Paper Citation Record · LEDGER

A priori error analysis of consistent PINNs for parabolic PDEs

As of 19 August 2026, this Paper Citation Record lists 36 of 36 outbound references and 2 inbound Pith citation observations for arXiv:2506.17614.

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

pith.paper-citation-record.v1
2506.17614 v1

Coverage vector

measured 36 of 36 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T19:12:54.374271Z

measured 38 of 38 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-19T06:32:44.657259+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-07-14T03:39:49.437017Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-11T17:51:08.383549Z

Reference resolution

36 of 36 outbound references displayed

verified exact5
verified fuzzy7
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 45fd6846-d565-4cb6-a55b-d5c873eb06d1 · outbound

This paper cites Error estimates for viscous Burgers' equation using deep learning method.

A priori error analysis of consistent PINNs for parabolic PDEs Error estimates for viscous Burgers' equation using deep learning method

Reference 1

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This paper cites In: Function spaces, differential operators and nonlinear analysis (Friedrichroda, 1992), Teubner-Texte Math., vol.

A priori error analysis of consistent PINNs for parabolic PDEs In: Function spaces, differential operators and nonlinear analysis (Friedrichroda, 1992), Teubner-Texte Math., vol

Reference 2

Resolution: verified exact; doi, observed 2026-08-15T19:12:54.638221Z

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Observation 40dfa492-d75b-427a-b7e5-c77e449c3af5 · outbound

This paper cites an unresolved cited work.

A priori error analysis of consistent PINNs for parabolic PDEs Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-08-15T19:12:55.024736Z

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Observation fd8ac219-4992-42ae-adae-49dc1cae25b6 · outbound

This paper cites Part 1, Jind˘rich Ne ˘cas Center for Mathematical Modeling Lecture Notes , vol.

A priori error analysis of consistent PINNs for parabolic PDEs Part 1, Jind˘rich Ne ˘cas Center for Mathematical Modeling Lecture Notes , vol

Reference 4

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Observation d088f9d7-4557-4c42-b977-213453b171a0 · outbound

This paper cites an unresolved cited work.

A priori error analysis of consistent PINNs for parabolic PDEs Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-08-15T19:12:54.996084Z

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Observation 2ed5fb85-1afd-42bc-b5c3-8eb5ad39ce46 · outbound

This paper cites Neurocomputing 317, 28–41 (2018).

A priori error analysis of consistent PINNs for parabolic PDEs Neurocomputing 317, 28–41 (2018)

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-15T19:12:54.202059Z

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Observation 29d9beca-7f83-412b-a4b8-7cf0ba534829 · outbound

This paper cites IMA Journal of Numerical Analysis p.

A priori error analysis of consistent PINNs for parabolic PDEs IMA Journal of Numerical Analysis p

Reference 7

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Observation 492df297-eeb9-4ef7-8cee-979c1ca611ff · outbound

This paper cites Acta Mech.

A priori error analysis of consistent PINNs for parabolic PDEs Acta Mech

Reference 8

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Observation f2d3113e-0ebf-4c42-ba0a-37e746405429 · outbound

This paper cites Journal of Scientific Computing 92(3), 88 (2022).

A priori error analysis of consistent PINNs for parabolic PDEs Journal of Scientific Computing 92(3), 88 (2022)

Reference 9

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A priori error analysis of consistent PINNs for parabolic PDEs Unresolved cited work

Reference 10

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Observation fc91d822-0daf-4d32-af02-a88c82074751 · outbound

This paper cites Manuscripta Math.

A priori error analysis of consistent PINNs for parabolic PDEs Manuscripta Math

Reference 11

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A priori error analysis of consistent PINNs for parabolic PDEs Unresolved cited work

Reference 12

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Observation a0d404b2-25be-468d-8847-c2f05df261a8 · outbound

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A priori error analysis of consistent PINNs for parabolic PDEs Unresolved cited work

Reference 13

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A priori error analysis of consistent PINNs for parabolic PDEs Unresolved cited work

Reference 14

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Observation 87e0642d-f950-49a0-8601-51e598f944be · outbound

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A priori error analysis of consistent PINNs for parabolic PDEs Unresolved cited work

Reference 15

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Observation 454563b0-805f-4d2b-83dc-48e8990fd311 · outbound

This paper cites On the Stability and Convergence of Physics Informed Neural Networks.

A priori error analysis of consistent PINNs for parabolic PDEs On the Stability and Convergence of Physics Informed Neural Networks

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-15T19:12:54.263631Z

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Observation 2c4f5621-4921-44a8-b24f-fa61b8e33b07 · outbound

This paper cites an unresolved cited work.

A priori error analysis of consistent PINNs for parabolic PDEs Unresolved cited work

Reference 17

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Observation 2f032c0b-2a87-48a3-ac30-7d6beb306069 · outbound

This paper cites Nature Reviews Physics 3(6), 422–440 (2021).

A priori error analysis of consistent PINNs for parabolic PDEs Nature Reviews Physics 3(6), 422–440 (2021)

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:12:54.972268Z

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Observation 94b4ef7a-6d85-46ec-b8a9-6e38384db339 · outbound

This paper cites an unresolved cited work.

A priori error analysis of consistent PINNs for parabolic PDEs Unresolved cited work

Reference 19

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Observation cf02f496-8b32-474b-a8e7-e7ef97ec192c · outbound

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A priori error analysis of consistent PINNs for parabolic PDEs Unresolved cited work

Reference 20

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Observation d8a61673-e748-4d2a-ba05-fabfa4eb51dd · outbound

This paper cites Communications of the American Mathematical Society 2(1), 1–21 (2022).

A priori error analysis of consistent PINNs for parabolic PDEs Communications of the American Mathematical Society 2(1), 1–21 (2022)

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-15T19:12:54.290098Z

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This paper cites International Conference on Learning Representations URL https://par.nsf.gov/ biblio/10337713.

A priori error analysis of consistent PINNs for parabolic PDEs International Conference on Learning Representations URL https://par.nsf.gov/ biblio/10337713

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-15T19:12:54.300418Z

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This paper cites In: Conference on learning theory, pp.

A priori error analysis of consistent PINNs for parabolic PDEs In: Conference on learning theory, pp

Reference 23

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Observation 54bc0c4f-b53f-45fc-9674-b3aa9286b1a5 · outbound

This paper cites Modern Birkh¨ auser Classics.

A priori error analysis of consistent PINNs for parabolic PDEs Modern Birkh¨ auser Classics

Reference 24

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Observation 923fab4c-37be-4e14-89a8-2e5be4000a6a · outbound

This paper cites an unresolved cited work.

A priori error analysis of consistent PINNs for parabolic PDEs Unresolved cited work

Reference 25

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This paper cites In: Mathematical and Scientific Machine Learning, pp.

A priori error analysis of consistent PINNs for parabolic PDEs In: Mathematical and Scientific Machine Learning, pp

Reference 26

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A priori error analysis of consistent PINNs for parabolic PDEs Unresolved cited work

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Observation 740d9abd-60fa-4651-b3f2-d575438ae38c · outbound

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A priori error analysis of consistent PINNs for parabolic PDEs Unresolved cited work

Reference 28

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A priori error analysis of consistent PINNs for parabolic PDEs Unresolved cited work

Reference 29

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This paper cites Journal of Machine Learning for Modeling and Computing 4(4) (2023).

A priori error analysis of consistent PINNs for parabolic PDEs Journal of Machine Learning for Modeling and Computing 4(4) (2023)

Reference 30

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A priori error analysis of consistent PINNs for parabolic PDEs Unresolved cited work

Reference 31

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A priori error analysis of consistent PINNs for parabolic PDEs Unresolved cited work

Reference 32

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Observation 27cfbdc3-c1b3-482b-b66f-80882ec42c94 · outbound

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A priori error analysis of consistent PINNs for parabolic PDEs 25, second edn

Reference 33

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Observation 9a17568a-d4b3-4123-adeb-058a0601df8a · outbound

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A priori error analysis of consistent PINNs for parabolic PDEs Unresolved cited work

Reference 34

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Observation 5b487ee2-4f41-4fb3-8b7e-76b1a107f716 · outbound

This paper cites Commu- nications in Mathematics and Statistics 6(1), 1–12 (2018).

A priori error analysis of consistent PINNs for parabolic PDEs Commu- nications in Mathematics and Statistics 6(1), 1–12 (2018)

Reference 35

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A priori error analysis of consistent PINNs for parabolic PDEs IMA Journal of Numerical Analysis p

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-15T19:12:54.374271Z

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Pith citing papers

Observation 8c69a16b-bdab-461c-a24e-de50a0aacbce · inbound

Structure-Preserving and Pressure-Robust PINNs for Incompressible Oseen Problems cites this paper.

Structure-Preserving and Pressure-Robust PINNs for Incompressible Oseen Problems A priori error analysis of consistent PINNs for parabolic PDEs

Reference 23

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Observation 481dfd7d-b30c-432c-8088-0fa82b661d4a · inbound

Inf-Sup Neural Networks for High Dimensional PDEs cites this paper.

Inf-Sup Neural Networks for High Dimensional PDEs A priori error analysis of consistent PINNs for parabolic PDEs

Reference 39

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Source-reported events for the cited work

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