{"id":"https://openalex.org/W7133218957","doi":"https://doi.org/10.48550/arxiv.2602.23859","title":"HYCO: A Formalism for Hybrid-Cooperative PDE Modelling","display_name":"HYCO: A Formalism for Hybrid-Cooperative PDE Modelling","publication_year":2026,"publication_date":"2026-02-27","ids":{"openalex":"https://openalex.org/W7133218957","doi":"https://doi.org/10.48550/arxiv.2602.23859"},"language":null,"primary_location":{"id":"pmh:doi:10.48550/arxiv.2602.23859","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"Article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":null,"any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5005336774","display_name":"Lorenzo Liverani","orcid":"https://orcid.org/0000-0003-2538-8868"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Liverani, Lorenzo","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5106674625","display_name":"Enrique Zuazua","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zuazua, Enrique","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5005336774"],"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":0.8291000127792358,"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":0.8291000127792358,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.0210999995470047,"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/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.01979999989271164,"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/parallelizable-manifold","display_name":"Parallelizable manifold","score":0.8240000009536743},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.7085000276565552},{"id":"https://openalex.org/keywords/formalism","display_name":"Formalism (music)","score":0.6363999843597412},{"id":"https://openalex.org/keywords/benchmark","display_name":"Benchmark (surveying)","score":0.40720000863075256},{"id":"https://openalex.org/keywords/interpretation","display_name":"Interpretation (philosophy)","score":0.33799999952316284},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.33469998836517334}],"concepts":[{"id":"https://openalex.org/C148047603","wikidata":"https://www.wikidata.org/wiki/Q1014612","display_name":"Parallelizable manifold","level":2,"score":0.8240000009536743},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.7085000276565552},{"id":"https://openalex.org/C73301696","wikidata":"https://www.wikidata.org/wiki/Q5469984","display_name":"Formalism (music)","level":3,"score":0.6363999843597412},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5073000192642212},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4921000003814697},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4350000023841858},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.40720000863075256},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3986000120639801},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.382099986076355},{"id":"https://openalex.org/C527412718","wikidata":"https://www.wikidata.org/wiki/Q855395","display_name":"Interpretation (philosophy)","level":2,"score":0.33799999952316284},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.33469998836517334},{"id":"https://openalex.org/C2781170535","wikidata":"https://www.wikidata.org/wiki/Q30587856","display_name":"Noisy data","level":2,"score":0.3246999979019165},{"id":"https://openalex.org/C46814582","wikidata":"https://www.wikidata.org/wiki/Q23389","display_name":"Nash equilibrium","level":2,"score":0.3034999966621399},{"id":"https://openalex.org/C2986605239","wikidata":"https://www.wikidata.org/wiki/Q925667","display_name":"Numerical models","level":3,"score":0.28600001335144043},{"id":"https://openalex.org/C160920958","wikidata":"https://www.wikidata.org/wiki/Q7662746","display_name":"Synthetic data","level":2,"score":0.2502000033855438}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:doi:10.48550/arxiv.2602.23859","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"Article"},{"id":"doi:10.48550/arxiv.2602.23859","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.23859","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":"article"}],"best_oa_location":{"id":"pmh:doi:10.48550/arxiv.2602.23859","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"Article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0],"present":[1],"Hybrid-Cooperative":[2],"Learning":[3],"(HYCO),":[4],"a":[5,77,81],"hybrid":[6],"modeling":[7],"framework":[8,75],"that":[9,21,62],"integrates":[10],"physics-based":[11],"and":[12,45,50,57,68],"data-driven":[13],"models":[14],"through":[15],"mutual":[16],"regularization.":[17],"Unlike":[18],"traditional":[19],"approaches":[20],"impose":[22],"physical":[23],"constraints":[24],"directly":[25],"on":[26,55,92],"synthetic":[27],"models,":[28],"HYCO":[29,63],"treats":[30],"both":[31],"components":[32],"as":[33,80],"co-trained":[34],"agents":[35],"nudged":[36],"toward":[37],"agreement.":[38],"This":[39,88],"cooperative":[40],"scheme":[41],"is":[42,90],"naturally":[43],"parallelizable":[44],"demonstrates":[46],"robustness":[47],"to":[48],"sparse":[49],"noisy":[51],"data.":[52],"Numerical":[53],"experiments":[54],"static":[56],"time-dependent":[58],"benchmark":[59],"problems":[60],"show":[61],"can":[64],"recover":[65],"accurate":[66],"solutions":[67],"model":[69],"parameters":[70],"under":[71],"ill-posed":[72],"conditions.":[73],"The":[74],"admits":[76],"game-theoretic":[78],"interpretation":[79],"Nash":[82],"equilibrium":[83],"problem,":[84],"enabling":[85],"alternating":[86],"optimization.":[87],"paper":[89],"based":[91],"the":[93],"extended":[94],"preprint:":[95],"arXiv:2509.14123":[96],".":[97]},"counts_by_year":[],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2026-03-03T00:00:00"}