{"id":"https://openalex.org/W4416013073","doi":"https://doi.org/10.48550/arxiv.2505.04263","title":"Physics-Informed DeepONets for drift-diffusion on metric graphs: simulation and parameter identification","display_name":"Physics-Informed DeepONets for drift-diffusion on metric graphs: simulation and parameter identification","publication_year":2025,"publication_date":"2025-05-07","ids":{"openalex":"https://openalex.org/W4416013073","doi":"https://doi.org/10.48550/arxiv.2505.04263"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2505.04263","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2505.04263","pdf_url":"https://arxiv.org/pdf/2505.04263","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2505.04263","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5053456353","display_name":"Jan Blechschmidt","orcid":"https://orcid.org/0000-0003-3606-0606"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Blechschmidt, Jan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057834665","display_name":"Tom-Christian Riemer","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Riemer, Tom-Christian","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5041353339","display_name":"Max Winkler","orcid":"https://orcid.org/0000-0002-5292-2280"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Winkler, Max","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055578402","display_name":"Martin Stoll","orcid":"https://orcid.org/0000-0003-0951-4756"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Stoll, Martin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5029122330","display_name":"Jan\u2010Frederik Pietschmann","orcid":"https://orcid.org/0000-0003-0383-8696"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Pietschmann, Jan-F.","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":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":0.39649999141693115,"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":0.39649999141693115,"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/T11273","display_name":"Advanced Graph Neural Networks","score":0.2498999983072281,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.05380000174045563,"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/metric","display_name":"Metric (unit)","score":0.6031000018119812},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5942999720573425},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.47540000081062317},{"id":"https://openalex.org/keywords/identification","display_name":"Identification (biology)","score":0.46880000829696655},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.4124000072479248},{"id":"https://openalex.org/keywords/system-identification","display_name":"System identification","score":0.4041000008583069},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3862000107765198},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.37599998712539673},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.37549999356269836}],"concepts":[{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.6031000018119812},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5942999720573425},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.49300000071525574},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.47540000081062317},{"id":"https://openalex.org/C116834253","wikidata":"https://www.wikidata.org/wiki/Q2039217","display_name":"Identification (biology)","level":2,"score":0.46880000829696655},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.4124000072479248},{"id":"https://openalex.org/C119247159","wikidata":"https://www.wikidata.org/wiki/Q1366192","display_name":"System identification","level":3,"score":0.4041000008583069},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3928999900817871},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3862000107765198},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.37599998712539673},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.37549999356269836},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.37130001187324524},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.37070000171661377},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3691999912261963},{"id":"https://openalex.org/C79610928","wikidata":"https://www.wikidata.org/wiki/Q1656743","display_name":"Parameter identification problem","level":3,"score":0.35269999504089355},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.34630000591278076},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.335999995470047},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.33230000734329224},{"id":"https://openalex.org/C76969082","wikidata":"https://www.wikidata.org/wiki/Q486902","display_name":"Mathematical model","level":2,"score":0.3244999945163727},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.32339999079704285},{"id":"https://openalex.org/C2780598303","wikidata":"https://www.wikidata.org/wiki/Q65921492","display_name":"Flexibility (engineering)","level":2,"score":0.31529998779296875},{"id":"https://openalex.org/C2983447341","wikidata":"https://www.wikidata.org/wiki/Q1413083","display_name":"Model parameter","level":2,"score":0.31439998745918274},{"id":"https://openalex.org/C22157029","wikidata":"https://www.wikidata.org/wiki/Q17080460","display_name":"Nonlinear system identification","level":4,"score":0.3109999895095825},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3068999946117401},{"id":"https://openalex.org/C131584629","wikidata":"https://www.wikidata.org/wiki/Q4308705","display_name":"Coupling (piping)","level":2,"score":0.29649999737739563},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.2946999967098236},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2702000141143799},{"id":"https://openalex.org/C116672817","wikidata":"https://www.wikidata.org/wiki/Q1454986","display_name":"Physical system","level":2,"score":0.26579999923706055},{"id":"https://openalex.org/C14037181","wikidata":"https://www.wikidata.org/wiki/Q215007","display_name":"Equations of motion","level":2,"score":0.2531999945640564}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2505.04263","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2505.04263","pdf_url":"https://arxiv.org/pdf/2505.04263","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2505.04263","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2505.04263","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":"pmh:oai:arXiv.org:2505.04263","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2505.04263","pdf_url":"https://arxiv.org/pdf/2505.04263","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4416013073.pdf","grobid_xml":"https://content.openalex.org/works/W4416013073.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,95,138],"develop":[1],"a":[2,25,49,74],"novel":[3],"physics":[4,65,151],"informed":[5,66],"deep":[6,67],"learning":[7],"approach":[8,99],"for":[9,77,107,121,145,157],"solving":[10,158],"nonlinear":[11],"drift-diffusion":[12,126],"equations":[13,83],"on":[14,132,163],"metric":[15,127],"graphs.":[16],"These":[17],"models":[18,106,120,152],"represent":[19],"an":[20,98,133],"important":[21],"model":[22,59],"class":[23],"with":[24,84],"large":[26,50],"number":[27],"of":[28,41,52,58,80,124,149],"applications":[29],"in":[30,35,55],"areas":[31],"ranging":[32],"from":[33],"transport":[34],"biological":[36],"cells":[37],"to":[38],"the":[39,56,78,85,122,125,146],"motion":[40],"human":[42],"crowds.":[43],"While":[44],"traditional":[45],"numerical":[46],"schemes":[47],"require":[48],"amount":[51],"tailoring,":[53],"especially":[54],"case":[57],"design":[60],"or":[61,160],"parameter":[62,92],"identification":[63,93],"problems,":[64],"operator":[68],"networks":[69],"(DeepONet)":[70],"have":[71],"emerged":[72],"as":[73],"versatile":[75],"tool":[76],"solution":[79,123],"partial":[81],"differential":[82],"particular":[86],"advantage":[87],"that":[88,140],"they":[89],"easily":[90],"incorporate":[91],"questions.":[94],"here":[96],"present":[97],"where":[100],"we":[101],"first":[102],"learn":[103],"three":[104],"DeepONet":[105],"representative":[108],"inflow,":[109],"inner":[110],"and":[111,115,153],"outflow":[112],"edges,":[113],"resp.,":[114],"then":[116],"subsequently":[117],"couple":[118],"these":[119,164],"graph":[128],"problem":[129],"by":[130],"relying":[131],"edge-based":[134],"domain":[135],"decomposition":[136],"approach.":[137],"illustrate":[139],"our":[141],"framework":[142],"is":[143,154],"applicable":[144],"accurate":[147],"evaluation":[148],"graph-coupled":[150],"well":[155],"suited":[156],"optimization":[159],"inverse":[161],"problems":[162],"coupled":[165],"networks.":[166]},"counts_by_year":[],"updated_date":"2026-07-03T08:13:44.112507","created_date":"2025-10-10T00:00:00"}