Pith Number

pith:FMKZXVAE

pith:2025:FMKZXVAEKSTVPZA5Z34MBGUTTE

not attested not anchored not stored refs resolved

Unsupervised simulation of incompressible flows with physics- and equality- constrained artificial neural networks

Inanc Senocak, Qifeng Hu

A pressure-Poisson objective with equality constraints enforced by an augmented Lagrangian method enables purely unsupervised neural simulation of incompressible flows at high Reynolds numbers.

arxiv:2511.18820 v2 · 2025-11-24 · physics.flu-dyn · cs.LG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FMKZXVAEKSTVPZA5Z34MBGUTTE}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

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

Notably, it captures the spontaneous onset of periodic vortex shedding in unsteady cylinder flow without external perturbations, starting from a randomly initialized network.

C2weakest assumption

That the pressure-Poisson residual can be minimized subject to momentum and continuity equations plus boundary conditions as equality constraints enforced by CA-ALM to strict tolerances while the adaptive vanishing entropy viscosity stabilizes training without influencing the converged solution.

C3one line summary

A pressure-Poisson objective combined with equality-constrained neural networks and adaptive viscosity enables unsupervised simulation of high-Reynolds-number incompressible flows including spontaneous vortex shedding.

References

49 extracted · 49 resolved · 1 Pith anchors

[1] F.H.Harlow, J.E.Welch, Numericalcalculationoftime-dependentviscousincompressible flow of fluid with free surface, Physics of Fluids 8 (1965) 2182–2189 1965

[2] A. J. Chorin, Numerical solution of the navier–stokes equations, Mathematics of Computation 22 (1968) 745–762 1968

[3] Témam, Sur l’approximation de la solution des équations de Navier-Stokes par la méthode des pas fractionnaires (II), Arch 1969

[4] A. A. Amsden, F. H. Harlow, A simplified MAC technique for incompressible fluid flow calculations, J. Comput. Phys. 6 (1970) 322–325 1970

[5] J. Kim, P. Moin, Application of a fractional-step method to incompressible navier-stokes equations, J. Comput. Phys. 59 (1985) 308–323 1985

Receipt and verification

First computed	2026-05-17T23:39:00.698058Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2b159bd40454a757e41dcef8c09a93991612c7121b3eeb5a052ec1dd867661b3

Aliases

arxiv: 2511.18820 · arxiv_version: 2511.18820v2 · doi: 10.48550/arxiv.2511.18820 · pith_short_12: FMKZXVAEKSTV · pith_short_16: FMKZXVAEKSTVPZA5 · pith_short_8: FMKZXVAE

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/FMKZXVAEKSTVPZA5Z34MBGUTTE \
  | 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: 2b159bd40454a757e41dcef8c09a93991612c7121b3eeb5a052ec1dd867661b3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5e6dfe0bcecb7234847e9c8a766065f157fc81cb3cebd74f903beffcbfc24d52",
    "cross_cats_sorted": [
      "cs.LG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "physics.flu-dyn",
    "submitted_at": "2025-11-24T06:54:20Z",
    "title_canon_sha256": "6403c7492d93ab772f6c7b2a1bcaf9d43dea26b1fa2b83cb6a6c66b2208df1fc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2511.18820",
    "kind": "arxiv",
    "version": 2
  }
}