{"id":"https://openalex.org/W7225627755","doi":"https://doi.org/10.3390/a19110973","title":"A Physics-Agnostic Tensor-Train Framework for Discretized Parametric Solution Maps of Dynamical Systems","display_name":"A Physics-Agnostic Tensor-Train Framework for Discretized Parametric Solution Maps of Dynamical Systems","publication_year":2026,"publication_date":"2026-11-08","ids":{"openalex":"https://openalex.org/W7225627755","doi":"https://doi.org/10.3390/a19110973"},"language":"en","primary_location":{"id":"doi:10.3390/a19110973","doi":"https://doi.org/10.3390/a19110973","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a19110973","pdf_url":null,"source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","jufo-1","norway-1","poland-40","russia-white-list-2","vabb-shw"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.3390/a19110973","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5014223403","display_name":"Gianmarco Manzini","orcid":"https://orcid.org/0000-0003-3626-3112","observed_orcids":["https://orcid.org/0000-0003-3626-3112"]},"institutions":[{"id":"https://openalex.org/I1343871089","display_name":"Los Alamos National Laboratory","ror":"https://ror.org/01e41cf67","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I1343871089","https://openalex.org/I198811213","https://openalex.org/I4210120050"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Gianmarco Manzini","raw_affiliation_strings":["Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA"],"raw_orcid":"https://orcid.org/0000-0003-3626-3112","affiliations":[{"raw_affiliation_string":"Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA","institution_ids":["https://openalex.org/I1343871089"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5077813019","display_name":"Yancey H. Sechrest","orcid":"https://orcid.org/0000-0002-0897-9298","observed_orcids":["https://orcid.org/0000-0002-0897-9298"]},"institutions":[{"id":"https://openalex.org/I1343871089","display_name":"Los Alamos National Laboratory","ror":"https://ror.org/01e41cf67","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I1343871089","https://openalex.org/I198811213","https://openalex.org/I4210120050"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yancey H. Sechrest","raw_affiliation_strings":["Intelligence and Space Research, Los Alamos National Laboratory, Los Alamos, NM 87545, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Intelligence and Space Research, Los Alamos National Laboratory, Los Alamos, NM 87545, USA","institution_ids":["https://openalex.org/I1343871089"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5014223403"],"corresponding_institution_ids":["https://openalex.org/I1343871089"],"apc_list":{"value":1600,"currency":"CHF","value_usd":1930},"apc_paid":{"value":1600,"currency":"CHF","value_usd":1930},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"19","issue":"11","first_page":"973","last_page":"973"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.7782999873161316,"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":0.7782999873161316,"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":0.16670000553131104,"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 Solvers for Ordinary Differential Equations","score":0.010300000198185444,"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/tensor-train","display_name":"tensor train","score":0.8500000238418579},{"id":"https://openalex.org/keywords/dynamical-systems","display_name":"dynamical systems","score":0.9620000123977661},{"id":"https://openalex.org/keywords/tensor-compression","display_name":"tensor compression","score":0.3070000112056732},{"id":"https://openalex.org/keywords/atmospheric-flight","display_name":"atmospheric flight","score":0.8899999856948853},{"id":"https://openalex.org/keywords/compartmental-epidemic-model","display_name":"compartmental epidemic model","score":0.9890000224113464},{"id":"https://openalex.org/keywords/uncertainty-quantification","display_name":"uncertainty quantification","score":0.718999981880188},{"id":"https://openalex.org/keywords/kriging-surrogate-model","display_name":"Kriging surrogate model","score":0.8410000205039978}],"concepts":[{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5914000272750854},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.5212000012397766},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.5098999738693237},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.5051000118255615},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.48429998755455017},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4823000133037567},{"id":"https://openalex.org/C114275822","wikidata":"https://www.wikidata.org/wiki/Q621512","display_name":"Linear dynamical system","level":3,"score":0.47099998593330383},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.4643000066280365},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.45809999108314514},{"id":"https://openalex.org/C99692599","wikidata":"https://www.wikidata.org/wiki/Q596577","display_name":"Dissipative system","level":2,"score":0.45190000534057617},{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.42980000376701355},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.38339999318122864},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.3540000021457672},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3528999984264374},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.34689998626708984},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.3343000113964081},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.33059999346733093},{"id":"https://openalex.org/C201362023","wikidata":"https://www.wikidata.org/wiki/Q658574","display_name":"Hermite polynomials","level":2,"score":0.3174000084400177},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.31130000948905945},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.3075999915599823},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.29269999265670776},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.288100004196167},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.2773999869823456},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.27709999680519104},{"id":"https://openalex.org/C197656079","wikidata":"https://www.wikidata.org/wiki/Q17147719","display_name":"Polynomial chaos","level":3,"score":0.2721000015735626},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.27140000462532043}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3390/a19110973","doi":"https://doi.org/10.3390/a19110973","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a19110973","pdf_url":null,"source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","jufo-1","norway-1","poland-40","russia-white-list-2","vabb-shw"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.3390/a19110973","doi":"https://doi.org/10.3390/a19110973","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a19110973","pdf_url":null,"source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","jufo-1","norway-1","poland-40","russia-white-list-2","vabb-shw"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W3208143138","https://openalex.org/W3087584314","https://openalex.org/W4283729117","https://openalex.org/W2460595379","https://openalex.org/W7095079643","https://openalex.org/W7167487830","https://openalex.org/W4399119074","https://openalex.org/W2088087394","https://openalex.org/W6889688782","https://openalex.org/W4416948187"],"abstract_inverted_index":{"Wepresent":[0],"a":[1,11,15,37,62,69,76,96,100,105,117,122,136,142,220,263],"computational":[2],"framework":[3,94],"that":[4,259],"builds":[5],"the":[6,30,34,41,44,51,81,93,130,148,156,164,170,173,177,182,186,189,201,204,213,223,233,247,260,270,273,282],"parametric":[7,264],"solution":[8,265],"map":[9,266],"of":[10,17,139,145,151,159,203,262,272,284],"dynamical":[12],"system":[13],"as":[14,209],"family":[16],"tensor":[18,63],"trains,":[19],"one":[20,66,85],"per":[21,87],"state":[22,42,74],"component,":[23],"by":[24,269,277,281],"cross-interpolation.":[25],"A":[26,237],"minimal":[27],"contract":[28],"separates":[29],"generic":[31],"machinery":[32],"from":[33],"specific":[35],"dynamics:":[36],"physics":[38],"module":[39],"supplies":[40],"derivative,":[43],"parameter":[45,89,253,274],"axes":[46],"with":[47,110,200,239],"their":[48],"ranges,":[49],"and":[50,54,104,121,158,185,207,242,255],"index-to-state":[52],"mapping,":[53],"nothing":[55],"else":[56],"changes":[57],"between":[58],"applications.":[59,236],"Time":[60],"is":[61,172,219,267],"axis,":[64],"so":[65],"integration":[67,86],"fills":[68],"complete":[70],"fiber":[71],"for":[72],"all":[73],"components;":[75],"bitwise-correct":[77],"caching":[78],"mechanism":[79],"reduces":[80],"construction":[82,134],"cost":[83],"to":[84,226],"distinct":[88],"point.":[90],"We":[91],"demonstrate":[92],"on":[95,147,155,163,246],"conservative":[97],"cislunar":[98],"problem,":[99,103],"dissipative":[101],"atmospheric-flight":[102],"compartmental":[106],"epidemic":[107,214],"model,":[108],"verified":[109],"instruments":[111],"including":[112],"an":[113],"analytic":[114],"vacuum":[115],"limit,":[116],"nonlinear":[118],"first":[119,149],"integral,":[120],"round-trip":[123],"closure":[124],"at":[125,141,153,161],"least":[126],"three":[127,249],"orders":[128],"below":[129,181],"reported":[131],"errors.":[132],"The":[133,166,196],"attains":[135],"held-out":[137],"accuracy":[138,191],"3.6\u00b710\u22127":[140],"compression":[143],"factor":[144],"8.9\u00b7105":[146],"benchmark,":[150],"6.6\u00b710\u22124":[152],"7.8\u00b7102":[154],"second,":[157],"9.2\u00b710\u22124":[160],"1.9\u00b7102":[162],"third.":[165],"rank":[167,179,197,224],"rather":[168,279],"than":[169,280],"grid":[171,183,187],"binding":[174],"constraint":[175],"while":[176,229],"required":[178],"stays":[180],"cardinality,":[184],"caps":[188],"attainable":[190],"once":[192],"it":[193,210,230],"does":[194],"not.":[195],"demand":[198],"grows":[199],"size":[202],"uncertainty":[205],"set":[206],"falls":[208,225],"contracts:":[211],"in":[212,232],"application,":[215],"where":[216],"every":[217],"axis":[218],"physical":[221],"uncertainty,":[222],"its":[227],"minimum,":[228],"plateaus":[231],"other":[234],"two":[235],"comparison":[238],"polynomial":[240],"chaos":[241],"Gaussian":[243],"process":[244],"surrogates":[245],"same":[248],"families,":[250],"under":[251],"identical":[252],"boxes":[254],"error":[256],"metrics,":[257],"indicates":[258],"difficulty":[261],"governed":[268],"width":[271],"box":[275],"direction":[276,278],"number":[283],"directions.":[285]},"counts_by_year":[],"updated_date":"2026-11-11T12:16:26.678958","created_date":"2026-11-10T00:00:00"}
