{"id":"https://openalex.org/W7224739427","doi":"https://doi.org/10.48550/arxiv.2610.39568","title":"Diffusion models for the $O(3)$ nonlinear sigma model","display_name":"Diffusion models for the $O(3)$ nonlinear sigma model","publication_year":2026,"publication_date":"2026-10-29","ids":{"openalex":"https://openalex.org/W7224739427","doi":"https://doi.org/10.48550/arxiv.2610.39568"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.39568","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.39568","pdf_url":"https://arxiv.org/pdf/2610.39568","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"raw_type":"text"},"volume":null,"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.39568","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5079217920","display_name":"Daniel Schubring","orcid":"https://orcid.org/0000-0001-8778-2399","observed_orcids":["https://orcid.org/0000-0001-8778-2399"]},"institutions":[{"id":"https://openalex.org/I125687163","display_name":"City College of New York","ror":"https://ror.org/00wmhkr98","country_code":"US","type":"education","lineage":["https://openalex.org/I125687163"]},{"id":"https://openalex.org/I174216632","display_name":"City University of New York","ror":"https://ror.org/00453a208","country_code":"US","type":"education","lineage":["https://openalex.org/I174216632"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Schubring, Daniel","raw_affiliation_strings":["Department of Physics , City College of New York , CUNY New York , NY 10031 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics , City College of New York , CUNY New York , NY 10031 , USA","institution_ids":["https://openalex.org/I125687163","https://openalex.org/I174216632"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5079217920"],"corresponding_institution_ids":["https://openalex.org/I125687163","https://openalex.org/I174216632"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.42480000853538513,"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"}},"topics":[{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.42480000853538513,"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/T10591","display_name":"Theoretical and Computational Physics","score":0.2842000126838684,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter 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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.031099999323487282,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/diffusion-models","display_name":"diffusion models","score":0.7670000195503235},{"id":"https://openalex.org/keywords/o-3-nonlinear-sigma-model","display_name":"O(3) sigma model","score":0.9210000038146973},{"id":"https://openalex.org/keywords/heisenberg-model","display_name":"Heisenberg model","score":0.8529999852180481},{"id":"https://openalex.org/keywords/score-based-diffusion","display_name":"score-based diffusion","score":0.6679999828338623},{"id":"https://openalex.org/keywords/coarse-graining","display_name":"coarse-graining","score":0.9010000228881836},{"id":"https://openalex.org/keywords/dyson-schwinger-equations","display_name":"Dyson-Schwinger equations","score":0.8790000081062317},{"id":"https://openalex.org/keywords/two-point-correlation-function","display_name":"two-point correlation function","score":0.9710000157356262},{"id":"https://openalex.org/keywords/boundary-layer-approximation","display_name":"boundary layer approximation","score":0.9200000166893005}],"concepts":[{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5940999984741211},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5903000235557556},{"id":"https://openalex.org/C2778049214","wikidata":"https://www.wikidata.org/wiki/Q7512234","display_name":"Sigma","level":2,"score":0.5475999712944031},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.5188000202178955},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.4848000109195709},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.4765999913215637},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.44670000672340393},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.44190001487731934},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.4408000111579895},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4205000102519989},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4140999913215637},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.39559999108314514},{"id":"https://openalex.org/C98856871","wikidata":"https://www.wikidata.org/wiki/Q1588488","display_name":"Radial basis function","level":3,"score":0.38440001010894775},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.3813999891281128},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.3499999940395355},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.34439998865127563},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.3440999984741211},{"id":"https://openalex.org/C202787564","wikidata":"https://www.wikidata.org/wiki/Q6510488","display_name":"Heat equation","level":2,"score":0.3301999866962433},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.323199987411499},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.30399999022483826},{"id":"https://openalex.org/C122280245","wikidata":"https://www.wikidata.org/wiki/Q620622","display_name":"Kernel method","level":3,"score":0.29490000009536743},{"id":"https://openalex.org/C52740198","wikidata":"https://www.wikidata.org/wiki/Q1539564","display_name":"Importance sampling","level":3,"score":0.28200000524520874},{"id":"https://openalex.org/C571446","wikidata":"https://www.wikidata.org/wiki/Q6510183","display_name":"Diffusion equation","level":3,"score":0.27720001339912415},{"id":"https://openalex.org/C51632099","wikidata":"https://www.wikidata.org/wiki/Q3985153","display_name":"Training set","level":2,"score":0.2583000063896179},{"id":"https://openalex.org/C2779530757","wikidata":"https://www.wikidata.org/wiki/Q1207505","display_name":"Quality (philosophy)","level":2,"score":0.25060001015663147}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.39568","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.39568","pdf_url":"https://arxiv.org/pdf/2610.39568","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2610.39568","doi":"https://doi.org/10.48550/arxiv.2610.39568","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.39568","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.39568","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.39568","pdf_url":"https://arxiv.org/pdf/2610.39568","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7224739427.pdf","grobid_xml":"https://content.openalex.org/works/W7224739427.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7160624982","https://openalex.org/W7171621286","https://openalex.org/W6964867545","https://openalex.org/W7214233193","https://openalex.org/W7161131270","https://openalex.org/W7133223170","https://openalex.org/W7223875479","https://openalex.org/W7167897744","https://openalex.org/W7166682352","https://openalex.org/W7214358237"],"abstract_inverted_index":{"A":[0],"score-based":[1],"diffusion":[2,79,99,136],"model":[3],"is":[4],"trained":[5,24],"on":[6,25,52,77,101],"the":[7,12,16,30,44,53,61,69,72,109,116,125],"two-dimensional":[8],"classical":[9],"Heisenberg":[10],"model,":[11],"lattice":[13],"representation":[14],"of":[15,29,49,71,107],"$O(3)$":[17],"nonlinear":[18],"sigma":[19],"model.":[20],"Neural":[21],"networks":[22],"are":[23,65,83],"three":[26],"different":[27],"coarse-grainings":[28],"same":[31],"training":[32,89],"set":[33],"to":[34,67,97,112,124,134],"implement":[35],"a":[36,105,121],"multiscale":[37],"sampling":[38,51],"scheme":[39],"that":[40,130],"modestly":[41],"improves":[42],"both":[43],"accuracy":[45],"and":[46,119],"computational":[47],"cost":[48],"direct":[50],"finest":[54],"lattice.":[55],"Stein":[56],"(or":[57],"Schwinger-Dyson)":[58],"diagnostics":[59,82],"for":[60],"two-point":[62],"correlation":[63],"function":[64],"introduced":[66],"assess":[68],"quality":[70],"learned":[73],"score":[74],"without":[75],"relying":[76],"reverse":[78],"sampling.":[80],"These":[81,103],"also":[84],"incorporated":[85],"into":[86],"an":[87],"additional":[88],"loss.":[90],"We":[91],"discuss":[92],"several":[93],"technical":[94],"considerations":[95],"relevant":[96],"implementing":[98],"models":[100],"$S^2$.":[102],"include":[104],"consideration":[106],"lifting":[108],"network":[110],"input":[111],"$S^3$,":[113],"as":[114],"in":[115],"$CP^1$":[117],"representation,":[118],"developing":[120],"boundary-layer":[122],"approximation":[123],"short-time":[126],"spherical":[127],"heat":[128],"kernel":[129],"extends":[131],"its":[132],"usefulness":[133],"larger":[135],"times.":[137]},"counts_by_year":[],"updated_date":"2026-11-02T09:45:03.842371","created_date":"2026-10-31T00:00:00"}