Pith Number

pith:SMJWUTUY

pith:2026:SMJWUTUYB6W6YQVVN6RK2PVSIM

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PerFlow: Physics-Embedded Rectified Flow for Efficient Reconstruction and Uncertainty Quantification of Spatiotemporal Dynamics

Han Wan, Hao Sun, Hao Zhou, Rui Zhang

PerFlow embeds hard physics constraints into rectified flows to reconstruct sparse spatiotemporal fields quickly and with uncertainty estimates.

arxiv:2605.03548 v2 · 2026-05-05 · cs.LG · cs.AI

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\pithnumber{SMJWUTUYB6W6YQVVN6RK2PVSIM}

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Record completeness

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4 Citations open

5 Replications open

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Claims

C1strongest claim

PerFlow decouples observation conditioning from physics enforcement, performing guidance-free conditioning by feeding observations into rectified-flow dynamics while embedding hard physics via a constraint-preserving projection, with invariance guarantees ensuring trajectories remain on the physics-consistent manifold, achieving competitive accuracy and up to 320x faster inference than 2000-step guided diffusion baselines.

C2weakest assumption

The constraint-preserving projection (e.g., for incompressibility or conservation) can be applied after each rectified-flow step without distorting the learned distribution or violating the invariance guarantees that keep trajectories on the physics-consistent manifold.

C3one line summary

PerFlow decouples observation conditioning from physics enforcement in rectified flows using constraint-preserving projections and invariance guarantees for fast, physics-consistent reconstruction of spatiotemporal dynamics.

References

42 extracted · 42 resolved · 7 Pith anchors

[1] Neural operators for accelerating scientific simulations and design.Nature Reviews Physics, 6(5):320–328, 2024

[2] [Bhaganagar and Chambers, 2025] Kiran Bhaganagar and David Chambers. Accelerated elliptical pde solver for computational fluid dynamics based on configurable u-net architecture: Analogy to v-cycle mul 2025

[3] Conditional neural field latent diffusion model for generating spatiotemporal turbulence.Nature Communications, 15(1):10416, 2024

[4] Pde-gcn: Novel architectures for graph neu- ral networks motivated by partial differential equa- tions.Advances in neural information processing systems, 34:3836–3849, 2021

[5] Gen- erative adversarial networks.Communications of the ACM, 63(11):139–144, 2020

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:00:40.619006Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

93136a4e980fadec42b56fa2ad3eb2433d2dd0e09e4ff283b955a84a176ac5a8

Aliases

arxiv: 2605.03548 · arxiv_version: 2605.03548v2 · doi: 10.48550/arxiv.2605.03548 · pith_short_12: SMJWUTUYB6W6 · pith_short_16: SMJWUTUYB6W6YQVV · pith_short_8: SMJWUTUY

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/SMJWUTUYB6W6YQVVN6RK2PVSIM \
  | 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: 93136a4e980fadec42b56fa2ad3eb2433d2dd0e09e4ff283b955a84a176ac5a8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4fbe4adbdee705d7344d2740f2e54c57b1b191aa211f497df68c26feb90ebab8",
    "cross_cats_sorted": [
      "cs.AI"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-05T09:19:09Z",
    "title_canon_sha256": "5439ae89b0967b57d033367f3b453ae4d2318b35ed0bafff32f8dfd5fe0935d7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.03548",
    "kind": "arxiv",
    "version": 2
  }
}