Pith Number

pith:CH7ZNEM7

pith:2026:CH7ZNEM7ATASMFIJBQN7X3IG3M

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Diagnosing Failure Modes of Neural Operators Across Diverse PDE Families

Lennon Shikhman

Strong in-distribution accuracy does not reliably predict robustness in neural PDE solvers across architectures and equation families.

arxiv:2601.11428 v7 · 2026-01-16 · cs.LG

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\usepackage{pith}
\pithnumber{CH7ZNEM7ATASMFIJBQN7X3IG3M}

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4 Citations 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

strong in-distribution accuracy does not reliably predict robustness, and that failure patterns depend jointly on architecture and PDE family.

C2weakest assumption

The chosen shifts in coefficients, boundary conditions, discretization, and rollout horizon, together with the five selected PDE families, are representative of deployment-relevant distribution shifts.

C3one line summary

A new stress-testing framework reveals that in-distribution accuracy does not reliably predict robustness of neural operators across diverse PDE families and architectures.

Receipt and verification

First computed	2026-05-26T01:02:30.868568Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

11ff96919f04c12615090c1bfbed06db1bac318c18cbd779238930e853d64ea4

Aliases

arxiv: 2601.11428 · arxiv_version: 2601.11428v7 · doi: 10.48550/arxiv.2601.11428 · pith_short_12: CH7ZNEM7ATAS · pith_short_16: CH7ZNEM7ATASMFIJ · pith_short_8: CH7ZNEM7

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/CH7ZNEM7ATASMFIJBQN7X3IG3M \
  | 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: 11ff96919f04c12615090c1bfbed06db1bac318c18cbd779238930e853d64ea4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "755fe80eca0eb1bce0a74a920e378c724f0d81f45736f2c1915e3b43be420adb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-01-16T16:47:44Z",
    "title_canon_sha256": "67c39cac47e5ab0157918302a8403d1c6748be8e982662a4c9c3cbafa3d16c81"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2601.11428",
    "kind": "arxiv",
    "version": 7
  }
}