{"id":"https://openalex.org/W4383815758","doi":"https://doi.org/10.1137/22m1477805","title":"Efficient Natural Gradient Descent Methods for Large-Scale PDE-Based Optimization Problems","display_name":"Efficient Natural Gradient Descent Methods for Large-Scale PDE-Based Optimization Problems","publication_year":2023,"publication_date":"2023-07-10","ids":{"openalex":"https://openalex.org/W4383815758","doi":"https://doi.org/10.1137/22m1477805"},"language":"en","primary_location":{"id":"doi:10.1137/22m1477805","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1477805","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5069946985","display_name":"Levon Nurbekyan","orcid":"https://orcid.org/0000-0002-6227-0941"},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Levon Nurbekyan","raw_affiliation_strings":["Department of Mathematics, University of California Los Angeles, Los Angeles, CA 90095 USA"],"raw_orcid":"https://orcid.org/0000-0002-6227-0941","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of California Los Angeles, Los Angeles, CA 90095 USA","institution_ids":["https://openalex.org/I161318765"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038146017","display_name":"Wanzhou Lei","orcid":null},"institutions":[{"id":"https://openalex.org/I2801851002","display_name":"Harvard University Press","ror":"https://ror.org/006v7bf86","country_code":"US","type":"other","lineage":["https://openalex.org/I136199984","https://openalex.org/I2801851002"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Wanzhou Lei","raw_affiliation_strings":["Harvard University, Cambridge, MA 02138 USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Harvard University, Cambridge, MA 02138 USA","institution_ids":["https://openalex.org/I2801851002"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5003942837","display_name":"Yunan Yang","orcid":"https://orcid.org/0000-0001-7238-7978"},"institutions":[{"id":"https://openalex.org/I205783295","display_name":"Cornell University","ror":"https://ror.org/05bnh6r87","country_code":"US","type":"education","lineage":["https://openalex.org/I205783295"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yunan Yang","raw_affiliation_strings":["Department of Mathematics, Cornell University, Ithaca, NY 14853 USA"],"raw_orcid":"https://orcid.org/0000-0001-7238-7978","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Cornell University, Ithaca, NY 14853 USA","institution_ids":["https://openalex.org/I205783295"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.3503,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.9282899,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":99},"biblio":{"volume":"45","issue":"4","first_page":"A1621","last_page":"A1655"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9998999834060669,"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"}},{"id":"https://openalex.org/T11304","display_name":"Advanced Neuroimaging Techniques and Applications","score":0.9976999759674072,"subfield":{"id":"https://openalex.org/subfields/2741","display_name":"Radiology, Nuclear Medicine and Imaging"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/jacobian-matrix-and-determinant","display_name":"Jacobian matrix and determinant","score":0.749768078327179},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7096147537231445},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.6120510697364807},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.588315486907959},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5313224196434021},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5302350521087646},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.5030164122581482},{"id":"https://openalex.org/keywords/gradient-method","display_name":"Gradient method","score":0.4314204454421997},{"id":"https://openalex.org/keywords/metric-space","display_name":"Metric space","score":0.41511833667755127},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.41510212421417236},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.37729665637016296},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.24343106150627136},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.19162532687187195}],"concepts":[{"id":"https://openalex.org/C200331156","wikidata":"https://www.wikidata.org/wiki/Q506041","display_name":"Jacobian matrix and determinant","level":2,"score":0.749768078327179},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7096147537231445},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.6120510697364807},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.588315486907959},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5313224196434021},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5302350521087646},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.5030164122581482},{"id":"https://openalex.org/C115680565","wikidata":"https://www.wikidata.org/wiki/Q5977448","display_name":"Gradient method","level":2,"score":0.4314204454421997},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.41511833667755127},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.41510212421417236},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.37729665637016296},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.24343106150627136},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.19162532687187195},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/22m1477805","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1477805","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G667366214","display_name":null,"funder_award_id":"MURI FA 9550 18-1-0502","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320327714","display_name":"ETH Z\u00fcrich Foundation","ror":null},{"id":"https://openalex.org/F4320332640","display_name":"Courant Institute of Mathematical Sciences, New York University","ror":"https://ror.org/0190ak572"},{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W71081281","https://openalex.org/W1520168181","https://openalex.org/W1585160083","https://openalex.org/W1970789124","https://openalex.org/W1980287119","https://openalex.org/W1990457366","https://openalex.org/W1995531958","https://openalex.org/W2035265321","https://openalex.org/W2100245965","https://openalex.org/W2104760318","https://openalex.org/W2117756735","https://openalex.org/W2125916088","https://openalex.org/W2126016605","https://openalex.org/W2130984546","https://openalex.org/W2172968643","https://openalex.org/W2899283552","https://openalex.org/W2963367966","https://openalex.org/W2963645788","https://openalex.org/W2967196698","https://openalex.org/W2969211630","https://openalex.org/W2969499516","https://openalex.org/W2989660359","https://openalex.org/W3014253345","https://openalex.org/W3014811424","https://openalex.org/W3025478249","https://openalex.org/W3092249998","https://openalex.org/W3098813942","https://openalex.org/W3120224631","https://openalex.org/W3139511156","https://openalex.org/W3151180318","https://openalex.org/W3152208773","https://openalex.org/W3186981831","https://openalex.org/W3203221938","https://openalex.org/W3206822015","https://openalex.org/W3215612457","https://openalex.org/W4229666556","https://openalex.org/W4282837570","https://openalex.org/W4301014524"],"related_works":["https://openalex.org/W263682811","https://openalex.org/W2846499288","https://openalex.org/W2564172750","https://openalex.org/W3197592642","https://openalex.org/W3199158697","https://openalex.org/W2356977358","https://openalex.org/W2302465375","https://openalex.org/W2098528027","https://openalex.org/W2088605360","https://openalex.org/W2379811207"],"abstract_inverted_index":{".We":[0],"propose":[1],"efficient":[2,53],"numerical":[3,56,123],"schemes":[4],"for":[5,12,95],"implementing":[6],"the":[7,28,47,64,67,70,76,128,132],"natural":[8,29,93],"gradient":[9,30,134],"descent":[10,135],"(NGD)":[11],"a":[13,33,36,96],"broad":[14],"range":[15],"of":[16,42,69,111,119],"metric":[17,143],"spaces":[18,144],"with":[19,73],"applications":[20],"to":[21,35,75,105,116],"PDE-based":[22],"optimization":[23,147],"problems.":[24],"Our":[25],"technique":[26],"represents":[27],"direction":[31],"as":[32],"solution":[34],"standard":[37,133],"least-squares":[38],"problem.":[39],"Hence,":[40],"instead":[41],"calculating,":[43],"storing,":[44],"or":[45,82],"inverting":[46],"information":[48],"matrix":[49],"directly,":[50],"we":[51,102],"apply":[52],"methods":[54,139],"from":[55],"linear":[57],"algebra.":[58],"We":[59,87],"treat":[60],"both":[61],"scenarios":[62],"where":[63],"Jacobian,":[65],"i.e.,":[66],"derivative":[68],"state":[71],"variable":[72],"respect":[74],"parameter,":[77],"is":[78],"either":[79],"explicitly":[80],"known":[81],"implicitly":[83],"given":[84],"through":[85],"constraints.":[86],"can":[88],"thus":[89],"reliably":[90],"compute":[91,106],"several":[92],"NGDs":[94],"large-scale":[97],"parameter":[98],"space.":[99],"In":[100],"particular,":[101],"are":[103],"able":[104],"Wasserstein":[107],"NGD":[108,138],"in":[109,145],"thousands":[110],"dimensions,":[112],"which":[113],"was":[114],"believed":[115],"be":[117],"out":[118],"reach.":[120],"Finally,":[121],"our":[122],"results":[124],"shed":[125],"light":[126],"on":[127,141],"qualitative":[129],"differences":[130],"between":[131],"and":[136],"various":[137],"based":[140],"different":[142],"nonconvex":[146],"problems.Keywordsnatural":[148],"gradientconstrained":[149],"optimizationleast-squares":[150],"methodgradient":[151],"flowinverse":[152],"problemMSC":[153],"codes65K1049M1549M4190C2649Q22":[154]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":5}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}