Pith Number

pith:UJ5KWMCF

pith:2026:UJ5KWMCF4HHHZ5IUNYIHHP6VGP

not attested not anchored not stored refs resolved

Frequency Bias and OOD Generalization in Neural Operators under a Variable-Coefficient Wave Equation

An Luo, Runlong Xie

FNO shows sharp error jumps on unseen high frequencies in wave equations while DeepONet degrades more gradually.

arxiv:2605.12997 v1 · 2026-05-13 · cs.LG

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Claims

C1strongest claim

Under frequency shifts, FNO exhibits a sharp increase in error under unseen high-frequency inputs, whereas DeepONet shows milder degradation despite higher overall error. These differences arise from how each architecture represents and responds to variations in frequency structure.

C2weakest assumption

That independently varying input frequency and coefficient smoothness produces distribution shifts representative of those encountered in practical PDE applications.

C3one line summary

FNO exhibits strong frequency bias with sharp OOD error growth on high-frequency inputs in wave equations, while DeepONet shows milder degradation despite higher baseline error.

References

71 extracted · 71 resolved · 1 Pith anchors

[1] Langley , title = 2000

[2] T. M. Mitchell. The Need for Biases in Learning Generalizations. 1980 1980

[3] M. J. Kearns , title =

[4] Machine Learning: An Artificial Intelligence Approach, Vol. I. 1983 1983

[5] R. O. Duda and P. E. Hart and D. G. Stork. Pattern Classification. 2000 2000

Receipt and verification

First computed	2026-05-18T03:09:00.477770Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a27aab3045e1ce7cf5146e1073bfd533c8e53bbe879e5d1e88d64158eb603ba1

Aliases

arxiv: 2605.12997 · arxiv_version: 2605.12997v1 · doi: 10.48550/arxiv.2605.12997 · pith_short_12: UJ5KWMCF4HHH · pith_short_16: UJ5KWMCF4HHHZ5IU · pith_short_8: UJ5KWMCF

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/UJ5KWMCF4HHHZ5IUNYIHHP6VGP \
  | 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: a27aab3045e1ce7cf5146e1073bfd533c8e53bbe879e5d1e88d64158eb603ba1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9d6b92ebfa1c8f6d742fdc4db5131c6d9d274b61dd5bf9e1ae51ffa84c8d8ba4",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-13T04:53:36Z",
    "title_canon_sha256": "1cdbe8c64e8de1a2b71c01b8db89e0a2dcfa6007075abb315a18a531ecf5a9ed"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.12997",
    "kind": "arxiv",
    "version": 1
  }
}