{"paper":{"title":"HYCO: Hybrid-Cooperative Learning for Data-Driven PDE Modeling","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA","math.AP","math.NA"],"primary_cat":"math.OC","authors_text":"Enrique Zuazua, Lorenzo Liverani","submitted_at":"2025-09-17T16:02:24Z","abstract_excerpt":"We introduce Hybrid-Cooperative Learning (HYCO), a framework for data-driven PDE modeling in which a physics-based solver and a flexible synthetic model are trained as two independent but cooperating components. Rather than imposing the governing equation as a residual on a single network, HYCO alternates between updating the physical parameters and the synthetic model, coupling them through agreement of their predictions.Each component therefore fits the information available to it while acting as a regularizer for the other. This modular formulation accommodates sparse, heterogeneous, or dis"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.14123","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2509.14123/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}