{"id":"https://openalex.org/W7223807374","doi":"https://doi.org/10.48550/arxiv.2610.33896","title":"Recovery of a source of anomalous diffusion from space-time sparse data","display_name":"Recovery of a source of anomalous diffusion from space-time sparse data","publication_year":2026,"publication_date":"2026-10-24","ids":{"openalex":"https://openalex.org/W7223807374","doi":"https://doi.org/10.48550/arxiv.2610.33896"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.33896","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.33896","pdf_url":"https://arxiv.org/pdf/2610.33896","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","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.33896","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5159969047","display_name":"Xing Cheng","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I163340411","display_name":"Hohai University","ror":"https://ror.org/01wd4xt90","country_code":"CN","type":"education","lineage":["https://openalex.org/I163340411"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Cheng, Xing","raw_affiliation_strings":["School of Mathematics , Hohai University , Nanjing 210098 , Jiangsu , China,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics , Hohai University , Nanjing 210098 , Jiangsu , China,","institution_ids":["https://openalex.org/I163340411"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039605463","display_name":"Bangti Jin","orcid":"https://orcid.org/0000-0002-3775-9155","observed_orcids":["https://orcid.org/0000-0002-3775-9155"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jin, Bangti","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5032812479","display_name":"Yavar Kian","orcid":"https://orcid.org/0000-0002-5588-3600","observed_orcids":["https://orcid.org/0000-0002-5588-3600"]},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I163340411","display_name":"Hohai University","ror":"https://ror.org/01wd4xt90","country_code":"CN","type":"education","lineage":["https://openalex.org/I163340411"]},{"id":"https://openalex.org/I4210105181","display_name":"Laboratoire de Math\u00e9matiques Rapha\u00ebl Salem","ror":"https://ror.org/01k1v7590","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I4210105181","https://openalex.org/I4210105918","https://openalex.org/I4210141950","https://openalex.org/I62396329"]},{"id":"https://openalex.org/I62396329","display_name":"Universit\u00e9 de Rouen Normandie","ror":"https://ror.org/03nhjew95","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210105918","https://openalex.org/I62396329"]}],"countries":["CN","FR"],"is_corresponding":false,"raw_author_name":"Kian, Yavar","raw_affiliation_strings":["Laboratory of Mathematical Modeling and Intelligent Computing for Water Systems , Hohai University , Nanjing 211100 , China","Univ Rouen Normandie , CNRS , Normandie Univ , LMRS UMR 6085 , F-76000 Rouen , France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratory of Mathematical Modeling and Intelligent Computing for Water Systems , Hohai University , Nanjing 211100 , China","institution_ids":["https://openalex.org/I163340411"]},{"raw_affiliation_string":"Univ Rouen Normandie , CNRS , Normandie Univ , LMRS UMR 6085 , F-76000 Rouen , France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I4210105181","https://openalex.org/I62396329"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5159848947","display_name":"Zhiyuan Li","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I109935558","display_name":"Ningbo University","ror":"https://ror.org/03et85d35","country_code":"CN","type":"education","lineage":["https://openalex.org/I109935558"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Li, Zhiyuan","raw_affiliation_strings":["School of Mathematics and Statistics , Ningbo University , Ningbo 315211 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics , Ningbo University , Ningbo 315211 , China","institution_ids":["https://openalex.org/I109935558"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"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/T11205","display_name":"Numerical methods in inverse problems","score":0.5874000191688538,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11205","display_name":"Numerical methods in inverse problems","score":0.5874000191688538,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.3285999894142151,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T12589","display_name":"Differential Equations and Boundary Problems","score":0.059700001031160355,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied 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/inverse-source-problem","display_name":"inverse source problem","score":0.968999981880188},{"id":"https://openalex.org/keywords/anomalous-diffusion","display_name":"anomalous diffusion","score":0.9829999804496765},{"id":"https://openalex.org/keywords/time-fractional-diffusion","display_name":"time-fractional diffusion","score":0.9129999876022339},{"id":"https://openalex.org/keywords/subdiffusion","display_name":"subdiffusion","score":0.8410000205039978},{"id":"https://openalex.org/keywords/superdiffusion","display_name":"superdiffusion","score":0.9980000257492065},{"id":"https://openalex.org/keywords/unit-disk","display_name":"unit disk","score":0.7749999761581421},{"id":"https://openalex.org/keywords/separated-variables","display_name":"separated variables","score":0.5820000171661377},{"id":"https://openalex.org/keywords/memory-effects","display_name":"memory effects","score":0.9089999794960022},{"id":"https://openalex.org/keywords/complex-analysis","display_name":"complex analysis","score":0.6389999985694885},{"id":"https://openalex.org/keywords/solution-representation","display_name":"solution representation","score":0.48500001430511475}],"concepts":[{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.711899995803833},{"id":"https://openalex.org/C124066611","wikidata":"https://www.wikidata.org/wiki/Q28684319","display_name":"Sparse approximation","level":2,"score":0.6948000192642212},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.5540000200271606},{"id":"https://openalex.org/C164602753","wikidata":"https://www.wikidata.org/wiki/Q567544","display_name":"Anomalous diffusion","level":3,"score":0.5483999848365784},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5256999731063843},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.4916999936103821},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.47999998927116394},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.46459999680519104},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.4440999925136566},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.4377000033855438},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4343000054359436},{"id":"https://openalex.org/C56372850","wikidata":"https://www.wikidata.org/wiki/Q1050404","display_name":"Sparse matrix","level":3,"score":0.4153999984264374},{"id":"https://openalex.org/C198082294","wikidata":"https://www.wikidata.org/wiki/Q3399648","display_name":"Position (finance)","level":2,"score":0.39959999918937683},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3869999945163727},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3840999901294708},{"id":"https://openalex.org/C58489278","wikidata":"https://www.wikidata.org/wiki/Q1172284","display_name":"Data set","level":2,"score":0.3246000111103058},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.31839999556541443},{"id":"https://openalex.org/C117258860","wikidata":"https://www.wikidata.org/wiki/Q895153","display_name":"Boundary representation","level":3,"score":0.3158000111579895},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.29789999127388},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2937000095844269},{"id":"https://openalex.org/C21080849","wikidata":"https://www.wikidata.org/wiki/Q13611879","display_name":"Data point","level":2,"score":0.2728999853134155},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.26809999346733093},{"id":"https://openalex.org/C148043351","wikidata":"https://www.wikidata.org/wiki/Q4456944","display_name":"Current (fluid)","level":2,"score":0.2630999982357025},{"id":"https://openalex.org/C571446","wikidata":"https://www.wikidata.org/wiki/Q6510183","display_name":"Diffusion equation","level":3,"score":0.25859999656677246}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:arXiv.org:2610.33896","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.33896","pdf_url":"https://arxiv.org/pdf/2610.33896","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":"pmh:oai:HAL:hal-05840253v1","doi":null,"is_oa":true,"landing_page_url":"https://hal.science/hal-05840253","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4405252976","host_organization_name":"Centre pour la Communication Scientifique Directe","host_organization_lineage":["https://openalex.org/I4405252976"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2026","raw_type":"info:eu-repo/semantics/preprint"},{"id":"doi:10.48550/arxiv.2610.33896","doi":"https://doi.org/10.48550/arxiv.2610.33896","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.33896","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:2610.33896","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.33896","pdf_url":"https://arxiv.org/pdf/2610.33896","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":[{"id":"https://openalex.org/G1920647447","display_name":null,"funder_award_id":"BK20230036","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G207775045","display_name":"Parameter identifications for anomalous diffusion","funder_award_id":"ANR-24-CE40-7039","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G2382013997","display_name":null,"funder_award_id":"2022YFC3202602","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6227346462","display_name":null,"funder_award_id":"12271277","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6856721283","display_name":null,"funder_award_id":"U2340221","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8446722958","display_name":null,"funder_award_id":"U2340221","funder_id":"https://openalex.org/F4320321605","funder_display_name":"Government of Jiangsu Province"},{"id":"https://openalex.org/G8478990708","display_name":null,"funder_award_id":"BK20230036","funder_id":"https://openalex.org/F4320321605","funder_display_name":"Government of Jiangsu Province"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321605","display_name":"Government of Jiangsu Province","ror":"https://ror.org/004svx814"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7223807374.pdf","grobid_xml":"https://content.openalex.org/works/W7223807374.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W7169753505"],"related_works":["https://openalex.org/W2470033128","https://openalex.org/W2753231176","https://openalex.org/W4379014370","https://openalex.org/W4402697700","https://openalex.org/W4415026243","https://openalex.org/W3190675385","https://openalex.org/W3013364719","https://openalex.org/W2911690358","https://openalex.org/W7134233429","https://openalex.org/W7149265457"],"abstract_inverted_index":{"We":[0,23],"study":[1],"an":[2],"inverse":[3],"source":[4],"problem":[5],"for":[6,34],"a":[7,28,60],"time-fractional":[8],"sub-":[9],"and":[10,49,86],"super-diffusive":[11],"anomalous":[12,35],"diffusion":[13],"equation":[14],"on":[15,59,75],"the":[16,25,68,76,80,87],"unit":[17],"disk":[18],"with":[19,37],"sparse":[20,45],"boundary":[21,41,57],"observations.":[22],"prove":[24],"recovery":[26],"of":[27,31,63,79,83,89],"general":[29],"class":[30],"$L^2$":[32],"sources":[33],"diffusion,":[36],"separated":[38],"variables,":[39],"from":[40],"measurements":[42],"that":[43],"are":[44],"in":[46],"both":[47],"space":[48],"time,":[50],"using":[51],"observations":[52],"at":[53],"two":[54],"carefully":[55],"chosen":[56],"points":[58],"discrete":[61],"set":[62],"times":[64],"arbitrarily":[65],"close":[66],"to":[67],"final":[69],"time.":[70],"The":[71],"analysis":[72,85],"relies":[73],"heavily":[74],"memory":[77],"effect":[78],"model,":[81],"properties":[82],"complex":[84],"representation":[88],"solutions.":[90]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-28T00:00:00"}