{"paper":{"title":"Hypernetwork-Conditioned WENO5 Conservative-Form CNNs for One-Dimensional Conservation Laws","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Hypernetwork conditions a CNN to predict WENO weights from coarse initial data and mesh info while keeping the conservative finite-volume update.","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Wei Guo, Xinghui Zhong, Yongsheng Chen","submitted_at":"2026-05-13T07:16:12Z","abstract_excerpt":"We study a conservative data-driven discretization for one-dimensional hyperbolic conservation laws based on the classical fifth-order WENO finite-volume scheme and a hypernetwork architecture. In the proposed Hyper--WENO5 Conservative-Form Convolutional Neural Network (Hyper--CFCNN), a lightweight target network predicts the nonlinear WENO weights on each stencil, while a hypernetwork generates the target-network parameters from problem metadata, including the mesh spacing, mesh layout, and coarse descriptors of the initial condition. The construction preserves the standard polynomial reconst"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Hyper--CFCNN attains accuracy comparable to classical WENO5, achieves near machine-precision conservation in the known-flux setting on fine meshes, and generalizes to unseen spatial resolutions and initial conditions without retraining.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The hypernetwork, given only coarse descriptors of the initial condition plus mesh spacing and layout, can produce target-network parameters that yield stable, high-order weights for problems outside the training distribution.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A hypernetwork conditions a conservative-form CNN to predict WENO5 weights from mesh and initial-condition metadata, preserving conservation and generalizing across resolutions for 1D hyperbolic conservation laws.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Hypernetwork conditions a CNN to predict WENO weights from coarse initial data and mesh info while keeping the conservative finite-volume update.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"c52f067ee0456846f4c93a998089bb23718384eb8dfc14910366e55b2a2a2714"},"source":{"id":"2605.13106","kind":"arxiv","version":1},"verdict":{"id":"4ec17442-2e99-43e0-9e98-6636b3eb6538","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T18:46:29.400376Z","strongest_claim":"Hyper--CFCNN attains accuracy comparable to classical WENO5, achieves near machine-precision conservation in the known-flux setting on fine meshes, and generalizes to unseen spatial resolutions and initial conditions without retraining.","one_line_summary":"A hypernetwork conditions a conservative-form CNN to predict WENO5 weights from mesh and initial-condition metadata, preserving conservation and generalizing across resolutions for 1D hyperbolic conservation laws.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The hypernetwork, given only coarse descriptors of the initial condition plus mesh spacing and layout, can produce target-network parameters that yield stable, high-order weights for problems outside the training distribution.","pith_extraction_headline":"Hypernetwork conditions a CNN to predict WENO weights from coarse initial data and mesh info while keeping the conservative finite-volume update."},"references":{"count":82,"sample":[{"doi":"10.1137/140951758","year":null,"title":"doi:10.1137/140951758 , journal =","work_id":"c4f150b6-e2bc-449e-8977-b1790884e96b","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Nick Higham , title =","work_id":"473e0434-e81c-49c4-a938-213553b887f7","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Kolda and Ali Pinar , eprint =","work_id":"6f14dad2-8293-4a96-8b99-c9584370ab96","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"and Zhang, Shanrong and Merritt, Matthew E","work_id":"3c01440b-8dbb-4e7b-8208-f66b1ff21c07","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1103/physreve.68.026121","year":2003,"title":"2003 , eid =","work_id":"1f883a11-b189-4e54-8feb-6eb5d0164858","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":82,"snapshot_sha256":"0ce3b8b9b5abff9e42a7bff29fcbb791e17618ad5d0cfc154454f0d292be62b8","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"}