Paper Citation Record · LEDGER

Domain Decomposition Subspace Neural Network Method for Solving Linear and Nonlinear Partial Differential Equations

As of 14 August 2026, this Paper Citation Record lists 27 of 27 outbound references and 0 inbound Pith citation observations for arXiv:2505.20818.

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

pith.paper-citation-record.v1
2505.20818 v1

Coverage vector

measured 27 of 27 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T13:52:38.202787Z

measured 27 of 27 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

27 of 27 outbound references displayed

verified exact2
verified fuzzy4
unresolved19
parse uncertain0
malformed identifier1
metadata mismatch1

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation af1d353e-4261-44c9-bf82-0d1da9496aba · outbound

This paper cites an unresolved cited work.

Domain Decomposition Subspace Neural Network Method for Solving Linear and Nonlinear Partial Differential Equations Unresolved cited work

Reference 1

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:52:42.697911Z

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.

Observation 53373f24-19f4-40fe-badf-0ac19a41a6d4 · outbound

This paper cites an unresolved cited work.

Domain Decomposition Subspace Neural Network Method for Solving Linear and Nonlinear Partial Differential Equations Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:52:42.426473Z

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.

Observation b2fdc95e-7c52-4a12-b9e6-0a97a6a81597 · outbound

This paper cites an unresolved cited work.

Domain Decomposition Subspace Neural Network Method for Solving Linear and Nonlinear Partial Differential Equations Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:52:42.327687Z

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.

Observation 05ad3617-4c44-4cbe-ae01-9af785c07b4d · outbound

This paper cites an unresolved cited work.

Domain Decomposition Subspace Neural Network Method for Solving Linear and Nonlinear Partial Differential Equations Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:52:42.090455Z

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.

Observation c119a6a8-3eae-4493-9518-e0e014fa72e2 · outbound

This paper cites Raissi, P.

Domain Decomposition Subspace Neural Network Method for Solving Linear and Nonlinear Partial Differential Equations Raissi, P

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:52:41.954155Z

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.

Observation a4ec3151-23c7-4e93-b2ae-342f28dd5bda · outbound

This paper cites an unresolved cited work.

Domain Decomposition Subspace Neural Network Method for Solving Linear and Nonlinear Partial Differential Equations Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:52:41.766436Z

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.

Observation c38d4651-1e1b-4d5c-a887-9970e15bd09b · outbound

This paper cites an unresolved cited work.

Domain Decomposition Subspace Neural Network Method for Solving Linear and Nonlinear Partial Differential Equations Unresolved cited work

Reference 7

Resolution: metadata mismatch; raw_fallback, observed 2026-08-07T13:52:39.146795Z

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.

Observation efe8252b-c0e6-498a-a123-e7aa86812e42 · outbound

This paper cites Subspace method based on neural networks for solving the partial differential equation.

Domain Decomposition Subspace Neural Network Method for Solving Linear and Nonlinear Partial Differential Equations Subspace method based on neural networks for solving the partial differential equation

Reference 8

Resolution: verified exact; local_arxiv, observed 2026-08-07T13:52:38.916964Z

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.

Observation baed381c-3c67-461f-8c75-c89b0b7f9582 · outbound

This paper cites Huang, Q.

Domain Decomposition Subspace Neural Network Method for Solving Linear and Nonlinear Partial Differential Equations Huang, Q

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:52:41.527981Z

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.

Observation e981fc27-725b-4c82-b62a-94e1fd53a5a5 · outbound

This paper cites an unresolved cited work.

Domain Decomposition Subspace Neural Network Method for Solving Linear and Nonlinear Partial Differential Equations Unresolved cited work

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-07T13:52:35.908269Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d735dd82-9c0e-4bb9-9dfd-ad549e75cbcd · outbound

This paper cites an unresolved cited work.

Domain Decomposition Subspace Neural Network Method for Solving Linear and Nonlinear Partial Differential Equations Unresolved cited work

Reference 11

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:52:41.391019Z

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.

Observation 246bb332-b7a7-48e7-b907-e50b177a0cac · outbound

This paper cites Basir, I.

Domain Decomposition Subspace Neural Network Method for Solving Linear and Nonlinear Partial Differential Equations Basir, I

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:52:41.158511Z

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.

Observation 414bfefd-a912-4d11-b33a-359873b19922 · outbound

This paper cites an unresolved cited work.

Domain Decomposition Subspace Neural Network Method for Solving Linear and Nonlinear Partial Differential Equations Unresolved cited work

Reference 13

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:52:40.984850Z

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.

Observation 2c75ddd9-42c9-45d3-8c11-305816ad2ba4 · outbound

This paper cites an unresolved cited work.

Domain Decomposition Subspace Neural Network Method for Solving Linear and Nonlinear Partial Differential Equations Unresolved cited work

Reference 14

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:52:40.733356Z

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.

Observation 223400b3-6a63-485d-98d3-d38ed967939b · outbound

This paper cites Bai, G.-R.

Domain Decomposition Subspace Neural Network Method for Solving Linear and Nonlinear Partial Differential Equations Bai, G.-R

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-07T13:52:36.565716Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 01932e5a-5df0-43a4-8b71-f8f30469f1c0 · outbound

This paper cites an unresolved cited work.

Domain Decomposition Subspace Neural Network Method for Solving Linear and Nonlinear Partial Differential Equations Unresolved cited work

Reference 16

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:52:40.485415Z

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.

Observation 78e5f1b0-a9dc-4853-9ee1-61b28a8945dd · outbound

This paper cites Dekhovich, M.

Domain Decomposition Subspace Neural Network Method for Solving Linear and Nonlinear Partial Differential Equations Dekhovich, M

Reference 17

Resolution: malformed identifier; doi_truncated, observed 2026-08-07T13:52:38.431135Z

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.

Observation c6e6353c-44f2-4a83-b321-b196a3f6419c · outbound

This paper cites an unresolved cited work.

Domain Decomposition Subspace Neural Network Method for Solving Linear and Nonlinear Partial Differential Equations Unresolved cited work

Reference 18

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:52:40.212280Z

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.

Observation 35a5dad3-fd8a-4ab9-92ee-992d77d402e8 · outbound

This paper cites Shang, F.

Domain Decomposition Subspace Neural Network Method for Solving Linear and Nonlinear Partial Differential Equations Shang, F

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:52:40.028277Z

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.

Observation 8a1c0aff-ba2b-49aa-aa39-337c690e1a83 · outbound

This paper cites Solving Maxwell's Equation in 2D with Neural Networks with Local Converging Inputs.

Domain Decomposition Subspace Neural Network Method for Solving Linear and Nonlinear Partial Differential Equations Solving Maxwell's Equation in 2D with Neural Networks with Local Converging Inputs

Reference 20

Resolution: verified exact; local_arxiv, observed 2026-08-07T13:52:38.715035Z

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.

Observation 264b420e-962c-4032-8d28-05ca2a65d87e · outbound

This paper cites Adaptive Neural Network Subspace Method for Solving Partial Differential Equations with High Accuracy.

Domain Decomposition Subspace Neural Network Method for Solving Linear and Nonlinear Partial Differential Equations Adaptive Neural Network Subspace Method for Solving Partial Differential Equations with High Accuracy

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-07T13:52:37.368569Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7805b5d4-a8ee-46b2-8af9-5bc204452d64 · outbound

This paper cites an unresolved cited work.

Domain Decomposition Subspace Neural Network Method for Solving Linear and Nonlinear Partial Differential Equations Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:52:39.694552Z

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.

Observation 5c622c42-ca82-4ab6-89e0-0e5142a4552e · outbound

This paper cites an unresolved cited work.

Domain Decomposition Subspace Neural Network Method for Solving Linear and Nonlinear Partial Differential Equations Unresolved cited work

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-07T13:52:37.701878Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 85684e58-9d14-440d-98e6-c272a14e992f · outbound

This paper cites an unresolved cited work.

Domain Decomposition Subspace Neural Network Method for Solving Linear and Nonlinear Partial Differential Equations Unresolved cited work

Reference 24

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:52:39.533386Z

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.

Observation 5519f865-7419-48e8-af91-8d495ddb9222 · outbound

This paper cites an unresolved cited work.

Domain Decomposition Subspace Neural Network Method for Solving Linear and Nonlinear Partial Differential Equations Unresolved cited work

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-07T13:52:37.929581Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 46e87d8d-83f2-4bf1-a949-ee9345903824 · outbound

This paper cites PDEformer: Towards a Foundation Model for One-Dimensional Partial Differential Equations.

Domain Decomposition Subspace Neural Network Method for Solving Linear and Nonlinear Partial Differential Equations PDEformer: Towards a Foundation Model for One-Dimensional Partial Differential Equations

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-07T13:52:38.108531Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f5887791-39e4-425d-9961-6feaf849a270 · outbound

This paper cites an unresolved cited work.

Domain Decomposition Subspace Neural Network Method for Solving Linear and Nonlinear Partial Differential Equations Unresolved cited work

Reference 27

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:52:39.331251Z

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.

Pith citing papers

No inbound Pith citation observations are available.