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Paper Citation Record · LEDGER

Multi-level datasets training method in Physics-Informed Neural Networks

As of 23 August 2026, this Paper Citation Record lists 61 of 61 outbound references and 0 inbound Pith citation observations for arXiv:2504.21328.

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

pith.paper-citation-record.v1
2504.21328 v1

Coverage vector

measured 61 of 61 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-16T05:13:11.111534Z

measured 61 of 61 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-23T06:30:58.430688+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

61 of 61 outbound references displayed

  • verified exact2
  • verified fuzzy16
  • unresolved42
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch1

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 7610bc05-582f-4b34-9466-538a18acd3fb · outbound

This paper cites Lee \ and\ author I.

Multi-level datasets training method in Physics-Informed Neural Networks Lee \ and\ author I

Reference 1

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Source-reported events for the cited work

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Observation e68643de-6e63-403b-a7bc-9afefb91b48c · outbound

This paper cites Meade \ and\ author A.

Multi-level datasets training method in Physics-Informed Neural Networks Meade \ and\ author A

Reference 2

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Observation a1976555-a5f0-4bf3-9436-8175a1e09967 · outbound

This paper cites Perdikaris P.

Multi-level datasets training method in Physics-Informed Neural Networks Perdikaris P

Reference 3

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

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Observation f4a86d95-a909-435d-aea0-fac763e7362c · outbound

This paper cites Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations.

Multi-level datasets training method in Physics-Informed Neural Networks Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations

Reference 4

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Observation 2e5a3dbb-15b8-4f3f-929c-b58a58e74125 · outbound

This paper cites Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations.

Multi-level datasets training method in Physics-Informed Neural Networks Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations

Reference 5

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Observation 9def4f8c-f817-40c5-8ccd-f82612487919 · outbound

This paper cites an unresolved cited work.

Multi-level datasets training method in Physics-Informed Neural Networks Unresolved cited work

Reference 6

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Observation 865c94b4-2618-4068-ae7b-351465916b53 · outbound

This paper cites an unresolved cited work.

Multi-level datasets training method in Physics-Informed Neural Networks Unresolved cited work

Reference 7

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Observation b625c46d-521b-44df-9f6e-08f629ed8137 · outbound

This paper cites an unresolved cited work.

Multi-level datasets training method in Physics-Informed Neural Networks Unresolved cited work

Reference 8

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No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

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Observation b654f34e-5339-44a3-81c3-6ca6a54c8b0b · outbound

This paper cites Jeong , author J.

Multi-level datasets training method in Physics-Informed Neural Networks Jeong , author J

Reference 9

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Observation 1c808cde-eed9-4e7d-a6c1-df4834c740d8 · outbound

This paper cites Kervadec , author J.

Multi-level datasets training method in Physics-Informed Neural Networks Kervadec , author J

Reference 10

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Observation b75ba7b5-0186-487d-bc81-970fb316be97 · outbound

This paper cites \ Chiu , author J.

Multi-level datasets training method in Physics-Informed Neural Networks \ Chiu , author J

Reference 11

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Observation 5c28cb6d-c9e1-43c5-9439-c8ebb7ddb2ec · outbound

This paper cites Zhang , author Y.

Multi-level datasets training method in Physics-Informed Neural Networks Zhang , author Y

Reference 12

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Observation 1f31c51f-b656-4635-a1b5-f9d67f70b17d · outbound

This paper cites Sharma , author W.

Multi-level datasets training method in Physics-Informed Neural Networks Sharma , author W

Reference 13

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Observation 2617979f-5387-471b-a5d1-fb15abb00e4c · outbound

This paper cites Pang , author L.

Multi-level datasets training method in Physics-Informed Neural Networks Pang , author L

Reference 14

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Observation 84c5e273-547c-4cd4-8939-d74479f19d11 · outbound

This paper cites \ Liao \ and\ author C.-A.

Multi-level datasets training method in Physics-Informed Neural Networks \ Liao \ and\ author C.-A

Reference 15

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Source-reported events for the cited work

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Observation 71538ab0-c25f-47b6-93ef-c595b37ecb08 · outbound

This paper cites an unresolved cited work.

Multi-level datasets training method in Physics-Informed Neural Networks Unresolved cited work

Reference 16

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Observation 8658dc64-e3cf-4d72-9d3d-57c22ce3bfaf · outbound

This paper cites an unresolved cited work.

Multi-level datasets training method in Physics-Informed Neural Networks Unresolved cited work

Reference 17

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Observation 9f63a0d7-f9d5-442c-b90d-aee266fa875a · outbound

This paper cites Sirignano , author J.

Multi-level datasets training method in Physics-Informed Neural Networks Sirignano , author J

Reference 18

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Observation 9561bcd2-1553-4946-8f63-5a9b69f2bbd2 · outbound

This paper cites Kochkov , author J.

Multi-level datasets training method in Physics-Informed Neural Networks Kochkov , author J

Reference 19

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Observation b9567b0a-faac-4660-9255-b183bd5cbdd8 · outbound

This paper cites Maulik , author O.

Multi-level datasets training method in Physics-Informed Neural Networks Maulik , author O

Reference 20

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Observation e1b6bf8d-6a7f-4f20-9fc3-87b9c557dd94 · outbound

This paper cites Finite Difference Neural Networks: Fast Prediction of Partial Differential Equations.

Multi-level datasets training method in Physics-Informed Neural Networks Finite Difference Neural Networks: Fast Prediction of Partial Differential Equations

Reference 21

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Observation 16c7e706-2cc1-43cf-9364-e06a2134e70c · outbound

This paper cites Sukumar \ and\ author A.

Multi-level datasets training method in Physics-Informed Neural Networks Sukumar \ and\ author A

Reference 22

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Observation df5f7504-bb31-47b8-98f6-083de40835d4 · outbound

This paper cites Wang , author Y.

Multi-level datasets training method in Physics-Informed Neural Networks Wang , author Y

Reference 23

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Multi-level datasets training method in Physics-Informed Neural Networks Unresolved cited work

Reference 24

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Observation 84d51b37-e569-4aaf-993a-91e6fee7d7ed · outbound

This paper cites Goswami , author C.

Multi-level datasets training method in Physics-Informed Neural Networks Goswami , author C

Reference 25

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Observation 8e606146-2e2a-45f7-a566-2c87b742526c · outbound

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Multi-level datasets training method in Physics-Informed Neural Networks Unresolved cited work

Reference 26

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Observation 64a73939-b4e8-456d-a1bc-44c4c6b368cb · outbound

This paper cites Penwarden , author S.

Multi-level datasets training method in Physics-Informed Neural Networks Penwarden , author S

Reference 27

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Observation c6f63bf7-8ee8-477c-9318-20954191b1aa · outbound

This paper cites Krishnapriyan , author A.

Multi-level datasets training method in Physics-Informed Neural Networks Krishnapriyan , author A

Reference 28

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Observation 73b2a603-4fe1-45cf-a796-e223e660a562 · outbound

This paper cites An Expert's Guide to Training Physics-informed Neural Networks.

Multi-level datasets training method in Physics-Informed Neural Networks An Expert's Guide to Training Physics-informed Neural Networks

Reference 29

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Observation 0f7b6058-4c15-4182-8e95-a094e2103520 · outbound

This paper cites Wang , author Y.

Multi-level datasets training method in Physics-Informed Neural Networks Wang , author Y

Reference 30

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Observation 548572bd-a608-4306-b9a3-74af2462e275 · outbound

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Multi-level datasets training method in Physics-Informed Neural Networks Rahaman , author A

Reference 31

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Observation d98b9121-c64a-48c2-924f-2ce1d8e93c7a · outbound

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Multi-level datasets training method in Physics-Informed Neural Networks Wang , author X

Reference 32

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Observation 156ae78a-cb1a-4bbe-8e22-d01e84f1c33f · outbound

This paper cites Multi-Task Learning Using Uncertainty to Weigh Losses for Scene Geometry and Semantics.

Multi-level datasets training method in Physics-Informed Neural Networks Multi-Task Learning Using Uncertainty to Weigh Losses for Scene Geometry and Semantics

Reference 33

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Observation 2dc345ee-9145-46e6-b968-2e8b9f1c084d · outbound

This paper cites Xiang , author W.

Multi-level datasets training method in Physics-Informed Neural Networks Xiang , author W

Reference 34

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Observation fb1e0092-b23c-4676-8855-e80dec2a9738 · outbound

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Multi-level datasets training method in Physics-Informed Neural Networks Tancik , author P

Reference 35

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Observation 1361fffb-f825-4ca5-90cd-b55f11867360 · outbound

This paper cites Wang , author H.

Multi-level datasets training method in Physics-Informed Neural Networks Wang , author H

Reference 36

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Observation 43d12340-35c8-4e7b-80ed-177c7e7c658d · outbound

This paper cites Jacot , author F.

Multi-level datasets training method in Physics-Informed Neural Networks Jacot , author F

Reference 37

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Source-reported events for the cited work

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Observation d34a5a84-6f75-4e02-9a77-b14eb3c566e6 · outbound

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Multi-level datasets training method in Physics-Informed Neural Networks Mojgani , author M

Reference 38

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Observation 7038e266-26db-4952-812a-d11ba0913f61 · outbound

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Multi-level datasets training method in Physics-Informed Neural Networks Unresolved cited work

Reference 39

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This paper cites Wienands \ and\ author W.

Multi-level datasets training method in Physics-Informed Neural Networks Wienands \ and\ author W

Reference 40

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T05:13:12.568048Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=arxiv_source observed=2026-08-16T05:13:11.040948Z digest=sha256:f6a50a96ebbcb858926a6f77ca67605e3b353348cd2ac5302dfe1c9796e9725b

Observation 0ea70a9f-a4fc-494d-a200-dfc473f6dc17 · outbound

This paper cites Margenberg , author D.

Multi-level datasets training method in Physics-Informed Neural Networks Margenberg , author D

Reference 41

Resolution
metadata mismatch
raw_fallback, observed 2026-08-16T05:13:11.547473Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=arxiv_source observed=2026-08-16T05:13:11.044274Z digest=sha256:714efea9c4405c0cc134103c71abbe9d72b213857b22d04198a29a9263add6c0

Observation 7bce5bc7-7487-4b75-ac53-2b5c2438ae82 · outbound

This paper cites Margenberg , author R.

Multi-level datasets training method in Physics-Informed Neural Networks Margenberg , author R

Reference 42

Resolution
unresolved
no resolver link, observed 2026-08-16T05:13:11.047547Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-16T05:13:11.047547Z digest=sha256:08cb6cf74dca6c9b5dbf720d2496378039467ab5c04edaeb057af754ef5160f0

Observation a1c8528b-f312-41bc-be5e-972f70497b08 · outbound

This paper cites an unresolved cited work.

Multi-level datasets training method in Physics-Informed Neural Networks Unresolved cited work

Reference 43

Resolution
unresolved
no resolver link, observed 2026-08-16T05:13:11.050954Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-16T05:13:11.050954Z digest=sha256:dd991e30a0f6cfff540cf8adf2d6f901dabe6b111ded7a41b5c34a28d7f05743

Observation 5dcc7e97-c148-4e98-b061-dbaa6fc78cc8 · outbound

This paper cites Wu , author M.

Multi-level datasets training method in Physics-Informed Neural Networks Wu , author M

Reference 44

Resolution
unresolved
no resolver link, observed 2026-08-16T05:13:11.054423Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-16T05:13:11.054423Z digest=sha256:a8e6c33331279112b334e10984a780d60a814d8d3e701413ba3a24d023c2bc56

Observation 13e74ab7-c998-4635-96fa-9850d09e09de · outbound

This paper cites Riccietti , author V.

Multi-level datasets training method in Physics-Informed Neural Networks Riccietti , author V

Reference 45

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T05:13:12.557797Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=arxiv_source observed=2026-08-16T05:13:11.058183Z digest=sha256:b8efe8cf973d18217aca9b6c1b495071db0c06e4c309a5740f9d1f183182bb65

Observation 348e2c84-0b44-4445-9a00-334a9c0e017d · outbound

This paper cites an unresolved cited work.

Multi-level datasets training method in Physics-Informed Neural Networks Unresolved cited work

Reference 46

Resolution
unresolved
no resolver link, observed 2026-08-16T05:13:11.061627Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-16T05:13:11.061627Z digest=sha256:881b159bbf647e07a5b468565e847885b913a11d691fd01aa48625b969f1f4f4

Observation 52bf0b17-89c7-401a-b24e-c850691a0c0b · outbound

This paper cites Torrey \ and\ author J.

Multi-level datasets training method in Physics-Informed Neural Networks Torrey \ and\ author J

Reference 47

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T05:13:12.546772Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=arxiv_source observed=2026-08-16T05:13:11.065061Z digest=sha256:6ae055d6a275b7ab15482dd714fac0a5bd358152d66ec2506ceeca62f0f7616a

Observation eee5e245-fd41-4500-8d9b-4eba6d320986 · outbound

This paper cites Cheng Wong , author C.

Multi-level datasets training method in Physics-Informed Neural Networks Cheng Wong , author C

Reference 48

Resolution
unresolved
no resolver link, observed 2026-08-16T05:13:11.068387Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-16T05:13:11.068387Z digest=sha256:39d5553e1f8af230590ddf1f3139e5575fc852e4206834dc520b0d1e47e9b220

Observation dddfbe30-b721-411b-915f-b9387ae51348 · outbound

This paper cites Searching for Activation Functions.

Multi-level datasets training method in Physics-Informed Neural Networks Searching for Activation Functions

Reference 49

Resolution
unresolved
no resolver link, observed 2026-08-16T05:13:11.071529Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-16T05:13:11.071529Z digest=sha256:a9b53b5442219b2c57e0d6374b34067d2984a2ca17d5147e96f33264fcf246c2

Observation 52f8ffff-ac7a-4912-9548-583701e0464a · outbound

This paper cites He , author X.

Multi-level datasets training method in Physics-Informed Neural Networks He , author X

Reference 50

Resolution
unresolved
no resolver link, observed 2026-08-16T05:13:11.075078Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-16T05:13:11.075078Z digest=sha256:5eb02a64c407a861c1369563f6bb6250caf483c31cc4287adcd5a75cdfd46597

Observation d236b841-027e-430c-847d-f518ab404a21 · outbound

This paper cites Sitzmann , author J.

Multi-level datasets training method in Physics-Informed Neural Networks Sitzmann , author J

Reference 51

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T05:13:12.536478Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=arxiv_source observed=2026-08-16T05:13:11.078793Z digest=sha256:196727e012eddfef1445b019c94834a00d3a234222a3d567c756fd5ee63a7ac1

Observation a8a5823b-3605-48a2-b514-24725f83aca4 · outbound

This paper cites Paszke , author S.

Multi-level datasets training method in Physics-Informed Neural Networks Paszke , author S

Reference 52

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T05:13:12.525722Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=arxiv_source observed=2026-08-16T05:13:11.082004Z digest=sha256:e9e859309727fe7d395eae5cf80c2f3dac7639b84ce32ada8c0ceda01e706527

Observation fdcb64fe-ebb6-4d84-9af8-7023cf14d4c3 · outbound

This paper cites Adam: A Method for Stochastic Optimization.

Multi-level datasets training method in Physics-Informed Neural Networks Adam: A Method for Stochastic Optimization

Reference 53

Resolution
unresolved
no resolver link, observed 2026-08-16T05:13:11.085434Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-16T05:13:11.085434Z digest=sha256:0fca48a4956b8fa2f8a09a69eccdbe26c8c9b944c836a98c0ade49d21059919e

Observation 1afccdc4-7836-40cf-8f3c-55bfff3cbc35 · outbound

This paper cites \ Chou \ and\ author C.-A.

Multi-level datasets training method in Physics-Informed Neural Networks \ Chou \ and\ author C.-A

Reference 54

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T05:13:12.513107Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=arxiv_source observed=2026-08-16T05:13:11.088990Z digest=sha256:7dad0f50c3eb9438af6b6778937372a6c4923e1767eff4b1cdc25bc0a274f984

Observation 574ca6a2-43bd-4f84-8b05-84b5ceeb759c · outbound

This paper cites Smith \ and\ author A.

Multi-level datasets training method in Physics-Informed Neural Networks Smith \ and\ author A

Reference 55

Resolution
verified exact
doi, observed 2026-08-16T05:13:11.151062Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=arxiv_source observed=2026-08-16T05:13:11.092236Z digest=sha256:4599e211eca5fff07134db373b186d90f3af252f38ec0c81ddaaf4b5bf37d6bc

Observation 72852b84-01a0-4a2b-9237-52960ef84efa · outbound

This paper cites Ghia , author K.

Multi-level datasets training method in Physics-Informed Neural Networks Ghia , author K

Reference 56

Resolution
unresolved
no resolver link, observed 2026-08-16T05:13:11.095526Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-16T05:13:11.095526Z digest=sha256:64f79802f5d2345bd06276d8a44dd86637eec45c7348a75dae632564baad30cc

Observation 041916eb-a73b-48b2-b306-8518d6c48bf1 · outbound

This paper cites Li \ and\ author X.

Multi-level datasets training method in Physics-Informed Neural Networks Li \ and\ author X

Reference 57

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T05:13:12.502108Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=arxiv_source observed=2026-08-16T05:13:11.098909Z digest=sha256:7563ea761a273377937395a2333fdebeba1458fcfdb9a46aa138f6e9ccba0ce5

Observation bb67600d-a04f-4124-b5ac-7efd889335ac · outbound

This paper cites Karniadakis , author Z.

Multi-level datasets training method in Physics-Informed Neural Networks Karniadakis , author Z

Reference 58

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T05:13:12.491335Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=arxiv_source observed=2026-08-16T05:13:11.102015Z digest=sha256:22fadaf2e8113d2dd671a1bbc4c30dfc44f4a5535c728301cc908f2041976b68

Observation 43917a75-de4e-4c83-a13e-e16a13f1e33d · outbound

This paper cites Jiang , author C.

Multi-level datasets training method in Physics-Informed Neural Networks Jiang , author C

Reference 59

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T05:13:12.479900Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=arxiv_source observed=2026-08-16T05:13:11.105403Z digest=sha256:8c55405d11a2a8c61e47a8e9a07625b9163f21f55f1fb178330a224899bd42b9

Observation a2f20487-5103-4141-b976-4a6e5c321fc5 · outbound

This paper cites Chen , author R.

Multi-level datasets training method in Physics-Informed Neural Networks Chen , author R

Reference 60

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T05:13:12.469082Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=arxiv_source observed=2026-08-16T05:13:11.108440Z digest=sha256:96fe571ad7ab6734538524f2c09cbc274a2d0324ca5551c4010f10e2f0042012

Observation c24361b0-50cb-4c77-bfe3-e6273c9d4eef · outbound

This paper cites Jin , author S.

Multi-level datasets training method in Physics-Informed Neural Networks Jin , author S

Reference 61

Resolution
unresolved
no resolver link, observed 2026-08-16T05:13:11.111534Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-16T05:13:11.111534Z digest=sha256:36a31daad1120c1987443b1f2c35693a86cfdee43f2fce6fb8b1d710034754c6

Pith citing papers

No inbound Pith citation observations are available.