Pith Number

pith:ATV4JSQX

pith:2026:ATV4JSQXNMYZHKTTHVKN7FJLUW

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Discovering Physical Directions in Weight Space: Composing Neural PDE Experts

Dong Ni, Guanyu Chen, Pengkai Wang, Pengwei Liu, Qixin Zhang, Xiaolong Li, Xingyu Ren, Yuanyi Wang, Yuting Kong, Zhongkai Hao

Fine-tuning endpoint experts on a shared neural PDE operator reveals a reusable physical direction in weight space for training-free regime composition.

arxiv:2605.14546 v1 · 2026-05-14 · cs.LG

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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

endpoint fine-tuning is not arbitrary checkpoint drift, but reveals a calibratable physical direction for training-free transfer across PDE regimes.

C2weakest assumption

that the observed separation of weight updates into family-shared adaptation and a direction aligned with the underlying physical parameter is stable, generalizable, and not an artifact of the specific fine-tuning procedure or chosen regimes.

C3one line summary

Fine-tuning neural PDE operators to regime endpoints reveals a physical direction in weight space that CCM uses to compose accurate merged models for new or extrapolated regimes from metadata or short prefixes.

References

61 extracted · 61 resolved · 5 Pith anchors

[1] Fourier Neural Operator for Parametric Partial Differential Equations 2010 · arXiv:2010.08895

[2] Neural operators for accelerating scientific simulations and design 2024

[3] Gnot: A general neural operator transformer for operator learning 2023

[4] Laplace neural operator for solving differential equations.Nature Machine Intelligence, 6(6):631–640, 2024 2024

[5] Neural Operator: Graph Kernel Network for Partial Differential Equations 2003 · arXiv:2003.03485

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-17T23:39:05.764339Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

04ebc4ca176b3193aa733d54df952ba5a6ef8123125170c3433db4da892421ce

Aliases

arxiv: 2605.14546 · arxiv_version: 2605.14546v1 · doi: 10.48550/arxiv.2605.14546 · pith_short_12: ATV4JSQXNMYZ · pith_short_16: ATV4JSQXNMYZHKTT · pith_short_8: ATV4JSQX

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/ATV4JSQXNMYZHKTTHVKN7FJLUW \
  | 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: 04ebc4ca176b3193aa733d54df952ba5a6ef8123125170c3433db4da892421ce

Canonical record JSON

{
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    "abstract_canon_sha256": "52d732371994c8e5ab8b763f46dce4dce7d00612d2e6def4f645463b3c44ac01",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-14T08:25:16Z",
    "title_canon_sha256": "b8008a0141f566cfe3feb19e231f920ef9ab9aa55d7ccddb03cfade9ebfe208a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.14546",
    "kind": "arxiv",
    "version": 1
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}