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pith:D3R4ACGR

pith:2026:D3R4ACGR6T3QV3FT2VBUTT32WP

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Curriculum Learning of Physics-Informed Neural Networks based on Spatial Correlation

Daming Shi, Letian Chen, Wenhui Fan, Xinyue Hu, Xujia Chen

Spatial curriculum learning guides PINN training from boundaries inward to reduce optimization failures on PDEs.

arxiv:2605.15254 v1 · 2026-05-14 · cs.LG

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Claims

C1strongest claim

Experiments on PDE benchmarks show that, under comparable computational cost, the proposed method alleviates training failures and improves solution accuracy.

C2weakest assumption

That guiding information propagation from near-boundary regions inward via spatial causal weights, combined with low-frequency consistency bridges, will systematically reduce optimization failures in PINNs for BVPs with strong spatial coupling.

C3one line summary

A spatially correlated curriculum learning framework for PINNs using causal weights, low-frequency bridges, and adaptive reweighting to reduce training failures on spatially coupled BVPs.

References

36 extracted · 36 resolved · 0 Pith anchors

[1] William F Ames.Numerical methods for partial differential equations. Academic press, 2014 2014

[2] Promising directions of machine learning for partial differential equations.Nature Computational Science, 4(7):483–494, 2024 2024

[3] Maziar Raissi, Paris Perdikaris, and George E Karniadakis. Physics-informed neural net- works: A deep learning framework for solving forward and inverse problems involving nonlinear partial differenti 2019

[4] Weiwei Zhang, Wei Suo, Jiahao Song, and Wenbo Cao. Physics-informed neural networks (pinns) as intelligent computing technique for solving partial differential equations: Limita- tion and future prosp 2026

[5] Wenhui Fan and Xujia Chen. Embedding physics into machine learning: A review of physics informed neural networks as partial differential equation forward solvers.Tsinghua Science and Technology, 31(3) 2026

Receipt and verification

First computed	2026-05-20T00:00:48.697016Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1ee3c008d1f4f70aecb3d54349cf7ab3ed199d687b5e1085e66ef69500d91ba2

Aliases

arxiv: 2605.15254 · arxiv_version: 2605.15254v1 · doi: 10.48550/arxiv.2605.15254 · pith_short_12: D3R4ACGR6T3Q · pith_short_16: D3R4ACGR6T3QV3FT · pith_short_8: D3R4ACGR

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/D3R4ACGR6T3QV3FT2VBUTT32WP \
  | 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: 1ee3c008d1f4f70aecb3d54349cf7ab3ed199d687b5e1085e66ef69500d91ba2

Canonical record JSON

{
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    "abstract_canon_sha256": "1491a62c708ca53d0e17e56358cc1a8976f1ad4083129b1dde6cc567cfd7d213",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-14T17:16:04Z",
    "title_canon_sha256": "a520bbacfae2d92ee4ea79db65733c8e1b277cfd86a9d5b3b757f2da538cde1a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15254",
    "kind": "arxiv",
    "version": 1
  }
}