Pith Number

pith:46O54PYV

pith:2025:46O54PYVCAHKMGZKY7RLMCQFOV

not attested not anchored not stored refs pending

SPDEBench: An Extensive Benchmark for Learning Stochastic PDEs

Bingguang Chen, Dai Shi, Hao Ni, Jose Miguel Lara Rangel, Luke Thompson, Oliver Nash, Qi Meng, Rongchan Zhu, Siran Li, Yuantu Zhu, Zheyan Li

SPDEBench supplies the first unified collection of ready-to-use datasets for machine learning models that approximate solutions to stochastic partial differential equations, including singular cases.

arxiv:2505.18511 v3 · 2025-05-24 · cs.LG · math.AP · physics.comp-ph

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\pithnumber{46O54PYVCAHKMGZKY7RLMCQFOV}

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Record completeness

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2 Internet Archive

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

SPDEBench is the first unified benchmark for ML-based SPDE learning that provides ready-to-use datasets for regular and singular SPDEs; numerical results show that SPDE-aware architectures generally achieve stronger performance than generic operator-learning baselines on accuracy, robustness, and out-of-distribution generalization.

C2weakest assumption

The data-generation procedures (noise approximation, basis choice, renormalization for singular SPDEs) produce representative datasets that enable unbiased model comparisons without hidden numerical artifacts or selection effects that would favor certain architectures.

C3one line summary

SPDEBench is the first unified benchmark providing ready-to-use datasets for regular and singular SPDEs, ML operator-learning baselines, and evaluations showing SPDE-aware models outperform generic ones on accuracy, robustness, and OOD generalization.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:00:20.312457Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e79dde3f15100ea61b2ac7e2b60a05757fad69d09368536ca804c4ae6f816ee4

Aliases

arxiv: 2505.18511 · arxiv_version: 2505.18511v3 · doi: 10.48550/arxiv.2505.18511 · pith_short_12: 46O54PYVCAHK · pith_short_16: 46O54PYVCAHKMGZK · pith_short_8: 46O54PYV

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/46O54PYVCAHKMGZKY7RLMCQFOV \
  | 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: e79dde3f15100ea61b2ac7e2b60a05757fad69d09368536ca804c4ae6f816ee4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "312767e2d07c8d93dfdffa54f4828d04d598425a8080f26f0bf4a0bdb8c235e5",
    "cross_cats_sorted": [
      "math.AP",
      "physics.comp-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2025-05-24T05:15:45Z",
    "title_canon_sha256": "4c7d39d845bb1f032154f2730cf437ace19b5d485b4666802f7715e35e66f417"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2505.18511",
    "kind": "arxiv",
    "version": 3
  }
}