{"id":"https://openalex.org/W7160451665","doi":"https://doi.org/10.48550/arxiv.2605.03080","title":"High-Dimensional Enhanced Sampling via Regularized Path-Dependent McKean--Vlasov Dynamics using Tensor Density Approximation","display_name":"High-Dimensional Enhanced Sampling via Regularized Path-Dependent McKean--Vlasov Dynamics using Tensor Density Approximation","publication_year":2026,"publication_date":"2026-05-04","ids":{"openalex":"https://openalex.org/W7160451665","doi":"https://doi.org/10.48550/arxiv.2605.03080"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.03080","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.03080","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":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2605.03080","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5004525330","display_name":"Liyao Lyu","orcid":"https://orcid.org/0000-0003-2994-1464"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lyu, Liyao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5106406898","display_name":"Siyu Guo","orcid":"https://orcid.org/0000-0003-4928-3219"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Guo, Siyu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5135466155","display_name":"Huan Lei","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lei, Huan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":[],"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.32690000534057617,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.32690000534057617,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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":0.07670000195503235,"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":0.05950000137090683,"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/regularization","display_name":"Regularization (linguistics)","score":0.5788999795913696},{"id":"https://openalex.org/keywords/convolution","display_name":"Convolution (computer science)","score":0.42739999294281006},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4244999885559082},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.41339999437332153},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.40130001306533813},{"id":"https://openalex.org/keywords/sampling","display_name":"Sampling (signal processing)","score":0.39570000767707825},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.3919999897480011},{"id":"https://openalex.org/keywords/marginal-distribution","display_name":"Marginal distribution","score":0.38499999046325684}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6563000082969666},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.5788999795913696},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4749000072479248},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4641999900341034},{"id":"https://openalex.org/C45347329","wikidata":"https://www.wikidata.org/wiki/Q5166604","display_name":"Convolution (computer science)","level":3,"score":0.42739999294281006},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4244999885559082},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.41339999437332153},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.40130001306533813},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3978999853134155},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.39570000767707825},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.3919999897480011},{"id":"https://openalex.org/C165216359","wikidata":"https://www.wikidata.org/wiki/Q670653","display_name":"Marginal distribution","level":3,"score":0.38499999046325684},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.3783999979496002},{"id":"https://openalex.org/C2781395549","wikidata":"https://www.wikidata.org/wiki/Q4680762","display_name":"Adaptive sampling","level":3,"score":0.36500000953674316},{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.35600000619888306},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3407999873161316},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.3260999917984009},{"id":"https://openalex.org/C52740198","wikidata":"https://www.wikidata.org/wiki/Q1539564","display_name":"Importance sampling","level":3,"score":0.29429998993873596},{"id":"https://openalex.org/C158424031","wikidata":"https://www.wikidata.org/wiki/Q1191905","display_name":"Gibbs sampling","level":3,"score":0.2816999852657318},{"id":"https://openalex.org/C70518039","wikidata":"https://www.wikidata.org/wiki/Q16000077","display_name":"Dimensionality reduction","level":2,"score":0.27570000290870667},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.2727999985218048},{"id":"https://openalex.org/C62644790","wikidata":"https://www.wikidata.org/wiki/Q3454689","display_name":"Variance reduction","level":3,"score":0.26750001311302185},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.2547999918460846},{"id":"https://openalex.org/C17618745","wikidata":"https://www.wikidata.org/wiki/Q207509","display_name":"Copula (linguistics)","level":2,"score":0.25440001487731934}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.03080","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.03080","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":"doi:10.48550/arxiv.2605.03080","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.03080","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":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","score":0.6866464018821716,"display_name":"Affordable and clean energy"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Sampling":[0],"from":[1],"high-dimensional":[2,65],"Gibbs":[3],"measures":[4],"poses":[5],"a":[6,59,79,106,151],"challenge":[7],"when":[8],"the":[9,29,43,46,51,71,75,83,88,92,96,102,115,122,135,166,169],"energy":[10],"landscape":[11],"consists":[12],"of":[13,45,54,74,82,121,168],"multiple":[14],"metastable":[15],"states.":[16],"Enhanced-sampling":[17],"methods":[18],"mitigate":[19],"this":[20],"difficulty":[21],"by":[22,42,50,78,105],"introducing":[23],"adaptive":[24,55,154],"biasing":[25,155],"potentials":[26,161],"to":[27,110,150,179],"facilitate":[28],"exploration":[30],"along":[31],"prescribed":[32],"collective":[33],"variables":[34],"(CVs),":[35],"but":[36],"their":[37],"scalability":[38],"is":[39,140],"often":[40],"limited":[41],"dimension":[44],"CV":[47,84,97,137,176],"space.":[48],"Motivated":[49],"Wasserstein-gradient-flow":[52],"interpretation":[53],"biasing,":[56],"we":[57],"propose":[58],"regularized":[60,124],"path-dependent":[61,126],"McKean--Vlasov":[62,89],"formulation":[63,69],"for":[64,172],"enhanced":[66],"sampling.":[67],"The":[68],"replaces":[70,101],"variational":[72],"regularization":[73,81],"Wasserstein":[76],"functional":[77,145],"direct":[80],"marginal":[85,138],"density":[86,139],"in":[87,114],"drift,":[90],"avoiding":[91],"outer":[93],"convolution":[94],"over":[95],"domain.":[98],"Furthermore,":[99],"it":[100],"instantaneous":[103],"law":[104],"weighted":[107],"path-history":[108],"measure":[109],"improve":[111],"statistical":[112],"stability":[113],"small-replica":[116],"regime.":[117],"We":[118],"establish":[119],"well-posedness":[120],"resulting":[123],"and":[125,162],"stochastic":[127],"dynamics":[128],"under":[129],"suitable":[130],"assumptions.":[131],"For":[132],"numerical":[133],"realization,":[134],"history-averaged":[136],"approximated":[141],"using":[142],"an":[143],"optimization-free":[144],"hierarchical":[146],"tensor":[147],"representation,":[148],"leading":[149],"scalable":[152],"density-based":[153],"scheme.":[156],"Numerical":[157],"experiments":[158],"on":[159],"benchmark":[160],"molecular":[163],"systems":[164],"demonstrate":[165],"effectiveness":[167],"proposed":[170],"method":[171],"sampling":[173],"problems":[174],"with":[175],"dimensions":[177],"up":[178],"64.":[180]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-05-07T00:00:00"}