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Paper Citation Record · LEDGER

A Learning-based Domain Decomposition Method

As of 14 August 2026, this Paper Citation Record lists 57 of 57 outbound references and 0 inbound Pith citation observations for arXiv:2507.17328.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2507.17328 v2

Coverage vector

measured 57 of 57 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T14:57:35.110816Z

measured 57 of 57 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-14T06:32:32.682623+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

57 of 57 outbound references displayed

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  • verified fuzzy18
  • unresolved38
  • parse uncertain0
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation d48cd160-a0b5-48ea-91f0-34734fb14c39 · outbound

This paper cites Bullo, A.

A Learning-based Domain Decomposition Method Bullo, A

Reference 1

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Source-reported events for the cited work

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Observation d8d8456d-1882-49bb-bc88-045ff7199d6f · outbound

This paper cites Leng, Z.-g.

A Learning-based Domain Decomposition Method Leng, Z.-g

Reference 2

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Observation 1d9a0e67-050e-4ebb-ac99-82fd1a330d95 · outbound

This paper cites an unresolved cited work.

A Learning-based Domain Decomposition Method Unresolved cited work

Reference 3

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Observation 74b71cc8-8195-44bf-bb18-3a3fa2041292 · outbound

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A Learning-based Domain Decomposition Method Unresolved cited work

Reference 4

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Source-reported events for the cited work

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Observation 84f9bf69-5446-4ea0-bc0d-a49c09ba518c · outbound

This paper cites Stepinski, T.

A Learning-based Domain Decomposition Method Stepinski, T

Reference 5

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

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Observation 03fe90c2-d589-486d-a347-a951b798b341 · outbound

This paper cites Gilbarg, N.

A Learning-based Domain Decomposition Method Gilbarg, N

Reference 6

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

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Observation 31405b8b-1ff6-4d64-93df-ab09a28a3b17 · outbound

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A Learning-based Domain Decomposition Method Unresolved cited work

Reference 7

Resolution
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Source-reported events for the cited work

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Observation e927f6cc-cb4c-4133-babe-bff1a94c990e · outbound

This paper cites an unresolved cited work.

A Learning-based Domain Decomposition Method Unresolved cited work

Reference 8

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Source-reported events for the cited work

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Observation 90361da8-36e3-461b-a0d7-19b586fe694a · outbound

This paper cites Raissi, P.

A Learning-based Domain Decomposition Method Raissi, P

Reference 9

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Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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Observation f37ceaf8-19bb-4317-aeb1-83f668409732 · outbound

This paper cites Yu, et al., The deep ritz method: a deep learning-based numerical algorithm for solving variational problems, Communications in Mathe- matics and Statistics 6 (1) (2018) 1–12.

A Learning-based Domain Decomposition Method Yu, et al., The deep ritz method: a deep learning-based numerical algorithm for solving variational problems, Communications in Mathe- matics and Statistics 6 (1) (2018) 1–12

Reference 10

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Source-reported events for the cited work

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Observation ac212a27-f355-4411-86d9-a5f45008be08 · outbound

This paper cites Variational Physics-Informed Neural Networks For Solving Partial Differential Equations.

A Learning-based Domain Decomposition Method Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

Reference 11

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Observation ee747f20-ac9c-4e04-aee7-d333ed2d9c02 · outbound

This paper cites Kovachki, Z.

A Learning-based Domain Decomposition Method Kovachki, Z

Reference 12

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Observation 6ca19842-6da4-492c-8699-7f584b9d9061 · outbound

This paper cites DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators.

A Learning-based Domain Decomposition Method DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators

Reference 13

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Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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Observation 0d3d0261-5adc-4d88-85b5-b901e9dd6231 · outbound

This paper cites Fourier Neural Operator for Parametric Partial Differential Equations.

A Learning-based Domain Decomposition Method Fourier Neural Operator for Parametric Partial Differential Equations

Reference 14

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Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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Observation d142c538-d332-4a79-b37f-b5a298219981 · outbound

This paper cites Neural Operator: Graph Kernel Network for Partial Differential Equations.

A Learning-based Domain Decomposition Method Neural Operator: Graph Kernel Network for Partial Differential Equations

Reference 15

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Observation 85858392-f8a1-44ad-992f-95e3e528fc0e · outbound

This paper cites an unresolved cited work.

A Learning-based Domain Decomposition Method Unresolved cited work

Reference 16

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

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Observation 83158c10-f259-47c2-a1d7-27c60b426699 · outbound

This paper cites an unresolved cited work.

A Learning-based Domain Decomposition Method Unresolved cited work

Reference 17

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Unavailable: canonical work link unavailable.

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Observation 9916202e-1246-4d87-9220-8c1a3b81417f · outbound

This paper cites Calvello, N.

A Learning-based Domain Decomposition Method Calvello, N

Reference 18

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Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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Observation 40d8ba9c-1e4e-4acd-8df5-a349761cfa12 · outbound

This paper cites Neural Interpretable PDEs: Harmonizing Fourier Insights with Attention for Scalable and Interpretable Physics Discovery.

A Learning-based Domain Decomposition Method Neural Interpretable PDEs: Harmonizing Fourier Insights with Attention for Scalable and Interpretable Physics Discovery

Reference 19

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

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Observation 341211fc-fbdb-4d9c-bb59-ac5e18c05560 · outbound

This paper cites Goswami, A.

A Learning-based Domain Decomposition Method Goswami, A

Reference 20

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

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Observation 57b3d059-5cfb-4ef6-b137-d0e9d53bfee2 · outbound

This paper cites an unresolved cited work.

A Learning-based Domain Decomposition Method Unresolved cited work

Reference 21

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Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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Observation 24d1d89d-71e7-43d4-befc-ad2970220bfd · outbound

This paper cites an unresolved cited work.

A Learning-based Domain Decomposition Method Unresolved cited work

Reference 22

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

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Observation 04a3de34-a14b-4353-acd7-a60e829ad5e1 · outbound

This paper cites Lions, et al., On the schwarz alternating method.

A Learning-based Domain Decomposition Method Lions, et al., On the schwarz alternating method

Reference 23

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verified fuzzy
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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

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Observation 1cb95a05-ed0d-4f40-a6ef-7e9b7ed9a14e · outbound

This paper cites an unresolved cited work.

A Learning-based Domain Decomposition Method Unresolved cited work

Reference 24

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

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Observation 2d677186-8459-4efe-b026-63adf85f545d · outbound

This paper cites Toselli, O.

A Learning-based Domain Decomposition Method Toselli, O

Reference 25

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

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Observation d161b24c-a4b4-4401-88b0-53749789e948 · outbound

This paper cites an unresolved cited work.

A Learning-based Domain Decomposition Method Unresolved cited work

Reference 26

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

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Observation ccb8aaf5-024a-44ed-b1a7-7ab7558b936d · outbound

This paper cites Klawonn, M.

A Learning-based Domain Decomposition Method Klawonn, M

Reference 27

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verified fuzzy
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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

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Observation 3f2040d3-215e-4e88-bcf0-6dd2023c14ef · outbound

This paper cites Heinlein, A.

A Learning-based Domain Decomposition Method Heinlein, A

Reference 28

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

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Observation f17ef403-400a-45a3-b091-6aac64022fd5 · outbound

This paper cites an unresolved cited work.

A Learning-based Domain Decomposition Method Unresolved cited work

Reference 29

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Unavailable: canonical work link unavailable.

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Observation bf9e155e-0bb0-4efc-b8b3-b965f68b587c · outbound

This paper cites an unresolved cited work.

A Learning-based Domain Decomposition Method Unresolved cited work

Reference 30

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

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Observation 6e8acc42-01c8-4ca7-8fc2-aec46d1a404e · outbound

This paper cites Stiller, F.

A Learning-based Domain Decomposition Method Stiller, F

Reference 31

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

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Observation 93c6f8ab-caee-41fa-ac50-d520f611fc65 · outbound

This paper cites Bischof, M.

A Learning-based Domain Decomposition Method Bischof, M

Reference 32

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

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Observation c7207a76-83d5-47e9-9cdf-426642ac7c1a · outbound

This paper cites an unresolved cited work.

A Learning-based Domain Decomposition Method Unresolved cited work

Reference 33

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

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Observation 963b480d-0901-4ab7-b117-d62611fc2705 · outbound

This paper cites Distributed physics informed neural network for data-efficient solution to partial differential equations.

A Learning-based Domain Decomposition Method Distributed physics informed neural network for data-efficient solution to partial differential equations

Reference 34

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Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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Observation c9f8f37d-a500-4275-ae25-a9a51036e84f · outbound

This paper cites A Generalized Schwarz-type Non-overlapping Domain Decomposition Method using Physics-constrained Neural Networks.

A Learning-based Domain Decomposition Method A Generalized Schwarz-type Non-overlapping Domain Decomposition Method using Physics-constrained Neural Networks

Reference 35

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Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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Observation b5ae2d8d-48c8-41f6-9a1a-13dd96a7926f · outbound

This paper cites Moseley, A.

A Learning-based Domain Decomposition Method Moseley, A

Reference 36

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T14:57:35.511617Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

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Observation 6ab00610-bec1-48b2-9c79-9c4db8b09d82 · outbound

This paper cites Dolean, A.

A Learning-based Domain Decomposition Method Dolean, A

Reference 37

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

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Observation 8fb070f1-503a-41ec-9b2d-467b0abdd481 · outbound

This paper cites an unresolved cited work.

A Learning-based Domain Decomposition Method Unresolved cited work

Reference 38

Resolution
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raw_fallback, observed 2026-08-06T14:57:35.491296Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

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Observation 70c463ef-6565-463e-97bc-58c17778ff2c · outbound

This paper cites an unresolved cited work.

A Learning-based Domain Decomposition Method Unresolved cited work

Reference 39

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

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Observation 913458b3-8513-4c4a-a333-bc83c732e748 · outbound

This paper cites Adams, J.

A Learning-based Domain Decomposition Method Adams, J

Reference 40

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

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Observation 212ae792-b6f0-467c-8681-7de9ced6267e · outbound

This paper cites FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators.

A Learning-based Domain Decomposition Method FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators

Reference 41

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Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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Observation 8f60a460-f412-44af-88fe-57e650ddb70d · outbound

This paper cites an unresolved cited work.

A Learning-based Domain Decomposition Method Unresolved cited work

Reference 42

Resolution
unresolved
raw_fallback, observed 2026-08-06T14:57:35.461071Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

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Observation ec0f1f3c-4df4-44d4-b861-416852c55aad · outbound

This paper cites Nonlocality and Nonlinearity Implies Universality in Operator Learning.

A Learning-based Domain Decomposition Method Nonlocality and Nonlinearity Implies Universality in Operator Learning

Reference 43

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Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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Observation 8e1ef2c0-5130-49d1-9839-b2fec9e136b5 · outbound

This paper cites Gilbarg, N.

A Learning-based Domain Decomposition Method Gilbarg, N

Reference 44

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

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Observation 9017b7fa-6f65-4245-aaa3-684014f3159a · outbound

This paper cites an unresolved cited work.

A Learning-based Domain Decomposition Method Unresolved cited work

Reference 45

Resolution
unresolved
raw_fallback, observed 2026-08-06T14:57:35.440167Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

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Observation a4d7583b-f6d7-41c9-a8c6-f293d0ac2f35 · outbound

This paper cites an unresolved cited work.

A Learning-based Domain Decomposition Method Unresolved cited work

Reference 46

Resolution
unresolved
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

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Observation 7aba9df7-8ecf-4fb5-b12d-007a0091d4e9 · outbound

This paper cites an unresolved cited work.

A Learning-based Domain Decomposition Method Unresolved cited work

Reference 47

Resolution
unresolved
raw_fallback, observed 2026-08-06T14:57:35.418301Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

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Observation 6f2acba8-0a9d-42f7-89ec-a34e3a8be794 · outbound

This paper cites Neural Operators with Localized Integral and Differential Kernels.

A Learning-based Domain Decomposition Method Neural Operators with Localized Integral and Differential Kernels

Reference 48

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no resolver link, observed 2026-08-06T14:57:35.076794Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T14:57:35.076794Z digest=sha256:99661e51c9e20dc9127e84371cd157bd36f85b5a5d5d8a42d340405a4667c52b

Observation 22fd9963-6b70-4149-95a9-5f18019528d0 · outbound

This paper cites Ronneberger, P.

A Learning-based Domain Decomposition Method Ronneberger, P

Reference 49

Resolution
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no resolver link, observed 2026-08-06T14:57:35.080715Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T14:57:35.080715Z digest=sha256:0b647f42e28292b4ac9ee975426d26c86d449df9c0b11ec689880c91f5da6e8c

Observation a4080e7f-d804-4f9b-83f3-d088efc48a26 · outbound

This paper cites Goodfellow, Y.

A Learning-based Domain Decomposition Method Goodfellow, Y

Reference 50

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T14:57:35.397578Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

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Observation 1ff3f585-5a49-42a1-be0e-bf81c1130d13 · outbound

This paper cites PyTorch: An Imperative Style, High-Performance Deep Learning Library.

A Learning-based Domain Decomposition Method PyTorch: An Imperative Style, High-Performance Deep Learning Library

Reference 51

Resolution
unresolved
no resolver link, observed 2026-08-06T14:57:35.088009Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T14:57:35.088009Z digest=sha256:4331c6af6d21d3967c83ade9da319aebaefe37c74283db2a50419a72459d4ebc

Observation 1828efe8-ea9d-4dca-bee1-3520d996a564 · outbound

This paper cites DeVore, G.

A Learning-based Domain Decomposition Method DeVore, G

Reference 52

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T14:57:35.386422Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

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Observation 3f1fbcaf-e914-4f7c-9ab4-34f8adb7c3e1 · outbound

This paper cites an unresolved cited work.

A Learning-based Domain Decomposition Method Unresolved cited work

Reference 53

Resolution
unresolved
raw_fallback, observed 2026-08-06T14:57:35.374729Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

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Observation 8cbd0894-768b-4a56-93e1-19cb9dbdc623 · outbound

This paper cites an unresolved cited work.

A Learning-based Domain Decomposition Method Unresolved cited work

Reference 54

Resolution
unresolved
no resolver link, observed 2026-08-06T14:57:35.100146Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T14:57:35.100146Z digest=sha256:fdf2850ebce699a794efdcaa7573bb8ebebf28be1e87e7737bd7230d2e333738

Observation 8ca38151-625d-4b6b-92ac-fbda6a7b1f19 · outbound

This paper cites Krizhevsky, I.

A Learning-based Domain Decomposition Method Krizhevsky, I

Reference 55

Resolution
unresolved
no resolver link, observed 2026-08-06T14:57:35.103696Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T14:57:35.103696Z digest=sha256:a3927ada76eb50abb10f68756d538aecec25cc30b7f7036bdf8cb6b0bf2df54a

Observation 3c82cd26-f957-42d7-b97d-5cdc7fcd9ff4 · outbound

This paper cites An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale.

A Learning-based Domain Decomposition Method An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale

Reference 56

Resolution
unresolved
no resolver link, observed 2026-08-06T14:57:35.107477Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T14:57:35.107477Z digest=sha256:5f70194f9c75ebef5c41910467504da45878d0e1c2d565770bfc55a47122a730

Observation 930d3bfb-43c8-4298-b285-54f429a83d16 · outbound

This paper cites Bhattacharya, N.

A Learning-based Domain Decomposition Method Bhattacharya, N

Reference 57

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T14:57:35.352435Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

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Pith citing papers

No inbound Pith citation observations are available.