Pith Number

pith:LFUVNLA6

pith:2026:LFUVNLA672S3LU4U36SSLHLYY5

not attested not anchored not stored refs resolved

Hypernetwork-Conditioned WENO5 Conservative-Form CNNs for One-Dimensional Conservation Laws

Wei Guo, Xinghui Zhong, Yongsheng Chen

Hypernetwork conditions a CNN to predict WENO weights from coarse initial data and mesh info while keeping the conservative finite-volume update.

arxiv:2605.13106 v1 · 2026-05-13 · math.NA · cs.NA

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\pithnumber{LFUVNLA672S3LU4U36SSLHLYY5}

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3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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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

Hyper--CFCNN attains accuracy comparable to classical WENO5, achieves near machine-precision conservation in the known-flux setting on fine meshes, and generalizes to unseen spatial resolutions and initial conditions without retraining.

C2weakest assumption

The hypernetwork, given only coarse descriptors of the initial condition plus mesh spacing and layout, can produce target-network parameters that yield stable, high-order weights for problems outside the training distribution.

C3one line summary

A hypernetwork conditions a conservative-form CNN to predict WENO5 weights from mesh and initial-condition metadata, preserving conservation and generalizing across resolutions for 1D hyperbolic conservation laws.

References

82 extracted · 82 resolved · 0 Pith anchors

[1] doi:10.1137/140951758 , journal = · doi:10.1137/140951758

[2] Nick Higham , title =

[3] Kolda and Ali Pinar , eprint =

[4] and Zhang, Shanrong and Merritt, Matthew E

[5] 2003 , eid = 2003 · doi:10.1103/physreve.68.026121

Receipt and verification

First computed	2026-05-18T03:08:58.164500Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

596956ac1efea5b5d394dfa5259d78c77c242c22ae18773fe7fad92b3de0a6a2

Aliases

arxiv: 2605.13106 · arxiv_version: 2605.13106v1 · doi: 10.48550/arxiv.2605.13106 · pith_short_12: LFUVNLA672S3 · pith_short_16: LFUVNLA672S3LU4U · pith_short_8: LFUVNLA6

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/LFUVNLA672S3LU4U36SSLHLYY5 \
  | 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: 596956ac1efea5b5d394dfa5259d78c77c242c22ae18773fe7fad92b3de0a6a2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bbcdf9d8869b400e978dc649cbd69edbf4f57b69ae3785aea0a06b43dd403539",
    "cross_cats_sorted": [
      "cs.NA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2026-05-13T07:16:12Z",
    "title_canon_sha256": "b38792ea0a94c2b61d2b5b2ac1ff2d4c3a14176591e66f5dc8ee1f9adc152c12"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13106",
    "kind": "arxiv",
    "version": 1
  }
}