Paper Citation Record · LEDGER

Error Analysis of the Deep Mixed Residual Method for High-order Elliptic Equations

As of 13 August 2026, this Paper Citation Record lists 34 of 34 outbound references and 0 inbound Pith citation observations for arXiv:2411.14151.

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

pith.paper-citation-record.v1
2411.14151 v2

Coverage vector

measured 34 of 34 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-12T15:40:19.909899Z

measured 34 of 34 standing notices

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Source: scholarly_work_events, retraction_status_cache, observed 2026-08-12T06:34:41.77262+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

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measured 0 of 1 external citation measurements

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Reference resolution

34 of 34 outbound references displayed

verified exact2
verified fuzzy18
unresolved14
parse uncertain0
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External citation measurements

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Outbound references

Observation 680a18a4-b090-4bb7-8f5d-0f7108d186c5 · outbound

This paper cites 2, 153–180.

Error Analysis of the Deep Mixed Residual Method for High-order Elliptic Equations 2, 153–180

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T15:40:20.533397Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 862656eb-cbe0-410a-a575-cedb15ae3462 · outbound

This paper cites 3, 930–945.

Error Analysis of the Deep Mixed Residual Method for High-order Elliptic Equations 3, 930–945

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T15:40:20.517330Z

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Observation 00b49271-0685-4b20-bf11-ef37d3edc3dd · outbound

This paper cites an unresolved cited work.

Error Analysis of the Deep Mixed Residual Method for High-order Elliptic Equations Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-08-12T15:40:20.496961Z

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Observation 40ccafc9-7686-4102-af9a-3d42307b1c3e · outbound

This paper cites 6, 1785–1799.

Error Analysis of the Deep Mixed Residual Method for High-order Elliptic Equations 6, 1785–1799

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T15:40:20.480735Z

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Observation 202768d2-a459-4bad-98c9-9d47470d3320 · outbound

This paper cites 38, 385704.

Error Analysis of the Deep Mixed Residual Method for High-order Elliptic Equations 38, 385704

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T15:40:20.464391Z

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Observation a61db796-c6f3-4408-b3d5-86216f31eba2 · outbound

This paper cites an unresolved cited work.

Error Analysis of the Deep Mixed Residual Method for High-order Elliptic Equations Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-08-12T15:40:20.447759Z

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Observation b9a51e0a-4289-4aa6-986d-af0470b79bf7 · outbound

This paper cites 159, Springer, 2004.

Error Analysis of the Deep Mixed Residual Method for High-order Elliptic Equations 159, Springer, 2004

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T15:40:20.429249Z

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Observation 42811d14-b867-48e9-bbe7-b00952783139 · outbound

This paper cites 5, Springer Science & Business Media, 2012.

Error Analysis of the Deep Mixed Residual Method for High-order Elliptic Equations 5, Springer Science & Business Media, 2012

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T15:40:20.413919Z

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Observation b0d0b16d-26cf-4ece-adc0-14980ac4024c · outbound

This paper cites 34, 8505–8510.

Error Analysis of the Deep Mixed Residual Method for High-order Elliptic Equations 34, 8505–8510

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T15:40:20.396629Z

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Observation a92c0a2b-7253-43dc-ac23-e2f57b332c15 · outbound

This paper cites A Priori Analysis of Stable Neural Network Solutions to Numerical PDEs.

Error Analysis of the Deep Mixed Residual Method for High-order Elliptic Equations A Priori Analysis of Stable Neural Network Solutions to Numerical PDEs

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-12T15:40:19.789185Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a23f165f-47ea-4c08-8849-dfb6a62c4832 · outbound

This paper cites 5, 051129.

Error Analysis of the Deep Mixed Residual Method for High-order Elliptic Equations 5, 051129

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T15:40:20.380914Z

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Observation 8ca34436-2798-494a-a4bd-e6c0f8e0dc2d · outbound

This paper cites 7, Elsevier, 2012.

Error Analysis of the Deep Mixed Residual Method for High-order Elliptic Equations 7, Elsevier, 2012

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T15:40:20.363298Z

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Observation d3f77f38-81d6-4b6d-9a9d-3a5f9c2b3d49 · outbound

This paper cites an unresolved cited work.

Error Analysis of the Deep Mixed Residual Method for High-order Elliptic Equations Unresolved cited work

Reference 13

Resolution: unresolved; raw_fallback, observed 2026-08-12T15:40:20.346156Z

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Observation 90d96d46-a498-4d93-b919-538520982c2a · outbound

This paper cites 1, 319–344.

Error Analysis of the Deep Mixed Residual Method for High-order Elliptic Equations 1, 319–344

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T15:40:20.330221Z

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Observation eb07e8e7-ffbe-4090-9edd-26431bb962a9 · outbound

This paper cites an unresolved cited work.

Error Analysis of the Deep Mixed Residual Method for High-order Elliptic Equations Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-08-12T15:40:20.314768Z

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Observation 1dbda58b-42f2-4c38-8b39-284debdaaa65 · outbound

This paper cites an unresolved cited work.

Error Analysis of the Deep Mixed Residual Method for High-order Elliptic Equations Unresolved cited work

Reference 16

Resolution: unresolved; raw_fallback, observed 2026-08-12T15:40:20.298563Z

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Observation 6a29026e-c6e0-4484-9847-f46183905b83 · outbound

This paper cites 4, 748–775.

Error Analysis of the Deep Mixed Residual Method for High-order Elliptic Equations 4, 748–775

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T15:40:20.282815Z

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Observation efad6116-278e-45ba-bb46-1f44710d8718 · outbound

This paper cites an unresolved cited work.

Error Analysis of the Deep Mixed Residual Method for High-order Elliptic Equations Unresolved cited work

Reference 18

Resolution: unresolved; raw_fallback, observed 2026-08-12T15:40:20.262729Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation bc794085-470c-4098-81d0-4469a13884b7 · outbound

This paper cites 2, 981–1022.

Error Analysis of the Deep Mixed Residual Method for High-order Elliptic Equations 2, 981–1022

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T15:40:20.245056Z

Source-reported events for the cited work

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Observation b062e963-8d70-4292-8c9f-a1108ef2e983 · outbound

This paper cites an unresolved cited work.

Error Analysis of the Deep Mixed Residual Method for High-order Elliptic Equations Unresolved cited work

Reference 20

Resolution: unresolved; raw_fallback, observed 2026-08-12T15:40:20.226930Z

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Observation e586e725-750f-4c58-84c3-9560af1a5b8d · outbound

This paper cites Error Estimates for the Deep Ritz Method with Boundary Penalty.

Error Analysis of the Deep Mixed Residual Method for High-order Elliptic Equations Error Estimates for the Deep Ritz Method with Boundary Penalty

Reference 21

Resolution: verified exact; local_arxiv, observed 2026-08-12T15:40:19.981345Z

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Observation 70a67fc4-7e1b-4ea9-a7e6-2f4103297fff · outbound

This paper cites an unresolved cited work.

Error Analysis of the Deep Mixed Residual Method for High-order Elliptic Equations Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-08-12T15:40:20.211520Z

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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation f4c0c308-9152-4d78-9f08-e5480e0e08cc · outbound

This paper cites an unresolved cited work.

Error Analysis of the Deep Mixed Residual Method for High-order Elliptic Equations Unresolved cited work

Reference 23

Resolution: unresolved; raw_fallback, observed 2026-08-12T15:40:20.195906Z

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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation d5829e0f-e602-4f43-a726-5c45558279be · outbound

This paper cites an unresolved cited work.

Error Analysis of the Deep Mixed Residual Method for High-order Elliptic Equations Unresolved cited work

Reference 24

Resolution: unresolved; raw_fallback, observed 2026-08-12T15:40:20.178044Z

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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 029da65c-ec90-4aa5-9a30-7b95918da5fb · outbound

This paper cites an unresolved cited work.

Error Analysis of the Deep Mixed Residual Method for High-order Elliptic Equations Unresolved cited work

Reference 25

Resolution: unresolved; raw_fallback, observed 2026-08-12T15:40:20.158442Z

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Observation ca4de7a1-29cf-4332-ab2c-a2af9ec7670d · outbound

This paper cites 1, 47–69.

Error Analysis of the Deep Mixed Residual Method for High-order Elliptic Equations 1, 47–69

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T15:40:20.141213Z

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Observation c580ce3e-729f-42ca-95a3-904a0cb806eb · outbound

This paper cites ERROR ANALYSIS OF MIM FOR HIGH-ORDER ELLIPTIC EQUATIONS 33.

Error Analysis of the Deep Mixed Residual Method for High-order Elliptic Equations ERROR ANALYSIS OF MIM FOR HIGH-ORDER ELLIPTIC EQUATIONS 33

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T15:40:20.124697Z

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Observation e525cac0-cf09-4915-80c2-087e94f012c2 · outbound

This paper cites an unresolved cited work.

Error Analysis of the Deep Mixed Residual Method for High-order Elliptic Equations Unresolved cited work

Reference 28

Resolution: unresolved; raw_fallback, observed 2026-08-12T15:40:20.107812Z

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Observation 666727f0-986a-4330-ba03-a725300724db · outbound

This paper cites 2, 04021154.

Error Analysis of the Deep Mixed Residual Method for High-order Elliptic Equations 2, 04021154

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T15:40:20.088159Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation aecbc1b6-9512-4529-ab9c-3d09bf9e3a0f · outbound

This paper cites 55 (2022), no.

Error Analysis of the Deep Mixed Residual Method for High-order Elliptic Equations 55 (2022), no

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T15:40:20.071065Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 8579d6aa-c38f-467a-bad6-16217c5b930d · outbound

This paper cites an unresolved cited work.

Error Analysis of the Deep Mixed Residual Method for High-order Elliptic Equations Unresolved cited work

Reference 31

Resolution: unresolved; raw_fallback, observed 2026-08-12T15:40:20.053754Z

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Observation 3f6d7280-98be-4ee9-97f4-a40ff5f115a4 · outbound

This paper cites A Unified Framework for the Error Analysis of Physics-Informed Neural Networks.

Error Analysis of the Deep Mixed Residual Method for High-order Elliptic Equations A Unified Framework for the Error Analysis of Physics-Informed Neural Networks

Reference 32

Resolution: verified exact; local_arxiv, observed 2026-08-12T15:40:19.957583Z

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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 68cc48bf-bab6-415e-8bd4-62293b8c87c5 · outbound

This paper cites Let us deﬁne the function class: Fcos(B) := { γ 1 + π4|k|4 1 cos ( π(k ·x) + b ) ⏐ ⏐ ⏐k ∈ Zd/{0}, |γ| ≤ B, b ∈ {0, 1} } , where B > 0 is a constant.

Error Analysis of the Deep Mixed Residual Method for High-order Elliptic Equations Let us deﬁne the function class: Fcos(B) := { γ 1 + π4|k|4 1 cos ( π(k ·x) + b ) ⏐ ⏐ ⏐k ∈ Zd/{0}, |γ| ≤ B, b ∈ {0, 1} } , where B > 0 is a constant

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T15:40:20.035660Z

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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation a1659e22-7dba-42a2-a6a6-e858e1861604 · outbound

This paper cites It follows that from property ( 5) (98) RN (L∗) ≤4 sup vθ ∈FReCU,m ‖P∗vθ −f ‖L∞ (Ω) ( RN (f ) + m∑ i=1 d∑ j=1 |ai||Wi,j|2RN ( σ(2)(G) ) ).

Error Analysis of the Deep Mixed Residual Method for High-order Elliptic Equations It follows that from property ( 5) (98) RN (L∗) ≤4 sup vθ ∈FReCU,m ‖P∗vθ −f ‖L∞ (Ω) ( RN (f ) + m∑ i=1 d∑ j=1 |ai||Wi,j|2RN ( σ(2)(G) ) )

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T15:40:20.017825Z

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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Pith citing papers

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