{"id":"https://openalex.org/W7220989880","doi":"https://doi.org/10.48550/arxiv.2610.09261","title":"A Sensitivity-based Framework for Calibrating Coupled Ordinary Differential Equations under Model Discrepancy","display_name":"A Sensitivity-based Framework for Calibrating Coupled Ordinary Differential Equations under Model Discrepancy","publication_year":2026,"publication_date":"2026-10-07","ids":{"openalex":"https://openalex.org/W7220989880","doi":"https://doi.org/10.48550/arxiv.2610.09261"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.09261","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.09261","pdf_url":"https://arxiv.org/pdf/2610.09261","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/2610.09261","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5002615895","display_name":"Mitchel J. Colebank","orcid":"https://orcid.org/0000-0002-2294-9124","observed_orcids":["https://orcid.org/0000-0002-2294-9124"]},"institutions":[{"id":"https://openalex.org/I155781252","display_name":"University of South Carolina","ror":"https://ror.org/02b6qw903","country_code":"US","type":"education","lineage":["https://openalex.org/I155781252"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Colebank, Mitchel J.","raw_affiliation_strings":["Department of Mathematics , University of South Carolina , Columbia , SC"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , University of South Carolina , Columbia , SC","institution_ids":["https://openalex.org/I155781252"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5004217207","display_name":"William Consagra","orcid":"https://orcid.org/0000-0001-5279-3469","observed_orcids":["https://orcid.org/0000-0001-5279-3469"]},"institutions":[{"id":"https://openalex.org/I155781252","display_name":"University of South Carolina","ror":"https://ror.org/02b6qw903","country_code":"US","type":"education","lineage":["https://openalex.org/I155781252"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Consagra, William","raw_affiliation_strings":["Department of Statistics , University of South Carolina , Columbia , SC"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics , University of South Carolina , Columbia , SC","institution_ids":["https://openalex.org/I155781252"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I155781252"],"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.4408999979496002,"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"}},"topics":[{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.4408999979496002,"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"}},{"id":"https://openalex.org/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.2280000001192093,"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/T11236","display_name":"Control Systems and Identification","score":0.1404999941587448,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/model-discrepancy","display_name":"model mismatch","score":0.9739999771118164},{"id":"https://openalex.org/keywords/sensitivity-equations","display_name":"sensitivity equations","score":0.7760000228881836},{"id":"https://openalex.org/keywords/identifiability","display_name":"identifiability","score":0.8479999899864197},{"id":"https://openalex.org/keywords/parameter-inference","display_name":"parameter inference","score":0.6290000081062317},{"id":"https://openalex.org/keywords/metropolis-within-gibbs","display_name":"Metropolis-within-Gibbs","score":0.8460000157356262},{"id":"https://openalex.org/keywords/adaptive-mcmc","display_name":"adaptive MCMC","score":0.5699999928474426},{"id":"https://openalex.org/keywords/mass-spring-system","display_name":"mass-spring system","score":0.9760000109672546}],"concepts":[{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.9003000259399414},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.8069000244140625},{"id":"https://openalex.org/C122770356","wikidata":"https://www.wikidata.org/wiki/Q1656753","display_name":"Identifiability","level":2,"score":0.7376999855041504},{"id":"https://openalex.org/C21200559","wikidata":"https://www.wikidata.org/wiki/Q7451068","display_name":"Sensitivity (control systems)","level":2,"score":0.5275999903678894},{"id":"https://openalex.org/C165838908","wikidata":"https://www.wikidata.org/wiki/Q736777","display_name":"Calibration","level":2,"score":0.5012000203132629},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.5008000135421753},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.48170000314712524},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4724999964237213},{"id":"https://openalex.org/C2780310539","wikidata":"https://www.wikidata.org/wiki/Q12547192","display_name":"Imperfect","level":2,"score":0.43549999594688416},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4268999993801117},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38679999113082886},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.385699987411499},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3743000030517578},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.3668000102043152},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.35269999504089355},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.3303999900817871},{"id":"https://openalex.org/C2983447341","wikidata":"https://www.wikidata.org/wiki/Q1413083","display_name":"Model parameter","level":2,"score":0.3156999945640564},{"id":"https://openalex.org/C185184677","wikidata":"https://www.wikidata.org/wiki/Q1366795","display_name":"Exact differential equation","level":4,"score":0.31040000915527344},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.3091999888420105},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.303600013256073},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.295199990272522},{"id":"https://openalex.org/C99656134","wikidata":"https://www.wikidata.org/wiki/Q2912993","display_name":"Ordinary least squares","level":2,"score":0.28519999980926514},{"id":"https://openalex.org/C76969082","wikidata":"https://www.wikidata.org/wiki/Q486902","display_name":"Mathematical model","level":2,"score":0.2590999901294708},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.25119999051094055}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.09261","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.09261","pdf_url":"https://arxiv.org/pdf/2610.09261","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.2610.09261","doi":"https://doi.org/10.48550/arxiv.2610.09261","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.09261","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":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.09261","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.09261","pdf_url":"https://arxiv.org/pdf/2610.09261","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/G6011265878","display_name":"An Echocardiography-driven Digital Twin for Ventricular Septal Defect","funder_award_id":"26CDA1599801","funder_id":"https://openalex.org/F4320306230","funder_display_name":"American Heart Association"},{"id":"https://openalex.org/G9000912129","display_name":"Big Data Health Science Fellow Program in Infectious Disease Research","funder_award_id":"R25AI164581","funder_id":"https://openalex.org/F4320337355","funder_display_name":"National Institute of Allergy and Infectious Diseases"}],"funders":[{"id":"https://openalex.org/F4320306230","display_name":"American Heart Association","ror":"https://ror.org/013kjyp64"},{"id":"https://openalex.org/F4320310846","display_name":"University of South Carolina","ror":"https://ror.org/02b6qw903"},{"id":"https://openalex.org/F4320319233","display_name":"South Carolina EPSCoR","ror":null},{"id":"https://openalex.org/F4320337355","display_name":"National Institute of Allergy and Infectious Diseases","ror":"https://ror.org/043z4tv69"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220989880.pdf","grobid_xml":"https://content.openalex.org/works/W7220989880.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7080766955","https://openalex.org/W4285088295","https://openalex.org/W7214162264","https://openalex.org/W4360998744","https://openalex.org/W4289645242","https://openalex.org/W2025909913","https://openalex.org/W3083827778","https://openalex.org/W2767176385","https://openalex.org/W3104367927","https://openalex.org/W2608858916"],"abstract_inverted_index":{"Coupled":[0],"systems":[1,116],"of":[2,179],"ordinary":[3],"differential":[4],"equations":[5],"(ODEs)":[6],"are":[7,40,134],"widely":[8],"used":[9],"to":[10,26,29,44,49,57,79,92,161,194,202],"model":[11,21,51,172,178],"complex":[12],"physical":[13],"and":[14,32,75,101,183,198],"biological":[15],"processes.":[16],"In":[17,35,103],"these":[18],"applications,":[19],"ODE":[20,115,143],"parameters":[22],"must":[23,54,87],"be":[24,55,99],"calibrated":[25],"field":[27],"data":[28],"enable":[30],"prediction":[31],"parameter":[33,60,196],"inference.":[34],"practice,":[36],"the":[37,45,95,123,142,162,168],"governing":[38],"ODEs":[39],"an":[41,156],"imperfect":[42],"approximation":[43],"true":[46],"system,":[47],"leading":[48,78],"non-negligible":[50],"discrepancy":[52,70,74,130],"that":[53,67,117,190],"incorporated":[56],"avoid":[58],"biased":[59],"estimates.":[61],"However,":[62],"it":[63],"is":[64,153],"well":[65],"known":[66],"highly":[68],"flexible":[69],"models":[71],"can":[72,98],"confound":[73],"simulator":[76],"parameters,":[77],"poor":[80],"identifiability.":[81],"As":[82],"a":[83,108,146,174,177,184],"result,":[84],"practitioners":[85],"often":[86],"impose":[88],"problem-specific":[89],"prior":[90],"constraints":[91,121],"adequately":[93],"regularize":[94],"discrepancy,":[96,124],"which":[97],"challenging":[100],"cumbersome.":[102],"this":[104],"work,":[105],"we":[106],"propose":[107],"novel":[109],"calibration":[110,204],"framework":[111],"for":[112],"coupled,":[113],"multi-output":[114],"enforces":[118],"automatic,":[119],"model-structural":[120],"on":[122,170],"improving":[125],"identifiability":[126],"without":[127],"requiring":[128],"application-specific":[129],"priors.":[131],"Forward-model":[132],"gradients":[133],"computed":[135],"via":[136],"sensitivity":[137],"equations,":[138],"solved":[139],"jointly":[140],"with":[141],"system":[144],"as":[145],"coupled":[147],"initial":[148],"value":[149],"problem.":[150],"Posterior":[151],"inference":[152,197],"performed":[154],"using":[155],"adaptive":[157],"Metropolis-within-Gibbs":[158],"sampler":[159],"tailored":[160],"resulting":[163],"constrained":[164],"posterior.":[165],"We":[166,188],"demonstrate":[167],"approach":[169],"three":[171],"systems:":[173],"mass-spring":[175],"oscillator,":[176],"infectious":[180],"disease":[181],"spread,":[182],"neuron":[185],"firing":[186],"model.":[187],"show":[189],"our":[191],"method":[192],"leads":[193],"improved":[195],"predictive":[199],"accuracy":[200],"compared":[201],"standard":[203],"approaches.":[205]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-10-09T00:00:00"}
