Paper Citation Record · LEDGER

Enforced Interface Constraints for Domain Decomposition Method of Discrete Physics-Informed Neural Networks

As of 22 August 2026, this Paper Citation Record lists 45 of 45 outbound references and 0 inbound Pith citation observations for arXiv:2505.10925.

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

pith.paper-citation-record.v1
2505.10925 v1

Coverage vector

measured 45 of 45 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T21:05:24.594316Z

measured 45 of 45 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-22T06:32:14.747728+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

45 of 45 outbound references displayed

verified exact8
verified fuzzy3
unresolved30
parse uncertain0
malformed identifier2
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External citation measurements

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Outbound references

Observation a91cd6dd-4858-4895-91b8-fac7ccccbbf4 · outbound

This paper cites an unresolved cited work.

Enforced Interface Constraints for Domain Decomposition Method of Discrete Physics-Informed Neural Networks Unresolved cited work

Reference 1

Resolution: unresolved; raw_fallback, observed 2026-08-15T21:05:26.035886Z

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No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation eaf0be5e-fc85-45f2-a86d-2a53d7176209 · outbound

This paper cites To ensure a well-posed problem, the boundary conditions ()k  are imposed on the domain 5 boundary k , with the prescribed boundary values ()kg x.

Enforced Interface Constraints for Domain Decomposition Method of Discrete Physics-Informed Neural Networks To ensure a well-posed problem, the boundary conditions ()k  are imposed on the domain 5 boundary k , with the prescribed boundary values ()kg x

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T21:05:26.013287Z

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Observation bc6437f1-4b0e-476e-aa93-27cf8f42165c · outbound

This paper cites an unresolved cited work.

Enforced Interface Constraints for Domain Decomposition Method of Discrete Physics-Informed Neural Networks Unresolved cited work

Reference 3

Resolution: malformed identifier; raw_fallback, observed 2026-08-15T21:05:25.990400Z

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Observation 39840afc-fbef-4ed6-bafd-b7a689a150b1 · outbound

This paper cites an unresolved cited work.

Enforced Interface Constraints for Domain Decomposition Method of Discrete Physics-Informed Neural Networks Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-08-15T21:05:25.966904Z

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Observation a3c56dd2-7974-4a19-a202-140b091419f0 · outbound

This paper cites Raissi, P.

Enforced Interface Constraints for Domain Decomposition Method of Discrete Physics-Informed Neural Networks Raissi, P

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-15T21:05:24.385067Z

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Observation 76e0d4cd-898b-47e2-84a2-652794f728e2 · outbound

This paper cites Cuomo, V .S.

Enforced Interface Constraints for Domain Decomposition Method of Discrete Physics-Informed Neural Networks Cuomo, V .S

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-15T21:05:24.390280Z

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Observation bb2a55c8-6b1f-421f-b337-54921288a406 · outbound

This paper cites an unresolved cited work.

Enforced Interface Constraints for Domain Decomposition Method of Discrete Physics-Informed Neural Networks Unresolved cited work

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-15T21:05:24.394521Z

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Observation 1ba4ea2e-55eb-407c-a262-090ef1da3528 · outbound

This paper cites an unresolved cited work.

Enforced Interface Constraints for Domain Decomposition Method of Discrete Physics-Informed Neural Networks Unresolved cited work

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-15T21:05:24.398408Z

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Observation c3df8071-0d4f-4f5a-8fe5-2eb96e2e69fb · outbound

This paper cites https://sc.panda985.com/extdomains/books.google.com/books/about/Domain_Decomposition_Methods_Algorithm s.html?hl=zh-CN&id=tpSPx68R3KwC (accessed April 6, 2025).

Enforced Interface Constraints for Domain Decomposition Method of Discrete Physics-Informed Neural Networks https://sc.panda985.com/extdomains/books.google.com/books/about/Domain_Decomposition_Methods_Algorithm s.html?hl=zh-CN&id=tpSPx68R3KwC (accessed April 6, 2025)

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T21:05:25.942123Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 0fabecfe-ef86-4f0e-a46b-94c141ff2a32 · outbound

This paper cites Smith, Domain Decomposition Methods for Partial Differ ential Equations, in: D.E.

Enforced Interface Constraints for Domain Decomposition Method of Discrete Physics-Informed Neural Networks Smith, Domain Decomposition Methods for Partial Differ ential Equations, in: D.E

Reference 10

Resolution: verified exact; doi, observed 2026-08-15T21:05:24.947533Z

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Observation 74ea3966-357f-47ce-a912-162e3a2cd826 · outbound

This paper cites Graham, P.O.

Enforced Interface Constraints for Domain Decomposition Method of Discrete Physics-Informed Neural Networks Graham, P.O

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-15T21:05:24.413453Z

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Observation 6a546e57-67f5-4e04-b755-5eb79e371447 · outbound

This paper cites Jagtap, E.

Enforced Interface Constraints for Domain Decomposition Method of Discrete Physics-Informed Neural Networks Jagtap, E

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-15T21:05:24.417546Z

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Observation 14676bd2-be70-464f-8f96-72ce4004cb37 · outbound

This paper cites Jagtap, G.E.

Enforced Interface Constraints for Domain Decomposition Method of Discrete Physics-Informed Neural Networks Jagtap, G.E

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-15T21:05:24.422111Z

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Observation c8268975-e247-4bd4-9539-7cc04be5954b · outbound

This paper cites Shukla, A.D.

Enforced Interface Constraints for Domain Decomposition Method of Discrete Physics-Informed Neural Networks Shukla, A.D

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-15T21:05:24.426405Z

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Observation 846aba7e-3982-470e-8f4a-e2f59c43898e · outbound

This paper cites Moseley, A.

Enforced Interface Constraints for Domain Decomposition Method of Discrete Physics-Informed Neural Networks Moseley, A

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-15T21:05:24.430501Z

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Observation ab6c14f8-6926-49ef-9f76-dee54a0b795b · outbound

This paper cites an unresolved cited work.

Enforced Interface Constraints for Domain Decomposition Method of Discrete Physics-Informed Neural Networks Unresolved cited work

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-15T21:05:24.434470Z

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Observation d9bd7d6c-cb97-4dea-b03f-5a9427c48752 · outbound

This paper cites Kharazmi, Z.

Enforced Interface Constraints for Domain Decomposition Method of Discrete Physics-Informed Neural Networks Kharazmi, Z

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-15T21:05:24.438735Z

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Observation 36942db9-48b6-4847-a8f7-ec6002710d7f · outbound

This paper cites an unresolved cited work.

Enforced Interface Constraints for Domain Decomposition Method of Discrete Physics-Informed Neural Networks Unresolved cited work

Reference 18

Resolution: metadata mismatch; raw_fallback, observed 2026-08-15T21:05:25.528270Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 499d96b1-4c47-4ace-9c81-3283fd7c9fa3 · outbound

This paper cites Huang, Q.-Y.

Enforced Interface Constraints for Domain Decomposition Method of Discrete Physics-Informed Neural Networks Huang, Q.-Y

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-15T21:05:24.446786Z

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Observation 4405d06e-fe4d-4ff8-a4d6-bf299b4e2eb7 · outbound

This paper cites Dwivedi, N.

Enforced Interface Constraints for Domain Decomposition Method of Discrete Physics-Informed Neural Networks Dwivedi, N

Reference 20

Resolution: verified exact; doi, observed 2026-08-15T21:05:24.884081Z

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Observation 365b0afd-70a0-4e57-afc1-b9abc219d666 · outbound

This paper cites an unresolved cited work.

Enforced Interface Constraints for Domain Decomposition Method of Discrete Physics-Informed Neural Networks Unresolved cited work

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-15T21:05:24.454510Z

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Observation 43d795bd-3914-45b0-b51f-d457d05709b0 · outbound

This paper cites an unresolved cited work.

Enforced Interface Constraints for Domain Decomposition Method of Discrete Physics-Informed Neural Networks Unresolved cited work

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-15T21:05:24.459222Z

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Observation 19cf00d6-a434-45e1-8ce0-fafb3b1eed60 · outbound

This paper cites Droniou, R.

Enforced Interface Constraints for Domain Decomposition Method of Discrete Physics-Informed Neural Networks Droniou, R

Reference 23

Resolution: verified exact; doi, observed 2026-08-15T21:05:24.866732Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 470f4577-2e61-49b7-86d7-9dacaeee2308 · outbound

This paper cites Wohlmuth, A Mortar Finite Element Method Using Dual Spaces for the Lagrange Multiplier, SIAM Journal on Numerical Analysis (2006).

Enforced Interface Constraints for Domain Decomposition Method of Discrete Physics-Informed Neural Networks Wohlmuth, A Mortar Finite Element Method Using Dual Spaces for the Lagrange Multiplier, SIAM Journal on Numerical Analysis (2006)

Reference 24

Resolution: verified exact; doi, observed 2026-08-15T21:05:24.851671Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 9cf0cdd3-4ad1-46b3-a84a-122944e0be0d · outbound

This paper cites Puso, T.A.

Enforced Interface Constraints for Domain Decomposition Method of Discrete Physics-Informed Neural Networks Puso, T.A

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-15T21:05:24.473614Z

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Unavailable: canonical work link unavailable.

Observation 7db70f34-8154-428a-9551-2d2b79244904 · outbound

This paper cites Shi, A convergence condition for the quadrilateral Wils on element, Numer.

Enforced Interface Constraints for Domain Decomposition Method of Discrete Physics-Informed Neural Networks Shi, A convergence condition for the quadrilateral Wils on element, Numer

Reference 26

Resolution: verified exact; doi, observed 2026-08-15T21:05:24.820651Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation d0f97969-b373-4c35-81e8-e040872d951a · outbound

This paper cites Hansbo, P.

Enforced Interface Constraints for Domain Decomposition Method of Discrete Physics-Informed Neural Networks Hansbo, P

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-15T21:05:24.483231Z

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Observation 2274efd2-12d8-4451-8256-e8530dfea049 · outbound

This paper cites Stummel, The Generalized Patch Test, SIAM Journal on Nu merical Analysis (2006).

Enforced Interface Constraints for Domain Decomposition Method of Discrete Physics-Informed Neural Networks Stummel, The Generalized Patch Test, SIAM Journal on Nu merical Analysis (2006)

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-15T21:05:24.488336Z

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Observation 2addd9c3-c6c8-4535-8ffe-d2db5d97ae48 · outbound

This paper cites Ainsworth, Essential boundary conditions and multi-poin t constraints in finite element analysis, Computer Methods in Applied Mechanics and Engineering 190 (2001) 6323–63 39.

Enforced Interface Constraints for Domain Decomposition Method of Discrete Physics-Informed Neural Networks Ainsworth, Essential boundary conditions and multi-poin t constraints in finite element analysis, Computer Methods in Applied Mechanics and Engineering 190 (2001) 6323–63 39

Reference 29

Resolution: malformed identifier; no resolver link, observed 2026-08-15T21:05:24.494388Z

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Observation 219a0c09-9502-4548-a43d-2af455ad7610 · outbound

This paper cites Nitsche, Über ein Variationsprinzip zur Lösung von Diri chlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind, Abh.Math.Semin.Uni v.Hambg.

Enforced Interface Constraints for Domain Decomposition Method of Discrete Physics-Informed Neural Networks Nitsche, Über ein Variationsprinzip zur Lösung von Diri chlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind, Abh.Math.Semin.Uni v.Hambg

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-15T21:05:24.499764Z

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Observation 1dba2691-e81f-4337-a098-9af9873fc3c2 · outbound

This paper cites Wilson, T.

Enforced Interface Constraints for Domain Decomposition Method of Discrete Physics-Informed Neural Networks Wilson, T

Reference 31

Resolution: metadata mismatch; raw_fallback, observed 2026-08-15T21:05:25.253719Z

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No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 7e7a278c-976f-4cf0-b5ed-3605c9e78e44 · outbound

This paper cites an unresolved cited work.

Enforced Interface Constraints for Domain Decomposition Method of Discrete Physics-Informed Neural Networks Unresolved cited work

Reference 32

Resolution: verified exact; doi, observed 2026-08-15T21:05:24.764586Z

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No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation da1bb459-78a1-4197-b5d5-7152afdc09dc · outbound

This paper cites Zhao, W.J.

Enforced Interface Constraints for Domain Decomposition Method of Discrete Physics-Informed Neural Networks Zhao, W.J

Reference 33

Resolution: verified exact; doi, observed 2026-08-15T21:05:24.751021Z

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No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation a2261146-729b-4bd4-ae23-897dc1bb682f · outbound

This paper cites Challenges in Training PINNs: A Loss Landscape Perspective.

Enforced Interface Constraints for Domain Decomposition Method of Discrete Physics-Informed Neural Networks Challenges in Training PINNs: A Loss Landscape Perspective

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-15T21:05:24.524362Z

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Observation fc7f4021-d385-4738-bfd1-7652d4422584 · outbound

This paper cites an unresolved cited work.

Enforced Interface Constraints for Domain Decomposition Method of Discrete Physics-Informed Neural Networks Unresolved cited work

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-15T21:05:24.529747Z

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Observation f6c82f40-c7d0-4b2a-8dd1-55786010a951 · outbound

This paper cites Szabó, Finite Element Analysis: Method, Verification and Validation, 2nd ed, John Wiley & Sons, Incorporated, Newark, 2021.

Enforced Interface Constraints for Domain Decomposition Method of Discrete Physics-Informed Neural Networks Szabó, Finite Element Analysis: Method, Verification and Validation, 2nd ed, John Wiley & Sons, Incorporated, Newark, 2021

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T21:05:25.924087Z

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Observation 16ca79be-c09f-4721-b608-ccb2371fefd5 · outbound

This paper cites an unresolved cited work.

Enforced Interface Constraints for Domain Decomposition Method of Discrete Physics-Informed Neural Networks Unresolved cited work

Reference 37

Resolution: unresolved; no resolver link, observed 2026-08-15T21:05:24.542878Z

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Observation d40bc5cd-841a-4f9d-9649-761545c9813b · outbound

This paper cites Fried, Numerical integration in the finite element meth od, Computers & Structures 4 (1974) 921–932.

Enforced Interface Constraints for Domain Decomposition Method of Discrete Physics-Informed Neural Networks Fried, Numerical integration in the finite element meth od, Computers & Structures 4 (1974) 921–932

Reference 38

Resolution: verified exact; doi, observed 2026-08-15T21:05:24.705047Z

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No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 3c078b88-5851-4604-a6c5-1e94a0f46655 · outbound

This paper cites Wang, Y .L.

Enforced Interface Constraints for Domain Decomposition Method of Discrete Physics-Informed Neural Networks Wang, Y .L

Reference 39

Resolution: unresolved; no resolver link, observed 2026-08-15T21:05:24.555506Z

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Observation 01ec94ab-f307-4100-8e07-6cdb6a4d3df3 · outbound

This paper cites Nguyen, P.

Enforced Interface Constraints for Domain Decomposition Method of Discrete Physics-Informed Neural Networks Nguyen, P

Reference 40

Resolution: unresolved; no resolver link, observed 2026-08-15T21:05:24.560600Z

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Observation a77fe76c-433f-4868-ad69-97f7312d1b3e · outbound

This paper cites an unresolved cited work.

Enforced Interface Constraints for Domain Decomposition Method of Discrete Physics-Informed Neural Networks Unresolved cited work

Reference 41

Resolution: unresolved; no resolver link, observed 2026-08-15T21:05:24.568339Z

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Observation 52f5d331-aca9-45ce-8f0b-90541650f06b · outbound

This paper cites Layer Normalization.

Enforced Interface Constraints for Domain Decomposition Method of Discrete Physics-Informed Neural Networks Layer Normalization

Reference 42

Resolution: unresolved; no resolver link, observed 2026-08-15T21:05:24.574447Z

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Observation 3b22a8e1-b073-4e0d-8752-da0b68319594 · outbound

This paper cites an unresolved cited work.

Enforced Interface Constraints for Domain Decomposition Method of Discrete Physics-Informed Neural Networks Unresolved cited work

Reference 43

Resolution: unresolved; no resolver link, observed 2026-08-15T21:05:24.583936Z

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Observation 0acfd2e0-5044-4fc1-ba93-308d0309ba93 · outbound

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

Enforced Interface Constraints for Domain Decomposition Method of Discrete Physics-Informed Neural Networks PyTorch: An Imperative Style, High-Performance Deep Learning Library

Reference 44

Resolution: unresolved; no resolver link, observed 2026-08-15T21:05:24.588829Z

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Observation d504aadf-46c4-4e35-8893-ae146fe304a3 · outbound

This paper cites Adam: A Method for Stochastic Optimization.

Enforced Interface Constraints for Domain Decomposition Method of Discrete Physics-Informed Neural Networks Adam: A Method for Stochastic Optimization

Reference 45

Resolution: unresolved; no resolver link, observed 2026-08-15T21:05:24.594316Z

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Pith citing papers

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