Pith Number

pith:E4TSHGPC

pith:2020:E4TSHGPCFGVUVUIWRCD2VQGDJ2

not attested not anchored not stored refs resolved

Neural Operator: Graph Kernel Network for Partial Differential Equations

Andrew Stuart, Anima Anandkumar, Burigede Liu, Kamyar Azizzadenesheli, Kaushik Bhattacharya, Nikola Kovachki, Zongyi Li

A single set of network parameters can describe mappings between infinite-dimensional spaces and their finite approximations using graph kernel networks.

arxiv:2003.03485 v1 · 2020-03-07 · cs.LG · cs.NA · math.NA · stat.ML

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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

A single set of network parameters, within a carefully designed network architecture, may be used to describe mappings between infinite-dimensional spaces and between different finite-dimensional approximations of those spaces.

C2weakest assumption

That message passing on graphs can faithfully approximate the required integral operators for the target PDE mappings without introducing discretization-dependent artifacts that break generalization.

C3one line summary

Graph Kernel Networks learn PDE solution operators that generalize across discretization methods and grid resolutions using graph-based kernel integration.

References

141 extracted · 141 resolved · 16 Pith anchors

[1] Kolda and Brett W 2009 · doi:10.1137/07070111x

[2] Hsu and Sham M 2012

[3] Tensor-train decomposition 2011 · doi:10.1137/090752286

[4] Fast adaptive interpolation of multi-dimensional arrays in tensor train format , isbn =

[5] Gorodetsky and Sertac Karaman and Youssef M 2016

Formal links

2 machine-checked theorem links

Cited by

40 papers in Pith

Algorithmically Designed Artificial Neural Networks (ADANNs): Higher order deep operator learning for parametric partial differential equations

Generative diffusion learning for parametric partial differential equations

Kernel Neural Operators (KNOs) for Scalable, Memory-efficient, Geometrically-flexible Operator Learning

Scalable Mechanistic Neural Networks for Differential Equations and Machine Learning

Walsh-Hadamard Neural Operators for Solving PDEs with Discontinuous Coefficients

Receipt and verification

First computed	2026-05-17T23:39:21.492591Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

27272399e229ab4ad1168887aac0c34e880760c485e704a9e33ce0b58ac7e632

Aliases

arxiv: 2003.03485 · arxiv_version: 2003.03485v1 · doi: 10.48550/arxiv.2003.03485 · pith_short_12: E4TSHGPCFGVU · pith_short_16: E4TSHGPCFGVUVUIW · pith_short_8: E4TSHGPC

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/E4TSHGPCFGVUVUIWRCD2VQGDJ2 \
  | 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: 27272399e229ab4ad1168887aac0c34e880760c485e704a9e33ce0b58ac7e632

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "26201da04c09f76f2fb8b3a3f189e55fb309433aa9f8feb44b6e922aef41479c",
    "cross_cats_sorted": [
      "cs.NA",
      "math.NA",
      "stat.ML"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2020-03-07T01:56:20Z",
    "title_canon_sha256": "a134ca4c27e49f81d72f760c4201ce7d598edec990ecca9c23d046cf4c9de232"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2003.03485",
    "kind": "arxiv",
    "version": 1
  }
}