{"id":"https://openalex.org/W7161574966","doi":"https://doi.org/10.48550/arxiv.2605.15754","title":"Spatiotemporal decoupled physics-informed Stone-Weierstrass neural operator for long-time prediction of time-dependent parametric PDEs","display_name":"Spatiotemporal decoupled physics-informed Stone-Weierstrass neural operator for long-time prediction of time-dependent parametric PDEs","publication_year":2026,"publication_date":"2026-05-15","ids":{"openalex":"https://openalex.org/W7161574966","doi":"https://doi.org/10.48550/arxiv.2605.15754"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.15754","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.15754","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":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2605.15754","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101562137","display_name":"Shan Ding","orcid":"https://orcid.org/0009-0001-3734-0020"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ding, Shan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5116319398","display_name":"Yuhan Tian","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tian, Yongfu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5136430006","display_name":"Lang Qin","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Qin, Lang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111177721","display_name":"H. Ma","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ma, Hongxiang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056923546","display_name":"Guofeng Su","orcid":"https://orcid.org/0000-0003-0795-7676"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Su, Guofeng","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5136413689","display_name":"Rui Yang","orcid":"https://orcid.org/0000-0002-1886-5286"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yang, Rui","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9922000169754028,"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":0.9922000169754028,"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 methods for differential equations","score":0.0013000000035390258,"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"}},{"id":"https://openalex.org/T12611","display_name":"Neural Networks and Reservoir Computing","score":0.0013000000035390258,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/artificial-neural-network","display_name":"Artificial neural network","score":0.6175000071525574},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5335000157356262},{"id":"https://openalex.org/keywords/bottleneck","display_name":"Bottleneck","score":0.5},{"id":"https://openalex.org/keywords/decoupling","display_name":"Decoupling (probability)","score":0.4090999960899353},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.4050999879837036},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.3937000036239624},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.3788999915122986},{"id":"https://openalex.org/keywords/encoding","display_name":"Encoding (memory)","score":0.3521000146865845},{"id":"https://openalex.org/keywords/deep-learning","display_name":"Deep learning","score":0.3434999883174896}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6847000122070312},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.6175000071525574},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5335000157356262},{"id":"https://openalex.org/C2780513914","wikidata":"https://www.wikidata.org/wiki/Q18210350","display_name":"Bottleneck","level":2,"score":0.5},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.46050000190734863},{"id":"https://openalex.org/C205606062","wikidata":"https://www.wikidata.org/wiki/Q5249645","display_name":"Decoupling (probability)","level":2,"score":0.4090999960899353},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.4050999879837036},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.3937000036239624},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.3788999915122986},{"id":"https://openalex.org/C125411270","wikidata":"https://www.wikidata.org/wiki/Q18653","display_name":"Encoding (memory)","level":2,"score":0.3521000146865845},{"id":"https://openalex.org/C108583219","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep learning","level":2,"score":0.3434999883174896},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.33219999074935913},{"id":"https://openalex.org/C47702885","wikidata":"https://www.wikidata.org/wiki/Q5441227","display_name":"Feedforward neural network","level":3,"score":0.31929999589920044},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.3012000024318695},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.29010000824928284},{"id":"https://openalex.org/C38858127","wikidata":"https://www.wikidata.org/wiki/Q5441228","display_name":"Feed forward","level":2,"score":0.28380000591278076},{"id":"https://openalex.org/C60008888","wikidata":"https://www.wikidata.org/wiki/Q6031013","display_name":"Information bottleneck method","level":3,"score":0.27649998664855957},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.2754000127315521},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.27309998869895935},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.2728999853134155},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.2702000141143799},{"id":"https://openalex.org/C147168706","wikidata":"https://www.wikidata.org/wiki/Q1457734","display_name":"Recurrent neural network","level":3,"score":0.26170000433921814},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.25619998574256897},{"id":"https://openalex.org/C24574437","wikidata":"https://www.wikidata.org/wiki/Q7135228","display_name":"Parametric model","level":3,"score":0.25600001215934753}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.15754","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.15754","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":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2605.15754","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.15754","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":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Driven":[0],"by":[1],"rapid":[2],"advances":[3],"in":[4,33,54,98,126],"artificial":[5],"intelligence":[6],"and":[7,84,149,190],"modern":[8],"GPU":[9],"computing":[10],"capabilities,":[11],"deep":[12],"learning":[13,45],"methods":[14],"based":[15],"on":[16],"the":[17,115,127,142,156,160,178],"optimization":[18],"paradigm":[19,129],"have":[20,50],"provided":[21],"new":[22],"pathways":[23],"to":[24,176],"solve":[25],"spatiotemporal":[26],"physical":[27],"problems,":[28],"whose":[29],"mathematical":[30],"core":[31],"lies":[32],"solving":[34],"partial":[35],"differential":[36],"equations":[37],"(PDEs).":[38],"As":[39],"an":[40],"emerging":[41],"class":[42],"of":[43,162,181,192],"function-space":[44],"methods,":[46],"neural":[47,61,102,111,118],"operators":[48],"(NOs)":[49],"exhibited":[51],"great":[52],"potential":[53],"efficient":[55],"PDE":[56],"solving.":[57],"However,":[58],"existing":[59],"mainstream":[60],"operator":[62,112,119],"frameworks":[63],"suffer":[64],"from":[65],"critical":[66],"bottlenecks":[67],"when":[68],"modeling":[69,183],"time-dependent":[70],"PDEs":[71],"over":[72,164,184],"long":[73],"time":[74,166,186],"horizons,":[75],"including":[76],"accuracy":[77],"degradation,":[78],"insufficient":[79],"stability,":[80],"high":[81],"training":[82],"costs,":[83],"excessive":[85],"memory":[86,179],"consumption,":[87],"which":[88],"severely":[89],"limit":[90],"their":[91],"practical":[92],"deployment.":[93],"To":[94],"address":[95],"these":[96],"challenges":[97],"long-time":[99],"prediction":[100],"with":[101,135],"operators,":[103],"we":[104,169],"propose":[105],"a":[106,171],"novel":[107],"spatiotemporally":[108],"decoupled":[109],"physics-informed":[110,116],"architecture,":[113],"termed":[114],"Stone-Weierstrass":[117,143],"(PI-SWNO).":[120],"The":[121],"design":[122],"is":[123],"theoretically":[124],"grounded":[125],"decoupling":[128],"combining":[130],"time-invariant":[131],"spatial":[132,148],"basis":[133],"functions":[134],"time-varying":[136],"evolution":[137],"coefficients,":[138],"as":[139,141],"well":[140],"approximation":[144],"theorem.":[145],"By":[146],"encoding":[147],"temporal":[150],"information":[151],"via":[152],"two":[153],"separate":[154],"subnetworks,":[155],"framework":[157],"structurally":[158],"mitigates":[159],"accumulation":[161],"errors":[163],"extended":[165,185],"intervals.":[167],"Furthermore,":[168],"introduce":[170],"time-marching":[172],"batch-wise":[173],"sampling":[174],"strategy":[175],"resolve":[177],"bottleneck":[180],"full-range":[182],"spans,":[187],"ensuring":[188],"continuity":[189],"convergence":[191],"full-time-domain":[193],"solutions.":[194]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-05-19T00:00:00"}