64],"extend":[66],"an":[67,158,163],"existing":[68],"framework":[69],"stationary":[71],"integral":[72,137],"to":[74,100,132],"time-dependent":[76],"case,":[77],"which":[78,115,139],"relevant":[80],"neuroscience":[82],"applications.":[83],"find":[85],"that":[86,167],"convergence":[88,106,234],"rate":[89,107],"scheme":[93],"determined":[99],"great":[102],"extent":[103],"by":[104],"operator.":[111],"This":[112],"abstract":[113],"analysis,":[114],"unifies":[116],"treatment":[118],"collocation":[120,196],"Galerkin":[122,205],"schemes,":[123],"carried":[125],"out":[126],"operator":[128],"form,":[129],"without":[130],"resorting":[131],"quadrature":[133],"rules":[134],"term,":[138],"introduced":[141],"only":[142],"at":[143],"later":[145],"stage,":[146],"whose":[148],"choice":[149,153],"depends":[150],"on":[151],"projector.":[156],"Using":[157],"elementary":[159],"time":[160,172,186],"stepper":[161,173],"as":[162],"example,":[164],"we":[165,216],"demonstrate":[166],"has":[174],"two":[175,195,204],"separate":[176],"contributions:":[177],"one":[178,183],"from":[179,184,220],"projector":[181],"discretization.":[187],"give":[189],"examples":[190],"concrete":[192],"methods:":[194],"schemes":[197,206],"(piecewise":[198],"linear":[199],"spectral":[201,210],"collocation)":[202],"(finite":[207],"element":[208],"Galerkin);":[211],"each":[213],"them":[215],"general":[222],"theory,":[223],"several":[225],"discrete":[226],"variants,":[227],"provide":[228],"implementation":[229],"details,":[230],"present":[232],"reproducible":[233],"tests.":[235]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2024,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}