{"id":"https://openalex.org/W3008327518","doi":"https://doi.org/10.1137/20m1321838","title":"Time Integration of Tree Tensor Networks","display_name":"Time Integration of Tree Tensor Networks","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3008327518","doi":"https://doi.org/10.1137/20m1321838","mag":"3008327518"},"language":"en","primary_location":{"id":"doi:10.1137/20m1321838","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1321838","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":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2002.11392","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5048965593","display_name":"Gianluca Ceruti","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Gianluca Ceruti","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065792988","display_name":"Christian Lubich","orcid":"https://orcid.org/0000-0003-0105-4927"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Christian Lubich","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5078166905","display_name":"Hanna Walach","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hanna Walach","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5048965593"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.414,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.5035461,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"59","issue":"1","first_page":"289","last_page":"313"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9642000198364258,"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":0.9480999708175659,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/integrator","display_name":"Integrator","score":0.8733245134353638},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.7553362846374512},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7178260087966919},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.6688012480735779},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.6327013373374939},{"id":"https://openalex.org/keywords/recursion","display_name":"Recursion (computer science)","score":0.5696660876274109},{"id":"https://openalex.org/keywords/connection","display_name":"Connection (principal bundle)","score":0.4827515482902527},{"id":"https://openalex.org/keywords/tree-structure","display_name":"Tree structure","score":0.4422774910926819},{"id":"https://openalex.org/keywords/tensor-field","display_name":"Tensor field","score":0.4100582003593445},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4097023010253906},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.31511610746383667},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.20347267389297485},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2033362090587616},{"id":"https://openalex.org/keywords/binary-tree","display_name":"Binary tree","score":0.18100011348724365},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1757144033908844},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.1726149022579193},{"id":"https://openalex.org/keywords/exact-solutions-in-general-relativity","display_name":"Exact solutions in general relativity","score":0.15528538823127747},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.13520196080207825}],"concepts":[{"id":"https://openalex.org/C79518650","wikidata":"https://www.wikidata.org/wiki/Q2081431","display_name":"Integrator","level":3,"score":0.8733245134353638},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.7553362846374512},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7178260087966919},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.6688012480735779},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.6327013373374939},{"id":"https://openalex.org/C168773036","wikidata":"https://www.wikidata.org/wiki/Q264164","display_name":"Recursion (computer science)","level":2,"score":0.5696660876274109},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.4827515482902527},{"id":"https://openalex.org/C163797641","wikidata":"https://www.wikidata.org/wiki/Q2067937","display_name":"Tree structure","level":3,"score":0.4422774910926819},{"id":"https://openalex.org/C166077713","wikidata":"https://www.wikidata.org/wiki/Q1758924","display_name":"Tensor field","level":3,"score":0.4100582003593445},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4097023010253906},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.31511610746383667},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.20347267389297485},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2033362090587616},{"id":"https://openalex.org/C197855036","wikidata":"https://www.wikidata.org/wiki/Q380172","display_name":"Binary tree","level":2,"score":0.18100011348724365},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1757144033908844},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.1726149022579193},{"id":"https://openalex.org/C520416788","wikidata":"https://www.wikidata.org/wiki/Q5419229","display_name":"Exact solutions in general relativity","level":2,"score":0.15528538823127747},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.13520196080207825},{"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/C2776257435","wikidata":"https://www.wikidata.org/wiki/Q1576430","display_name":"Bandwidth (computing)","level":2,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1137/20m1321838","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1321838","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:EVASTAR-Karlsruhe.de:1000117729","is_oa":false,"landing_page_url":"https://publikationen.bibliothek.kit.edu/1000117729","pdf_url":null,"source":{"id":"https://openalex.org/S4306401992","display_name":"Repository KITopen (Karlsruhe Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I102335020","host_organization_name":"Karlsruhe Institute of Technology","host_organization_lineage":["https://openalex.org/I102335020"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ISSN: 2365-662X","raw_type":"doc-type:report"},{"id":"pmh:oai:arXiv.org:2002.11392","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2002.11392","pdf_url":"https://arxiv.org/pdf/2002.11392","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":"text"},{"id":"mag:3008327518","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2002.11392.pdf","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.2002.11392","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2002.11392","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"},{"id":"doi:10.5445/ir/1000117729","is_oa":true,"landing_page_url":"https://doi.org/10.5445/ir/1000117729","pdf_url":null,"source":{"id":"https://openalex.org/S7407052948","display_name":"KITopen","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"report"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2002.11392","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2002.11392","pdf_url":"https://arxiv.org/pdf/2002.11392","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":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G325672550","display_name":null,"funder_award_id":"SFB 1173","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G4314459898","display_name":null,"funder_award_id":"58734477","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G5106512922","display_name":null,"funder_award_id":"Deutsche Forschungsgemeinschaft (DFG","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G5951043421","display_name":null,"funder_award_id":"Project-ID 258734477","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G8238022873","display_name":null,"funder_award_id":"258734477","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G8562152207","display_name":null,"funder_award_id":"GRK 1838","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W50417968","https://openalex.org/W220248508","https://openalex.org/W1515678755","https://openalex.org/W1539130646","https://openalex.org/W1580989833","https://openalex.org/W1585991502","https://openalex.org/W1972710290","https://openalex.org/W1993482030","https://openalex.org/W2008931657","https://openalex.org/W2013912476","https://openalex.org/W2024165284","https://openalex.org/W2036463035","https://openalex.org/W2051456448","https://openalex.org/W2064404969","https://openalex.org/W2096434207","https://openalex.org/W2102688209","https://openalex.org/W2118115288","https://openalex.org/W2133512121","https://openalex.org/W2152279941","https://openalex.org/W2895724779","https://openalex.org/W2962793222","https://openalex.org/W2962883250","https://openalex.org/W3005527956","https://openalex.org/W3012661739","https://openalex.org/W3100045827","https://openalex.org/W3102980502","https://openalex.org/W3104980255"],"related_works":["https://openalex.org/W3000163442","https://openalex.org/W2429756633","https://openalex.org/W1967859589","https://openalex.org/W2049119935","https://openalex.org/W1858056047","https://openalex.org/W2099219395","https://openalex.org/W2177413370","https://openalex.org/W2034356527","https://openalex.org/W2889166470","https://openalex.org/W2560362633","https://openalex.org/W2079048889","https://openalex.org/W2057670872","https://openalex.org/W2972657769","https://openalex.org/W2886376036","https://openalex.org/W2091488052","https://openalex.org/W2889573008","https://openalex.org/W3131942543","https://openalex.org/W2360711434","https://openalex.org/W2908392507","https://openalex.org/W2118621948"],"abstract_inverted_index":{"Dynamical":[0],"low-rank":[1,49,73,189],"approximation":[2,12,50,190],"by":[3,51,191],"tree":[4,30,35,103,139,147,153,192],"tensor":[5,22,31,75,113,140,148,193],"networks":[6,32,114,149],"is":[7,37,58,67,157],"studied":[8],"for":[9,29,47,104,131,183],"the":[10,43,72,81,87,96,99,102,105,126,129,132,135,138,151,160,170,180,184,187],"data-sparse":[11],"of":[13,33,101,107,134,150,163,169],"large":[14],"time-dependent":[15,146],"data":[16],"tensors":[17,56],"and":[18,39,53,57,85,118,120,156],"unknown":[19],"solutions":[20],"to":[21,60,98,128,159,175,179],"differential":[23,181],"equations.":[24],"A":[25],"time":[26,79],"integration":[27],"method":[28],"prescribed":[34],"rank":[36,154],"presented":[38],"analyzed.":[40],"It":[41],"extends":[42],"known":[44],"projector-splitting":[45],"integrators":[46,177],"dynamical":[48,188],"matrices":[52],"rank-constrained":[54],"Tucker":[55,74],"shown":[59],"inherit":[61],"their":[62],"favorable":[63],"properties.":[64],"The":[65,142],"integrator":[66,82,143],"based":[68],"on":[69,111],"recursively":[70],"applying":[71],"integrator.":[76],"In":[77],"every":[78],"step,":[80],"climbs":[83],"up":[84],"down":[86],"tree:":[88],"it":[89],"uses":[90],"a":[91],"recursion":[92,122],"that":[93,123],"passes":[94,124],"from":[95,125],"root":[97,130],"leaves":[100,127],"construction":[106],"initial":[108],"value":[109],"problems":[110],"subtree":[112],"using":[115],"appropriate":[116],"restrictions":[117],"prolongations,":[119],"another":[121],"update":[133],"factors":[136,185],"in":[137,167,173,186],"network.":[141],"reproduces":[144],"given":[145],"specified":[152],"exactly":[155],"robust":[158],"typical":[161],"presence":[162],"small":[164],"singular":[165],"values":[166],"matricizations":[168],"connection":[171],"tensors,":[172],"contrast":[174],"standard":[176],"applied":[178],"equations":[182],"networks.":[194]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}