{"id":"https://openalex.org/W7161111030","doi":"https://doi.org/10.48550/arxiv.2605.13260","title":"Unified generalization analysis for physics informed neural networks","display_name":"Unified generalization analysis for physics informed neural networks","publication_year":2026,"publication_date":"2026-05-13","ids":{"openalex":"https://openalex.org/W7161111030","doi":"https://doi.org/10.48550/arxiv.2605.13260"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.13260","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.13260","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":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2605.13260","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5136108945","display_name":"Yuka Hashimoto","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hashimoto, Yuka","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5034538103","display_name":"Tomoharu Iwata","orcid":"https://orcid.org/0000-0003-4425-1971"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Iwata, Tomoharu","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":0.9843999743461609,"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":0.9843999743461609,"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/T12611","display_name":"Neural Networks and Reservoir Computing","score":0.006000000052154064,"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"}},{"id":"https://openalex.org/T11273","display_name":"Advanced Graph Neural Networks","score":0.0012000000569969416,"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/generalization","display_name":"Generalization","score":0.8363999724388123},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.7167999744415283},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.626800000667572},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5799000263214111},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.4803999960422516},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.42089998722076416}],"concepts":[{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.8363999724388123},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.7167999744415283},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.626800000667572},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5799000263214111},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4803999960422516},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4332999885082245},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.42089998722076416},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4154999852180481},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.38040000200271606},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.37599998712539673},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.373199999332428},{"id":"https://openalex.org/C70915906","wikidata":"https://www.wikidata.org/wiki/Q1058681","display_name":"Differential operator","level":2,"score":0.32659998536109924},{"id":"https://openalex.org/C49766605","wikidata":"https://www.wikidata.org/wiki/Q207643","display_name":"Linear map","level":2,"score":0.3197999894618988},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.2922999858856201},{"id":"https://openalex.org/C158946198","wikidata":"https://www.wikidata.org/wiki/Q131187","display_name":"Taylor series","level":2,"score":0.2637999951839447},{"id":"https://openalex.org/C812465","wikidata":"https://www.wikidata.org/wiki/Q5058375","display_name":"Cellular neural network","level":3,"score":0.2572000026702881}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.13260","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.13260","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":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2605.13260","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.13260","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":"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":{"Physics-Informed":[0],"Neural":[1],"Networks":[2],"(PINNs)":[3],"and":[4,27,62,90],"their":[5],"variational":[6],"counterparts":[7],"(VPINNs)":[8],"are":[9],"neural":[10,50],"networks":[11,51,94],"that":[12,52,92,107],"incorporate":[13],"physical":[14],"laws,":[15],"making":[16],"them":[17],"useful":[18],"for":[19,25,49],"scientific":[20],"problems.":[21],"Existing":[22],"generalization":[23,47],"analyses":[24],"PINNs":[26,61],"VPINNs":[28,63],"remain":[29],"limited,":[30],"often":[31],"requiring":[32],"restrictive":[33],"assumptions":[34],"such":[35],"as":[36,77],"stability":[37],"conditions":[38],"or":[39],"linear":[40,78],"ellipticity.":[41],"In":[42],"this":[43],"paper,":[44],"we":[45],"derive":[46],"bounds":[48],"involve":[53],"differentiation":[54],"with":[55],"respect":[56],"to":[57,72],"input":[58],"variables,":[59],"covering":[60],"under":[64],"a":[65,81],"unified":[66],"framework.":[67],"We":[68,104],"apply":[69],"Taylor":[70],"expansion":[71],"represent":[73],"nonlinear":[74],"differential":[75,102,112],"operators":[76,79],"on":[80,122],"high-dimensional":[82],"space,":[83],"enabling":[84],"the":[85,108,111,116],"use":[86],"of":[87,110],"Koopman-based":[88],"analysis":[89],"showing":[91],"high-rank":[93],"can":[95],"generalize":[96],"well":[97],"even":[98],"in":[99],"settings":[100],"involving":[101],"operators.":[103],"also":[105],"show":[106],"nonlinearity":[109],"operator":[113],"exponentially":[114],"enlarges":[115],"bound,":[117],"highlighting":[118],"its":[119],"significant":[120],"impact":[121],"generalization.":[123]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-05-15T00:00:00"}
