{"paper":{"title":"Verified residual-specific explicit derivative kernels for physics-informed learning and discretized PDE adjoints","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.comp-ph","authors_text":"Weiwei Zhang, Wenbo Cao, Zhe Lu","submitted_at":"2026-06-29T02:09:56Z","abstract_excerpt":"Derivative computation is central to scientific computing, from space-time derivatives in physics-informed neural networks (PINNs) to residual Jacobian actions and discrete-adjoint operators in computational fluid dynamics (CFD). General-purpose automatic differentiation (AD) reduces implementation effort, but can incur substantial runtime and memory overhead for high-order residuals and complex discretized operators. Explicit derivative kernels can exploit problem-specific structure and provide efficient, controllable evaluations, but their use has been limited by derivation and implementatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.29702","kind":"arxiv","version":1},"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/2606.29702/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"}