{"paper":{"title":"Structure-Aware Tensorial Model Reduction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Tensor factorization lets reduced bases for parameterized PDEs vary nonlinearly with parameters by encoding snapshots offline and interpolating online.","cross_cats":["cs.NA","math.DS"],"primary_cat":"math.NA","authors_text":"Anthony Gruber, Arjun Vijaywargiya, Eric C. Cyr","submitted_at":"2026-04-29T04:21:03Z","abstract_excerpt":"This work investigates a two-stage method for constructing projection-based reduced-order models (ROMs) of parameterized partial differential equations (PDEs). Based on established tensorial ROM methodology, the proposed approach reduces dimensionality offline by encoding solution snapshots using a multi-linear Tucker factorization, so that a reduced basis which varies nonlinearly with PDE parameters can be rapidly constructed online and used in a Galerkin ROM. Two novel extensions of this strategy, tailored to the cases of structured PDEs and sparse parameter sampling, are presented: the cons"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"The proposed nonlinear basis ROM can effectively mitigate linear restrictions on Kolmogorov n-width while improving upon previous tensorial ROM technology, particularly in the highly nonlinear and data-limited regimes characteristic of practical use cases.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the Tucker-encoded states admit accurate RBF interpolation and that the orthonormalization with respect to a general discrete inner product preserves the error bounds sufficiently for the target PDEs when parameter sampling is sparse.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A structure-aware tensorial ROM method with orthonormalized bases and RBF interpolation of encoded states reduces dimensionality for parameterized PDEs while mitigating Kolmogorov n-width limitations in nonlinear and data-sparse regimes.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Tensor factorization lets reduced bases for parameterized PDEs vary nonlinearly with parameters by encoding snapshots offline and interpolating online.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"9d077cb84c2503aa3843077f46fe6efa88f9524e75b87e0981e7ec323f64d145"},"source":{"id":"2604.26280","kind":"arxiv","version":2},"verdict":{"id":"300a1f8b-bc12-435d-82fc-a6b255e1559c","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-07T13:05:39.559896Z","strongest_claim":"The proposed nonlinear basis ROM can effectively mitigate linear restrictions on Kolmogorov n-width while improving upon previous tensorial ROM technology, particularly in the highly nonlinear and data-limited regimes characteristic of practical use cases.","one_line_summary":"A structure-aware tensorial ROM method with orthonormalized bases and RBF interpolation of encoded states reduces dimensionality for parameterized PDEs while mitigating Kolmogorov n-width limitations in nonlinear and data-sparse regimes.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the Tucker-encoded states admit accurate RBF interpolation and that the orthonormalization with respect to a general discrete inner product preserves the error bounds sufficiently for the target PDEs when parameter sampling is sparse.","pith_extraction_headline":"Tensor factorization lets reduced bases for parameterized PDEs vary nonlinearly with parameters by encoding snapshots offline and interpolating online."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.26280/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-21T00:39:32.806723Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T20:22:39.407508Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"c9d11e83cd2e153624e8d922e234b21b2994a58ffd61996403ce380852b2ff04"},"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"}