{"paper":{"title":"Optimize discrete loss with finite-difference physics constraint and time-stepping for PDE solving","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Finite-difference time-stepping optimization solves incompressible flow equations with reduced memory and error.","cross_cats":[],"primary_cat":"physics.flu-dyn","authors_text":"Gang Wei, Heng Zhang, Jingyu Wang, Mingjie Zhang, Xiaogang Deng, Yali Luo, Yiye Zou","submitted_at":"2026-03-07T11:25:07Z","abstract_excerpt":"Computational Fluid Dynamics (CFD) is an important approach for analyzing flow phenomena and predicting engineering-relevant quantities. The governing physics is formulated as partial differential equations(PDEs) and solved numerically on computational grids. Physics-informed neural networks(PINNs) have emerged as a popular optimization-based approach for solving PDEs, but they often suffer from ill-conditioned objectives and the high cost of automatic differentiation. Optimization-based discretizations such as ODIL mitigate several PINN drawbacks by optimizing discrete variables directly, yet"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"FDTO enables accurate, stable, and memory-efficient discrete-loss optimization for incompressible-flow solutions, while remaining applicable to other PDE models.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The finite-difference discretization of the physics residuals combined with the sequential time-stepping decomposition preserves the accuracy and stability of the underlying continuous PDE without introducing significant truncation or optimization errors.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"FDTO optimizes discrete finite-difference physics losses via time-stepping on curvilinear body-fitted grids to solve time-dependent PDEs, achieving 82.6% lower GPU memory and 3-5x lower error than PINNs on lid-driven cavity and flow-mixing cases.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Finite-difference time-stepping optimization solves incompressible flow equations with reduced memory and error.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"b5f2e438effd84ca356b18a0bd5e51da45bf2536480a78a304c9529cc54e7367"},"source":{"id":"2603.07151","kind":"arxiv","version":3},"verdict":{"id":"bfa5675d-e642-41e0-b7a3-eb7ecaa35af1","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T15:41:14.881442Z","strongest_claim":"FDTO enables accurate, stable, and memory-efficient discrete-loss optimization for incompressible-flow solutions, while remaining applicable to other PDE models.","one_line_summary":"FDTO optimizes discrete finite-difference physics losses via time-stepping on curvilinear body-fitted grids to solve time-dependent PDEs, achieving 82.6% lower GPU memory and 3-5x lower error than PINNs on lid-driven cavity and flow-mixing cases.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The finite-difference discretization of the physics residuals combined with the sequential time-stepping decomposition preserves the accuracy and stability of the underlying continuous PDE without introducing significant truncation or optimization errors.","pith_extraction_headline":"Finite-difference time-stepping optimization solves incompressible flow equations with reduced memory and error."},"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"}