Paper Citation Record · LEDGER

Applications and Manipulations of Physics-Informed Neural Networks in Solving Differential Equations

As of 7 August 2026, this Paper Citation Record lists 13 of 13 outbound references and 0 inbound Pith citation observations for arXiv:2507.19522.

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

pith.paper-citation-record.v1
2507.19522 v1

Coverage vector

measured 13 of 13 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T16:12:21.969370Z

measured 13 of 13 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

13 of 13 outbound references displayed

verified exact1
verified fuzzy8
unresolved3
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 9012a13f-3566-4367-9bb2-4e07587909e0 · outbound

This paper cites Lecture 6: Finite diﬀerence methods.

Applications and Manipulations of Physics-Informed Neural Networks in Solving Differential Equations Lecture 6: Finite diﬀerence methods

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:12:23.629835Z

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.

Observation ebf0427a-40bd-49bd-995e-caded4e6e6ef · outbound

This paper cites Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next.

Applications and Manipulations of Physics-Informed Neural Networks in Solving Differential Equations Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-06T16:12:20.734391Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 213a5422-5bbb-47b8-8712-641ea7e70a5a · outbound

This paper cites url: http:// home.

Applications and Manipulations of Physics-Informed Neural Networks in Solving Differential Equations url: http:// home

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:12:23.488043Z

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.

Observation 7de1af3f-02c1-41b9-8297-272bfabbbd54 · outbound

This paper cites Machine learning and deep learning.

Applications and Manipulations of Physics-Informed Neural Networks in Solving Differential Equations Machine learning and deep learning

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:12:23.331800Z

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.

Observation 15a418fd-7d04-48d2-be51-27856655d8d2 · outbound

This paper cites Adam: A Method for Stochastic Optimization.

Applications and Manipulations of Physics-Informed Neural Networks in Solving Differential Equations Adam: A Method for Stochastic Optimization

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-06T16:12:21.115950Z

Source-reported events for the cited work

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Observation 515a70d6-a19f-425d-a450-052412866fee · outbound

This paper cites url: https://www.youtube.com/watch?v=G_hIppUWcsc.

Applications and Manipulations of Physics-Informed Neural Networks in Solving Differential Equations url: https://www.youtube.com/watch?v=G_hIppUWcsc

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:12:23.214416Z

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.

Observation e416cadc-b7aa-4e73-9dfc-5ba30b534662 · outbound

This paper cites Deep learning in neural networks: An ov erview.

Applications and Manipulations of Physics-Informed Neural Networks in Solving Differential Equations Deep learning in neural networks: An ov erview

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:12:23.025308Z

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.

Observation 1e881ac5-0911-424e-a8ec-9896cac7ecd7 · outbound

This paper cites url: https: //benmoseley.blog/my- research/so- what- is- a- physics- informed- neural-network/ (visited on 06/26/2024).

Applications and Manipulations of Physics-Informed Neural Networks in Solving Differential Equations url: https: //benmoseley.blog/my- research/so- what- is- a- physics- informed- neural-network/ (visited on 06/26/2024)

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:12:22.856552Z

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.

Observation da6919ff-2560-444e-88fc-e96a18a68095 · outbound

This paper cites A comprehensive survey on regular ization strategies in machine learning.

Applications and Manipulations of Physics-Informed Neural Networks in Solving Differential Equations A comprehensive survey on regular ization strategies in machine learning

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-06T16:12:21.636242Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c492822e-5345-4c8e-ab7d-9577cdf76784 · outbound

This paper cites What is Adam Optimizer? en.

Applications and Manipulations of Physics-Informed Neural Networks in Solving Differential Equations What is Adam Optimizer? en

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:12:22.659905Z

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.

Observation 6fc424cd-f349-4829-94b2-3e94feeb637f · outbound

This paper cites Physics-informed Neural Networks: a simple tutorial with P y- Torch.

Applications and Manipulations of Physics-Informed Neural Networks in Solving Differential Equations Physics-informed Neural Networks: a simple tutorial with P y- Torch

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:12:22.451242Z

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.

Observation 819933fa-373e-4c58-b41c-6de4ee43a6d4 · outbound

This paper cites Personalized Predictions of Glioblastoma Infiltration: Mathematical Models, Physics-Informed Neural Networks and Multimodal Scans.

Applications and Manipulations of Physics-Informed Neural Networks in Solving Differential Equations Personalized Predictions of Glioblastoma Infiltration: Mathematical Models, Physics-Informed Neural Networks and Multimodal Scans

Reference 12

Resolution: verified exact; local_arxiv, observed 2026-08-06T16:12:22.222490Z

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.

Observation f7891b73-0d50-4f3a-974c-4fd221dd03dc · outbound

This paper cites doi: 10.1007/s12525- 021- 00475- 2.

Applications and Manipulations of Physics-Informed Neural Networks in Solving Differential Equations doi: 10.1007/s12525- 021- 00475- 2

Reference 695

Resolution: malformed identifier; no resolver link, observed 2026-08-06T16:12:21.001767Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.