{"paper":{"title":"Pressure reconstruction from error-embedded gradient measurements: a Gaussian-process generalization of Green's function integration","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Gaussian process regression generalizes Green's function integration to reconstruct pressure from noisy gradient data without boundary conditions.","cross_cats":[],"primary_cat":"physics.flu-dyn","authors_text":"Mohamed Amine Abassi, Qi Wang, Xiaofeng Liu, Zejian You","submitted_at":"2026-05-11T22:25:01Z","abstract_excerpt":"Reconstructing scalar fields from error-embedded gradient measurements is a fundamental linear inverse problem with broad applications in computational physics. Conventional approaches, such as Poisson-based solvers and the Green's Function Integration (GFI) method, require explicit boundary conditions extracted from the same error-embedded observations. In this study we assess the accuracy of a Gaussian Process Regression (GPR) framework for reconstructing pressure fields in turbulent flows from error-embedded pressure-gradient data derived from kinematic measurements. The probabilistic natur"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"A central theoretical result of the present work is that GFI is the noiseless limit of GPR, which on the unbounded plane reduces to the well-known logarithmic kernel and in three dimensions to the inverse-distance kernel.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The pressure field obeys Gaussian statistics with a stationary correlation structure that can be accurately captured by fitting a mixture-of-Gaussians kernel to the same turbulence data used for validation.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Gaussian process regression reconstructs pressure from error-embedded gradients by treating the field as a random process with a fitted correlation kernel, generalizing Green's function integration as its zero-noise limit and outperforming it under noise with calibrated uncertainty.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Gaussian process regression generalizes Green's function integration to reconstruct pressure from noisy gradient data without boundary conditions.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"c6ae7c5b3eb2c7b06d7c639f66f75752ad096f429122a873ac2f4fdcf820d17e"},"source":{"id":"2605.11293","kind":"arxiv","version":2},"verdict":{"id":"a24c62b3-03a1-4967-a5e8-739be1a1e098","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-13T02:05:11.253236Z","strongest_claim":"A central theoretical result of the present work is that GFI is the noiseless limit of GPR, which on the unbounded plane reduces to the well-known logarithmic kernel and in three dimensions to the inverse-distance kernel.","one_line_summary":"Gaussian process regression reconstructs pressure from error-embedded gradients by treating the field as a random process with a fitted correlation kernel, generalizing Green's function integration as its zero-noise limit and outperforming it under noise with calibrated uncertainty.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The pressure field obeys Gaussian statistics with a stationary correlation structure that can be accurately captured by fitting a mixture-of-Gaussians kernel to the same turbulence data used for validation.","pith_extraction_headline":"Gaussian process regression generalizes Green's function integration to reconstruct pressure from noisy gradient data without boundary conditions."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.11293/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"claim_evidence","ran_at":"2026-05-20T04:42:00.719218Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T12:38:47.803438Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-19T10:01:17.149676Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T08:33:11.117648Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"cc3a5ecfde1f2378b9ab99c138c7acc246b206512cd749fa145965d61dcb1d70"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"d70681e74bde0cc8a60faae951be85294018e04e1f8257b5a469ae93c48d2e64"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}