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Paper Citation Record · LEDGER

PVD-ONet: A Multi-scale Neural Operator Method for Singularly Perturbed Boundary Layer Problems

As of 7 August 2026, this Paper Citation Record lists 56 of 56 outbound references and 0 inbound Pith citation observations for arXiv:2507.21437.

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

pith.paper-citation-record.v1
2507.21437 v2

Coverage vector

measured 56 of 56 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-05-19T03:09:22.055541Z

measured 56 of 56 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-07T06:34:17.273281+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

56 of 56 outbound references displayed

  • verified exact34
  • verified fuzzy6
  • unresolved14
  • parse uncertain0
  • malformed identifier2
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation e6d75b3e-c5ea-4176-a8ff-ce16e0705094 · outbound

This paper cites an unresolved cited work.

PVD-ONet: A Multi-scale Neural Operator Method for Singularly Perturbed Boundary Layer Problems Unresolved cited work

Reference 1

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raw_fallback, observed 2026-05-19T03:12:01.817451Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

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Observation 468a8f1d-eea0-4974-ac77-4f96a2754f49 · outbound

This paper cites an unresolved cited work.

PVD-ONet: A Multi-scale Neural Operator Method for Singularly Perturbed Boundary Layer Problems Unresolved cited work

Reference 2

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raw_fallback, observed 2026-05-19T03:12:01.811483Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

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Observation 2795b8ec-fa1d-4418-8e65-7dca71204dba · outbound

This paper cites Schoppa, F.

PVD-ONet: A Multi-scale Neural Operator Method for Singularly Perturbed Boundary Layer Problems Schoppa, F

Reference 3

Resolution
verified exact
doi, observed 2026-05-19T03:12:00.540364Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

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Observation ee0a59b8-0cf5-48b9-9994-a0226b6d47c1 · outbound

This paper cites an unresolved cited work.

PVD-ONet: A Multi-scale Neural Operator Method for Singularly Perturbed Boundary Layer Problems Unresolved cited work

Reference 4

Resolution
unresolved
raw_fallback, observed 2026-05-19T03:12:01.823187Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-05-19T03:09:22.055541Z digest=sha256:2da495b14ee26321fdd98b262eb70311ea3388ca7ca76d50cc3c985618e23f51

Observation 3af3d753-6ba0-467f-b901-d7e73deb8952 · outbound

This paper cites Anderson, Fundamentals of Aerodynamics, McGraw Hill.

PVD-ONet: A Multi-scale Neural Operator Method for Singularly Perturbed Boundary Layer Problems Anderson, Fundamentals of Aerodynamics, McGraw Hill

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-05-19T03:12:01.820372Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-05-19T03:09:22.055541Z digest=sha256:10eb57255246b3454fd665bb212f256cc59f119382c5bc32400bfdd2a1c8f1d6

Observation 02c47625-9257-45ef-aa61-2dea74345067 · outbound

This paper cites an unresolved cited work.

PVD-ONet: A Multi-scale Neural Operator Method for Singularly Perturbed Boundary Layer Problems Unresolved cited work

Reference 6

Resolution
verified exact
doi, observed 2026-05-19T03:12:00.543466Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-05-19T03:09:22.055541Z digest=sha256:7a3c9cf0c4bc5ba88169b62ffe254820ea9e353d0b2f9e695482dcac38ef5ee5

Observation ea5a5967-ef02-4249-993f-5ea2803e2b08 · outbound

This paper cites Chien, Large deflection of a circular clamped plate under uniform pressure, Chinese Journal of Physics 7 (2) (1947) 102–113.

PVD-ONet: A Multi-scale Neural Operator Method for Singularly Perturbed Boundary Layer Problems Chien, Large deflection of a circular clamped plate under uniform pressure, Chinese Journal of Physics 7 (2) (1947) 102–113

Reference 7

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verified fuzzy
raw_fallback, observed 2026-05-19T03:12:01.802489Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

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Observation b070f260-973e-465e-95a1-a45de9567848 · outbound

This paper cites an unresolved cited work.

PVD-ONet: A Multi-scale Neural Operator Method for Singularly Perturbed Boundary Layer Problems Unresolved cited work

Reference 8

Resolution
verified exact
doi, observed 2026-05-19T03:12:00.534435Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-05-19T03:09:22.055541Z digest=sha256:2598a5cc02f25a51ae741e49010b8a5ef1fc119a98f4bd12e687243ffecaf1f3

Observation b594c52c-0d1e-4f4e-b15e-2300d90455cc · outbound

This paper cites Arzani, A.

PVD-ONet: A Multi-scale Neural Operator Method for Singularly Perturbed Boundary Layer Problems Arzani, A

Reference 9

Resolution
malformed identifier
raw_fallback, observed 2026-05-19T03:12:01.826526Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-05-19T03:09:22.055541Z digest=sha256:8707fb7a8b47963b7240dbf94342649ff928c768ff90dd2927ed5347f7ceb462

Observation 30d91516-61f0-4425-9898-d2876646e5d0 · outbound

This paper cites an unresolved cited work.

PVD-ONet: A Multi-scale Neural Operator Method for Singularly Perturbed Boundary Layer Problems Unresolved cited work

Reference 10

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raw_fallback, observed 2026-05-19T03:12:01.805213Z

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No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

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Observation 16269735-0c25-48ba-83bf-3cc9edf5e3b8 · outbound

This paper cites Prandtl, On fluid motions with very small friction, Verhldg 3 (1904) 484–491.

PVD-ONet: A Multi-scale Neural Operator Method for Singularly Perturbed Boundary Layer Problems Prandtl, On fluid motions with very small friction, Verhldg 3 (1904) 484–491

Reference 11

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raw_fallback, observed 2026-05-19T03:12:01.808511Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

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Observation 9e0e63c4-338f-4128-8466-dd52ad21f4af · outbound

This paper cites Von K´ arm´ an, Uber laminare und turbulente reibung, Z.

PVD-ONet: A Multi-scale Neural Operator Method for Singularly Perturbed Boundary Layer Problems Von K´ arm´ an, Uber laminare und turbulente reibung, Z

Reference 12

Resolution
verified exact
doi, observed 2026-05-19T03:12:00.537795Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-05-19T03:09:22.055541Z digest=sha256:47278f0bab3dab0e5d8244f6936deff92987e6a8a4e08f437b43724b55b7e2cc

Observation c3733f01-5e75-40f8-b152-27fd9d477691 · outbound

This paper cites Van Dyke, Higher approximations in boundary-layer theory part 1.

PVD-ONet: A Multi-scale Neural Operator Method for Singularly Perturbed Boundary Layer Problems Van Dyke, Higher approximations in boundary-layer theory part 1

Reference 13

Resolution
verified exact
doi, observed 2026-05-19T03:12:00.549965Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-05-19T03:09:22.055541Z digest=sha256:e2852ad02fe15485cdb99ee0b6c7dbefcfad49cfb1fe3aa45f3096e483e2aa95

Observation 49227ef0-af7b-47a4-a772-068a12521d0e · outbound

This paper cites Van Dyke, Higher approximations in boundary-layer theory part 2.

PVD-ONet: A Multi-scale Neural Operator Method for Singularly Perturbed Boundary Layer Problems Van Dyke, Higher approximations in boundary-layer theory part 2

Reference 14

Resolution
verified exact
doi, observed 2026-05-19T03:12:00.547182Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-05-19T03:09:22.055541Z digest=sha256:5ba40f7063a6b18c76e85953e17f802db8009b44afff9f20696a41aad92d3b85

Observation 21b73580-c882-481f-9812-9f24f2e57fe1 · outbound

This paper cites Van Dyke, Higher approximations in boundary-layer theory part 3.

PVD-ONet: A Multi-scale Neural Operator Method for Singularly Perturbed Boundary Layer Problems Van Dyke, Higher approximations in boundary-layer theory part 3

Reference 15

Resolution
verified exact
doi, observed 2026-05-19T03:12:00.522714Z

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No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

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Observation 9dfd20b9-446f-4411-b7d0-f59e2e0efa47 · outbound

This paper cites an unresolved cited work.

PVD-ONet: A Multi-scale Neural Operator Method for Singularly Perturbed Boundary Layer Problems Unresolved cited work

Reference 16

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No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

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Observation 2b5b0387-bc47-403d-85d7-b7080127f8ab · outbound

This paper cites an unresolved cited work.

PVD-ONet: A Multi-scale Neural Operator Method for Singularly Perturbed Boundary Layer Problems Unresolved cited work

Reference 17

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doi, observed 2026-05-19T03:12:00.441716Z

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No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

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Observation fa374998-4f10-4d5c-a698-da4fe359f953 · outbound

This paper cites an unresolved cited work.

PVD-ONet: A Multi-scale Neural Operator Method for Singularly Perturbed Boundary Layer Problems Unresolved cited work

Reference 18

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raw_fallback, observed 2026-05-19T03:12:01.860194Z

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No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

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Observation 82df668e-1bbd-442f-8c16-2c309313ceae · outbound

This paper cites an unresolved cited work.

PVD-ONet: A Multi-scale Neural Operator Method for Singularly Perturbed Boundary Layer Problems Unresolved cited work

Reference 19

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verified exact
doi, observed 2026-05-19T03:12:00.449186Z

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No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

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Observation 28896d31-e767-4539-9a17-3a091289bb2e · outbound

This paper cites an unresolved cited work.

PVD-ONet: A Multi-scale Neural Operator Method for Singularly Perturbed Boundary Layer Problems Unresolved cited work

Reference 20

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No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

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Observation c5606871-f95c-47aa-818d-444137a257dc · outbound

This paper cites an unresolved cited work.

PVD-ONet: A Multi-scale Neural Operator Method for Singularly Perturbed Boundary Layer Problems Unresolved cited work

Reference 21

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No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

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Observation afde7214-7eea-495e-b039-c196948f2d18 · outbound

This paper cites an unresolved cited work.

PVD-ONet: A Multi-scale Neural Operator Method for Singularly Perturbed Boundary Layer Problems Unresolved cited work

Reference 22

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doi, observed 2026-05-19T03:12:00.515139Z

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No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

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Observation a8eabe40-ca22-446a-848f-7925f3e9054f · outbound

This paper cites an unresolved cited work.

PVD-ONet: A Multi-scale Neural Operator Method for Singularly Perturbed Boundary Layer Problems Unresolved cited work

Reference 23

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raw_fallback, observed 2026-05-19T03:12:01.846096Z

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No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

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Observation 011d910b-381f-457d-b222-f464382571cd · outbound

This paper cites Eymard, T.

PVD-ONet: A Multi-scale Neural Operator Method for Singularly Perturbed Boundary Layer Problems Eymard, T

Reference 24

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doi, observed 2026-05-19T03:12:00.509349Z

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No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

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Observation f71be010-8976-4a16-ac90-f8b9d33ccd75 · outbound

This paper cites an unresolved cited work.

PVD-ONet: A Multi-scale Neural Operator Method for Singularly Perturbed Boundary Layer Problems Unresolved cited work

Reference 25

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raw_fallback, observed 2026-05-19T03:12:01.829430Z

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No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-05-19T03:09:22.055541Z digest=sha256:f26def08f1abdbb12420c72b51b9f0762d68a30f7c08f9334600ab1b41d664bb

Observation 9ea65b2e-5c78-45da-86ca-92f4fe186d62 · outbound

This paper cites John L Lumley.

PVD-ONet: A Multi-scale Neural Operator Method for Singularly Perturbed Boundary Layer Problems John L Lumley

Reference 26

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doi, observed 2026-05-19T03:12:00.503759Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-05-19T03:09:22.055541Z digest=sha256:041a54d8a223a7537dd17f802b22f71f2b7fba9604e72285ef3833f0e23c70a9

Observation 8cb38453-fb1f-4ca8-a708-9baf07906a77 · outbound

This paper cites Predictions of turbulent shear flows using deep neural networks.

PVD-ONet: A Multi-scale Neural Operator Method for Singularly Perturbed Boundary Layer Problems Predictions of turbulent shear flows using deep neural networks

Reference 27

Resolution
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doi, observed 2026-05-19T03:12:00.475124Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-05-19T03:09:22.055541Z digest=sha256:5dec77e0fb9a5b7249097fbc98c7b644a94dfd102c9373a6d3f5566dd41a5433

Observation 5dbc79b5-5d48-4029-bd83-a036f73a7dd2 · outbound

This paper cites Jiang, R.

PVD-ONet: A Multi-scale Neural Operator Method for Singularly Perturbed Boundary Layer Problems Jiang, R

Reference 28

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doi, observed 2026-05-19T03:12:00.466332Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-05-19T03:09:22.055541Z digest=sha256:c3d3b8fa49e3f18ae43f0b7f99401cd12df8ca83c71839f24a11871761f2ecff

Observation 1996591b-3786-4972-9364-cb2a395951f2 · outbound

This paper cites Machine Learning for Fluid Mechanics.

PVD-ONet: A Multi-scale Neural Operator Method for Singularly Perturbed Boundary Layer Problems Machine Learning for Fluid Mechanics

Reference 29

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doi, observed 2026-05-19T03:12:00.446390Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-05-19T03:09:22.055541Z digest=sha256:f9658658f9d76e68628b1c1f96c432e58d8498fd81c60e0b098047e38e91f791

Observation c1da6222-492e-4ae5-a4d1-b2f02ebd22b2 · outbound

This paper cites Raissi, P.

PVD-ONet: A Multi-scale Neural Operator Method for Singularly Perturbed Boundary Layer Problems Raissi, P

Reference 30

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doi, observed 2026-05-19T03:12:00.531557Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-05-19T03:09:22.055541Z digest=sha256:108fd3db4b4be8cdabe46a4ee41b710d51d546ed6cc34f529f8f6e945580f70b

Observation ca428204-cd3b-45ef-b87b-2661294322db · outbound

This paper cites Lu , author X.

PVD-ONet: A Multi-scale Neural Operator Method for Singularly Perturbed Boundary Layer Problems Lu , author X

Reference 31

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doi, observed 2026-05-19T03:12:00.462575Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-05-19T03:09:22.055541Z digest=sha256:31093fd4d19fa294187857682279df3a5414ce0417ed1251672a5ed7cbbe1fb2

Observation 7053a6c4-c339-48fe-a0ec-43b0eae187a8 · outbound

This paper cites Arzani, J.-X.

PVD-ONet: A Multi-scale Neural Operator Method for Singularly Perturbed Boundary Layer Problems Arzani, J.-X

Reference 32

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doi, observed 2026-05-19T03:12:00.478053Z

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No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-05-19T03:09:22.055541Z digest=sha256:842325d277da0b41a1f3801a5402a9ebded332f67284878e82f9e1a9ac22d901

Observation f5f06d3f-2669-4b0a-a1dc-822a7a56a490 · outbound

This paper cites Stiff-PINN: Physics-Informed Neural Network for Stiff Chemical Kinetics.

PVD-ONet: A Multi-scale Neural Operator Method for Singularly Perturbed Boundary Layer Problems Stiff-PINN: Physics-Informed Neural Network for Stiff Chemical Kinetics

Reference 33

Resolution
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doi, observed 2026-05-19T03:12:00.485270Z

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No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-05-19T03:09:22.055541Z digest=sha256:a9a09f4c2760850e626705259628c418c38cdfff5ddaa5290ee0896c93686b24

Observation 6069aa49-8464-4802-8cd2-7983a49ef7a2 · outbound

This paper cites an unresolved cited work.

PVD-ONet: A Multi-scale Neural Operator Method for Singularly Perturbed Boundary Layer Problems Unresolved cited work

Reference 34

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raw_fallback, observed 2026-05-19T03:12:01.857750Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-05-19T03:09:22.055541Z digest=sha256:2ef1eab61b41d4e06118ce412a221de2d506d1c6545a8e0d923ac038848fab52

Observation 1ab96b93-d2a0-4f15-b3bc-3f44c26155d7 · outbound

This paper cites Computer Methods in Applied Mechanics and Engineering 360, 112789 (2020) https://doi.org/10.1016/j.cma.2019.112789.

PVD-ONet: A Multi-scale Neural Operator Method for Singularly Perturbed Boundary Layer Problems Computer Methods in Applied Mechanics and Engineering 360, 112789 (2020) https://doi.org/10.1016/j.cma.2019.112789

Reference 35

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arxiv_id, observed 2026-05-19T03:12:00.458917Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

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Observation cfbffbaf-f246-4f4d-85e6-cba53b66fb58 · outbound

This paper cites an unresolved cited work.

PVD-ONet: A Multi-scale Neural Operator Method for Singularly Perturbed Boundary Layer Problems Unresolved cited work

Reference 36

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doi, observed 2026-05-19T03:12:00.512011Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

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Observation c20e6b1a-c711-45d9-8de5-32c6e39dd355 · outbound

This paper cites Shukla, A.

PVD-ONet: A Multi-scale Neural Operator Method for Singularly Perturbed Boundary Layer Problems Shukla, A

Reference 37

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arxiv_id, observed 2026-05-19T03:12:00.500965Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

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Observation 4a42ec53-6706-406a-ae0c-4df3b14c0b09 · outbound

This paper cites an unresolved cited work.

PVD-ONet: A Multi-scale Neural Operator Method for Singularly Perturbed Boundary Layer Problems Unresolved cited work

Reference 38

Resolution
unresolved
raw_fallback, observed 2026-05-19T03:12:01.851852Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

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Observation 0fdd69b9-51d6-4a42-9d1e-4b04222c64df · outbound

This paper cites Raissi, P.

PVD-ONet: A Multi-scale Neural Operator Method for Singularly Perturbed Boundary Layer Problems Raissi, P

Reference 39

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doi_truncated, observed 2026-05-19T03:12:00.488590Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

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Observation 6cd4739f-6db8-4f80-928f-ad4ea40a8a2e · outbound

This paper cites Extended Ph ysics-Informed Neural Networks (XPINNs): A Generalized Space-Time Domain Decomposition Based Deep Learning Framework for Nonlinear Partial Differential Equations.

PVD-ONet: A Multi-scale Neural Operator Method for Singularly Perturbed Boundary Layer Problems Extended Ph ysics-Informed Neural Networks (XPINNs): A Generalized Space-Time Domain Decomposition Based Deep Learning Framework for Nonlinear Partial Differential Equations

Reference 40

Resolution
verified exact
doi, observed 2026-05-19T03:12:00.527706Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

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Observation eb1e43b9-04f1-4b31-b87a-b3569a68c404 · outbound

This paper cites Efficienttrainingofphysics-informedneuralnetworksviaimportancesampling.

PVD-ONet: A Multi-scale Neural Operator Method for Singularly Perturbed Boundary Layer Problems Efficienttrainingofphysics-informedneuralnetworksviaimportancesampling

Reference 41

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verified exact
doi, observed 2026-05-19T03:12:00.506360Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

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Observation af0d5f0b-93ef-4664-b67f-a557a28c5398 · outbound

This paper cites On the Eigenvector Bias of Fourier Feature Networks: From Regression to Solving Multi-Scale PDEs with Physics-Informed Neural Networks.

PVD-ONet: A Multi-scale Neural Operator Method for Singularly Perturbed Boundary Layer Problems On the Eigenvector Bias of Fourier Feature Networks: From Regression to Solving Multi-Scale PDEs with Physics-Informed Neural Networks

Reference 42

Resolution
verified exact
arxiv_id, observed 2026-05-19T03:12:00.519453Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-05-19T03:09:22.055541Z digest=sha256:744b01a9569c5169b40088b2d98859c6a899d55d8f00860e6faf175c4361553f

Observation 9fde0362-4982-425d-bfbf-6cca55d921ac · outbound

This paper cites Kaplun, P.

PVD-ONet: A Multi-scale Neural Operator Method for Singularly Perturbed Boundary Layer Problems Kaplun, P

Reference 43

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verified fuzzy
raw_fallback, observed 2026-05-19T03:12:01.849078Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-05-19T03:09:22.055541Z digest=sha256:73ce112985b27efb7393b4df44df99e7c160527e44e8eb35b6f4d554a205cd2d

Observation 9f4b8b08-ab88-438f-b757-66c0cd445426 · outbound

This paper cites Zhang, G.

PVD-ONet: A Multi-scale Neural Operator Method for Singularly Perturbed Boundary Layer Problems Zhang, G

Reference 44

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arxiv_id, observed 2026-05-19T03:12:00.471305Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-05-19T03:09:22.055541Z digest=sha256:85ded273786c6085f598e34c1bafccd19752a7ecf2beb81616a30c8301dc6bae

Observation cdc8d406-6228-47f5-add6-5dc8de60594f · outbound

This paper cites an unresolved cited work.

PVD-ONet: A Multi-scale Neural Operator Method for Singularly Perturbed Boundary Layer Problems Unresolved cited work

Reference 45

Resolution
verified exact
doi, observed 2026-05-19T03:12:00.491828Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-05-19T03:09:22.055541Z digest=sha256:2924a9045f36d17e2df464a828f0dc28a3e415c55b0eda08c21499b52b062654

Observation f8b9589f-8f05-474f-ae92-9ce487f9b514 · outbound

This paper cites Huang, R.

PVD-ONet: A Multi-scale Neural Operator Method for Singularly Perturbed Boundary Layer Problems Huang, R

Reference 46

Resolution
verified exact
arxiv_id, observed 2026-05-19T03:12:00.496440Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-05-19T03:09:22.055541Z digest=sha256:5bedcafa811bcd324efe78fdf96a7972f4ae059fae35bd848553ecbdc382406e

Observation 2ac9c83a-d839-44cc-8815-380b92e8ea0a · outbound

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

PVD-ONet: A Multi-scale Neural Operator Method for Singularly Perturbed Boundary Layer Problems Neural Operator: Graph Kernel Network for Partial Differential Equations

Reference 47

Resolution
verified exact
local_arxiv, observed 2026-05-19T03:12:00.722861Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-05-19T03:09:22.055541Z digest=sha256:7d9e3635af64cb640841b91d892f61133171237edf6b83c2ea2d4c9f5bbb7e72

Observation 43dfa698-12b2-4d20-a7ad-8d3b27042dc9 · outbound

This paper cites an unresolved cited work.

PVD-ONet: A Multi-scale Neural Operator Method for Singularly Perturbed Boundary Layer Problems Unresolved cited work

Reference 48

Resolution
unresolved
raw_fallback, observed 2026-05-19T03:12:01.842863Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-05-19T03:09:22.055541Z digest=sha256:ca5e2bf904ff3c96cc61532fe12c42415998c68ef1b20296bceb48f25005cb87

Observation 22e4b103-4cee-43db-9567-09f7eeef2394 · outbound

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

PVD-ONet: A Multi-scale Neural Operator Method for Singularly Perturbed Boundary Layer Problems Fourier Neural Operator for Parametric Partial Differential Equations

Reference 49

Resolution
verified exact
local_arxiv, observed 2026-05-19T03:12:00.734621Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-05-19T03:09:22.055541Z digest=sha256:ee92e12dfef7599414389c8a2a0b52f28b41f3a24ea7e8d7d09b1ea0dcf83a73

Observation d10ec6d5-5afd-47ce-84d5-3d8aab551066 · outbound

This paper cites Kovachki, Z.

PVD-ONet: A Multi-scale Neural Operator Method for Singularly Perturbed Boundary Layer Problems Kovachki, Z

Reference 50

Resolution
verified fuzzy
raw_fallback, observed 2026-05-19T03:12:01.840184Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-05-19T03:09:22.055541Z digest=sha256:7d44cc94a4b997f9de4d46c8f896e8ea9ae64171f1098292425637fd26e965aa

Observation 211427b4-f269-4926-82eb-b62755b457f7 · outbound

This paper cites Approximation and Generalization of DeepONets for Learning Operators Arising from a Class of Singularly Perturbed Problems.

PVD-ONet: A Multi-scale Neural Operator Method for Singularly Perturbed Boundary Layer Problems Approximation and Generalization of DeepONets for Learning Operators Arising from a Class of Singularly Perturbed Problems

Reference 51

Resolution
verified exact
arxiv_id, observed 2026-05-19T03:12:00.716595Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-05-19T03:09:22.055541Z digest=sha256:daa8d314dcc8a8cde911623677f80dfbf729cbf207813e0a6a38061404151d73

Observation d511a04c-1a50-44f8-80c0-e68e4790c13a · outbound

This paper cites Learning the solution operator of parametric partial differential equations with physics-informed DeepONets.

PVD-ONet: A Multi-scale Neural Operator Method for Singularly Perturbed Boundary Layer Problems Learning the solution operator of parametric partial differential equations with physics-informed DeepONets

Reference 52

Resolution
verified exact
doi, observed 2026-05-19T03:12:00.453781Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-05-19T03:09:22.055541Z digest=sha256:6d94a0eb898f34afb6baa9ad429163bf48d340e7a9071153c216e89557b60756

Observation aaa718b0-8c69-4b00-a390-2cdb05421da1 · outbound

This paper cites Erd´ elyi, An expansion procedure for singular perturbations, Atti Accad.

PVD-ONet: A Multi-scale Neural Operator Method for Singularly Perturbed Boundary Layer Problems Erd´ elyi, An expansion procedure for singular perturbations, Atti Accad

Reference 53

Resolution
verified fuzzy
raw_fallback, observed 2026-05-19T03:12:01.837486Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

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Observation 80cdf19a-e98e-461d-a525-68769d0bf66e · outbound

This paper cites an unresolved cited work.

PVD-ONet: A Multi-scale Neural Operator Method for Singularly Perturbed Boundary Layer Problems Unresolved cited work

Reference 54

Resolution
unresolved
raw_fallback, observed 2026-05-19T03:12:01.834268Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-05-19T03:09:22.055541Z digest=sha256:3e848a688d5bbf8ded0d7b960f2b95295c808ed4e60dc2179151a3eba08d0c36

Observation 1087b967-44d5-4604-9431-f6b6d4527275 · outbound

This paper cites Adam: A Method for Stochastic Optimization.

PVD-ONet: A Multi-scale Neural Operator Method for Singularly Perturbed Boundary Layer Problems Adam: A Method for Stochastic Optimization

Reference 55

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local_arxiv, observed 2026-05-19T03:12:00.728423Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-05-19T03:09:22.055541Z digest=sha256:88ae430cef7c5fa33751d4edf81c16f773e5470a77cab047c1a580e658e0e3cb

Observation c5a422f9-d836-4736-aa6e-38e92386b85d · outbound

This paper cites an unresolved cited work.

PVD-ONet: A Multi-scale Neural Operator Method for Singularly Perturbed Boundary Layer Problems Unresolved cited work

Reference 56

Resolution
unresolved
raw_fallback, observed 2026-05-19T03:12:01.814412Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-05-19T03:09:22.055541Z digest=sha256:7a7393a19cde945327c261c09e65dca9f1c306b8055a849c211a7e050c430356

Pith citing papers

No inbound Pith citation observations are available.