{"id":"https://openalex.org/W4417293689","doi":"https://doi.org/10.48550/arxiv.2512.10083","title":"Metric-driven numerical methods","display_name":"Metric-driven numerical methods","publication_year":2025,"publication_date":"2025-12-10","ids":{"openalex":"https://openalex.org/W4417293689","doi":"https://doi.org/10.48550/arxiv.2512.10083"},"language":null,"primary_location":{"id":"pmh:oai:arXiv.org:2512.10083","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2512.10083","pdf_url":"https://arxiv.org/pdf/2512.10083","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2512.10083","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5061248986","display_name":"Patrick Henning","orcid":"https://orcid.org/0000-0002-6432-5504"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Henning, Patrick","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5120791271","display_name":"Laura Huynh","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Huynh, Laura","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5014228488","display_name":"Daniel Peterseim","orcid":"https://orcid.org/0000-0001-7213-556X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Peterseim, Daniel","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5061248986"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.36419999599456787,"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"}},"topics":[{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.36419999599456787,"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"}},{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.18569999933242798,"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/T11804","display_name":"Quantum many-body systems","score":0.04569999873638153,"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/sobolev-space","display_name":"Sobolev space","score":0.613099992275238},{"id":"https://openalex.org/keywords/focus","display_name":"Focus (optics)","score":0.6098999977111816},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.5633000135421753},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5587000250816345},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.4796000123023987},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.4641000032424927},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.447299987077713},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.3653999865055084}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6195999979972839},{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.613099992275238},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.6098999977111816},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5874000191688538},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.5633000135421753},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5587000250816345},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.4796000123023987},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.4641000032424927},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.447299987077713},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.41190001368522644},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3691999912261963},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.3653999865055084},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.3587999939918518},{"id":"https://openalex.org/C2778258933","wikidata":"https://www.wikidata.org/wiki/Q16918986","display_name":"Decomposition method (queueing theory)","level":2,"score":0.3463999927043915},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.31709998846054077},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.31520000100135803},{"id":"https://openalex.org/C198880260","wikidata":"https://www.wikidata.org/wiki/Q5289813","display_name":"Domain decomposition methods","level":3,"score":0.3138999938964844},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.31049999594688416},{"id":"https://openalex.org/C2986878899","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical approximation","level":3,"score":0.2639999985694885},{"id":"https://openalex.org/C23463724","wikidata":"https://www.wikidata.org/wiki/Q2308831","display_name":"Spectral method","level":2,"score":0.26010000705718994},{"id":"https://openalex.org/C145242015","wikidata":"https://www.wikidata.org/wiki/Q774123","display_name":"Approximation theory","level":2,"score":0.2563000023365021},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.2556000053882599}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2512.10083","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2512.10083","pdf_url":"https://arxiv.org/pdf/2512.10083","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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.2512.10083","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2512.10083","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":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2512.10083","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2512.10083","pdf_url":"https://arxiv.org/pdf/2512.10083","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"In":[0,121],"this":[1],"paper,":[2],"we":[3,123,155],"explore":[4],"the":[5,38,43,56,70,89,115,133,148,162],"concept":[6],"of":[7,19,31,45,48,91,128,147,165],"metric-driven":[8,60,98,149],"numerical":[9],"methods":[10,61],"as":[11],"a":[12,46,125,141,145,152],"powerful":[13],"tool":[14],"for":[15,62,151],"solving":[16],"various":[17],"types":[18],"multiscale":[20,119,129],"partial":[21],"differential":[22],"equations.":[23],"Our":[24],"focus":[25],"is":[26],"on":[27,132],"computing":[28],"constrained":[29],"minimizers":[30],"functionals":[32],"-":[33,42],"or,":[34],"equivalently,":[35],"by":[36],"considering":[37],"associated":[39],"Euler-Lagrange":[40],"equations":[41],"solution":[44,116],"class":[47,127],"eigenvalue":[49],"problems":[50,64],"that":[51,72,88],"may":[52],"involve":[53],"nonlinearities":[54],"in":[55,77,110],"eigenfunctions.":[57],"We":[58,86],"introduce":[59],"such":[63],"via":[65],"Riemannian":[66],"gradient":[67],"techniques,":[68],"leveraging":[69],"idea":[71],"gradients":[73],"can":[74],"be":[75],"represented":[76],"different":[78],"metrics":[79],"(so-called":[80],"Sobolev":[81],"gradients)":[82],"to":[83,96,160],"accelerate":[84],"convergence.":[85],"show":[87],"choice":[90],"metric":[92],"not":[93],"only":[94],"leads":[95],"specific":[97],"iterative":[99],"schemes,":[100],"but":[101],"also":[102,156],"induces":[103],"approximation":[104],"spaces":[105,130],"with":[106],"enhanced":[107],"properties,":[108],"particularly":[109],"low-regularity":[111],"regimes":[112],"or":[113],"when":[114],"exhibits":[117],"heterogeneous":[118],"features.":[120],"fact,":[122],"recover":[124],"well-known":[126],"based":[131],"Localized":[134],"Orthogonal":[135],"Decomposition":[136],"(LOD),":[137],"now":[138],"derived":[139],"from":[140],"new":[142],"perspective.":[143],"Alongside":[144],"discussion":[146],"approach":[150],"model":[153],"problem,":[154],"demonstrate":[157],"its":[158],"application":[159],"simulating":[161],"ground":[163],"states":[164],"spin-orbit-coupled":[166],"Bose-Einstein":[167],"condensates.":[168]},"counts_by_year":[],"updated_date":"2026-03-07T16:01:11.037858","created_date":"2025-12-13T00:00:00"}
