{"id":"https://openalex.org/W7128740772","doi":"https://doi.org/10.48550/arxiv.2602.10392","title":"Tensor Methods: A Unified and Interpretable Approach for Material Design","display_name":"Tensor Methods: A Unified and Interpretable Approach for Material Design","publication_year":2026,"publication_date":"2026-02-11","ids":{"openalex":"https://openalex.org/W7128740772","doi":"https://doi.org/10.48550/arxiv.2602.10392"},"language":null,"primary_location":{"id":"pmh:doi:10.48550/arxiv.2602.10392","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":null,"any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5109818905","display_name":"Shaan Pakala","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Pakala, Shaan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088506135","display_name":"Aldair E. Gongora","orcid":"https://orcid.org/0000-0002-1287-1570"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gongora, Aldair E.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5125735859","display_name":"Brian Giera","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Giera, Brian","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5054849323","display_name":"Evangelos E. Papalexakis","orcid":"https://orcid.org/0000-0002-3411-8483"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Papalexakis, Evangelos E.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5109818905"],"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/T11948","display_name":"Machine Learning in Materials Science","score":0.7860000133514404,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11948","display_name":"Machine Learning in Materials Science","score":0.7860000133514404,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials 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":0.09520000219345093,"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/T12303","display_name":"Tensor decomposition and applications","score":0.013199999928474426,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/interpretability","display_name":"Interpretability","score":0.7567999958992004},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.7386000156402588},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.6877999901771545},{"id":"https://openalex.org/keywords/sampling","display_name":"Sampling (signal processing)","score":0.5546000003814697},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.531499981880188},{"id":"https://openalex.org/keywords/tensor-contraction","display_name":"Tensor contraction","score":0.375},{"id":"https://openalex.org/keywords/material-design","display_name":"Material Design","score":0.3662000000476837}],"concepts":[{"id":"https://openalex.org/C2781067378","wikidata":"https://www.wikidata.org/wiki/Q17027399","display_name":"Interpretability","level":2,"score":0.7567999958992004},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.7386000156402588},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.6877999901771545},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.5546000003814697},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5356000065803528},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.531499981880188},{"id":"https://openalex.org/C124007464","wikidata":"https://www.wikidata.org/wiki/Q428091","display_name":"Tensor contraction","level":3,"score":0.375},{"id":"https://openalex.org/C2777152284","wikidata":"https://www.wikidata.org/wiki/Q17590603","display_name":"Material Design","level":2,"score":0.3662000000476837},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3637999892234802},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.36320000886917114},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.34630000591278076},{"id":"https://openalex.org/C131675550","wikidata":"https://www.wikidata.org/wiki/Q7646884","display_name":"Surrogate model","level":2,"score":0.335099995136261},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.3203999996185303},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3084999918937683},{"id":"https://openalex.org/C166077713","wikidata":"https://www.wikidata.org/wiki/Q1758924","display_name":"Tensor field","level":3,"score":0.30820000171661377},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.30809998512268066},{"id":"https://openalex.org/C64835786","wikidata":"https://www.wikidata.org/wiki/Q17004583","display_name":"Cartesian tensor","level":5,"score":0.3018999993801117},{"id":"https://openalex.org/C34559072","wikidata":"https://www.wikidata.org/wiki/Q2334061","display_name":"Design of experiments","level":2,"score":0.29919999837875366},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.2881999909877777},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.288100004196167},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.2736999988555908},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.2578999996185303}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:doi:10.48550/arxiv.2602.10392","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"doi:10.48550/arxiv.2602.10392","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.10392","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:doi:10.48550/arxiv.2602.10392","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities","score":0.40877509117126465}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"When":[0],"designing":[1],"new":[2],"materials,":[3],"it":[4],"is":[5,266],"often":[6,88],"necessary":[7],"to":[8,15,19,65,78,93,135,169,202,211,268,277],"tailor":[9],"the":[10,28,34,40,67,100,109,114,143,161,174,184,189,218,236,257,271,284],"material":[11,47,83],"design":[12,17,31,68,110,237],"(with":[13],"respect":[14],"its":[16],"parameters)":[18],"have":[20],"some":[21,287],"desired":[22],"properties":[23],"(e.g.":[24],"Young's":[25],"modulus).":[26],"As":[27],"set":[29],"of":[30,45,108,116,146,160,188,220,223,235,289],"parameters":[32],"grow,":[33],"search":[35,66],"space":[36],"grows":[37],"exponentially,":[38],"making":[39],"actual":[41],"synthesis":[42],"and":[43,95,126,282],"evaluation":[44],"all":[46],"combinations":[48],"virtually":[49],"impossible.":[50],"Even":[51],"using":[52],"traditional":[53,138],"computational":[54],"methods":[55,71,87,119,132,244,274],"such":[56],"as":[57,120,157],"Finite":[58],"Element":[59],"Analysis":[60],"becomes":[61],"too":[62],"computationally":[63],"heavy":[64],"space.":[69,111,238],"Recent":[70],"use":[72,115],"machine":[73],"learning":[74],"(ML)":[75],"surrogate":[76,224],"models":[77,225],"more":[79,241],"efficiently":[80],"determine":[81],"optimal":[82],"designs;":[84],"unfortunately,":[85],"these":[86,194,251],"(i)":[89],"are":[90,133,152,167,181,209],"notoriously":[91],"difficult":[92],"interpret":[94],"(ii)":[96],"under":[97],"perform":[98],"when":[99,226],"training":[101,229],"data":[102,230],"comes":[103,260],"from":[104,231,261],"a":[105,158,232,262],"non-uniform":[106,233],"sampling":[107,234,253],"We":[112,128,215,239,255],"suggest":[113],"tensor":[117,131,149,175,195,243,263],"completion":[118],"an":[121],"all-in-one":[122],"approach":[123],"for":[124,155],"interpretability":[125],"predictions.":[127],"observe":[129,240],"classical":[130],"able":[134,168,210,267],"compete":[136],"with":[137,142,183],"ML":[139,273],"in":[140,250,286],"predictions,":[141],"added":[144],"benefit":[145],"their":[147],"interpretable":[148],"factors":[150,196],"(which":[151],"given":[153,207],"completely":[154],"free,":[156],"result":[159],"prediction).":[162],"In":[163],"our":[164,179],"experiments,":[165],"we":[166,208,227],"rediscover":[170,212],"physical":[171],"phenomena":[172],"via":[173],"factors,":[176],"indicating":[177],"that":[178,245],"predictions":[180],"aligned":[182],"true":[185],"underlying":[186],"physics":[187],"problem.":[190],"This":[191],"also":[192,216],"means":[193],"could":[197],"be":[198],"used":[199],"by":[200,275],"experimentalists":[201],"identify":[203],"potentially":[204],"novel":[205],"patterns,":[206],"existing":[213],"ones.":[214],"study":[217],"effects":[219],"both":[221],"types":[222],"encounter":[228],"specialized":[242],"can":[246],"give":[247],"better":[248],"generalization":[249,259],"non-uniforms":[252],"scenarios.":[254],"find":[256],"best":[258],"model,":[264],"which":[265],"improve":[269],"upon":[270],"baseline":[272],"up":[276],"5%":[278],"on":[279],"aggregate":[280],"$R^2$,":[281],"halve":[283],"error":[285],"out":[288],"distribution":[290],"regions.":[291]},"counts_by_year":[],"updated_date":"2026-05-05T08:41:31.759640","created_date":"2026-02-13T00:00:00"}
