Pith Number

pith:UD4YEYH6

pith:2026:UD4YEYH6YP62J5NAYOI7ESDOKS

not attested not anchored not stored refs pending

Optimize discrete loss with finite-difference physics constraint and time-stepping for PDE solving

Gang Wei, Heng Zhang, Jingyu Wang, Mingjie Zhang, Xiaogang Deng, Yali Luo, Yiye Zou

Finite-difference time-stepping optimization solves incompressible flow equations with reduced memory and error.

arxiv:2603.07151 v3 · 2026-03-07 · physics.flu-dyn

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\usepackage{pith}
\pithnumber{UD4YEYH6YP62J5NAYOI7ESDOKS}

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Record completeness

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

FDTO enables accurate, stable, and memory-efficient discrete-loss optimization for incompressible-flow solutions, while remaining applicable to other PDE models.

C2weakest 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.

C3one 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.

Receipt and verification

First computed	2026-05-18T03:09:22.991461Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a0f98260fec3fda4f5a0c391f2486e549d706c6c2ad75c2b1820cf017a48daff

Aliases

arxiv: 2603.07151 · arxiv_version: 2603.07151v3 · doi: 10.48550/arxiv.2603.07151 · pith_short_12: UD4YEYH6YP62 · pith_short_16: UD4YEYH6YP62J5NA · pith_short_8: UD4YEYH6

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/UD4YEYH6YP62J5NAYOI7ESDOKS \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: a0f98260fec3fda4f5a0c391f2486e549d706c6c2ad75c2b1820cf017a48daff

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8a1f2f6e67089b4b4dddd426768dc66911d9a9f7830e7121563ae1efb3ca379c",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "physics.flu-dyn",
    "submitted_at": "2026-03-07T11:25:07Z",
    "title_canon_sha256": "896a58122f8eb7f3ccb0b780d9b6b2ad6544a2028fe6f8d15647049355acbbeb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2603.07151",
    "kind": "arxiv",
    "version": 3
  }
}