Paper Citation Record · LEDGER

Approximation Theory and Applications of Randomized Neural Networks for Solving High-Dimensional PDEs

As of 15 August 2026, this Paper Citation Record lists 43 of 43 outbound references and 5 inbound Pith citation observations for arXiv:2501.12145.

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

pith.paper-citation-record.v1
2501.12145 v1

Coverage vector

measured 43 of 43 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-10T17:42:25.431806Z

measured 48 of 48 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-15T06:32:42.880941+00:00

measured 5 of 5 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-06-29T23:47:02.293881Z

measured 1 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-08-05T02:28:24.338817Z

Reference resolution

43 of 43 outbound references displayed

verified exact1
verified fuzzy29
unresolved13
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External citation measurements

2
arxiv_reference, observed 2026-08-05T02:28:24.338817Z

Outbound references

Observation a89015d8-16c8-4513-9676-c954f666bfbe · outbound

This paper cites an unresolved cited work.

Approximation Theory and Applications of Randomized Neural Networks for Solving High-Dimensional PDEs Unresolved cited work

Reference 1

Resolution: unresolved; raw_fallback, observed 2026-08-10T17:42:26.155417Z

Source-reported events for the cited work

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Observation dc9808df-02bb-4276-aabd-8329efce18e1 · outbound

This paper cites an unresolved cited work.

Approximation Theory and Applications of Randomized Neural Networks for Solving High-Dimensional PDEs Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-08-10T17:42:26.139735Z

Source-reported events for the cited work

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Observation d9b41403-88f6-40e0-a716-a81eb1a54894 · outbound

This paper cites Dang and F.

Approximation Theory and Applications of Randomized Neural Networks for Solving High-Dimensional PDEs Dang and F

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T17:42:26.124221Z

Source-reported events for the cited work

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Observation 08ef6e0a-1f67-4ee7-8892-6639be2d32b1 · outbound

This paper cites De Ryck, F.

Approximation Theory and Applications of Randomized Neural Networks for Solving High-Dimensional PDEs De Ryck, F

Reference 4

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Observation 47b530e5-4eec-44b8-a382-da8edb91a946 · outbound

This paper cites De Ryck and S.

Approximation Theory and Applications of Randomized Neural Networks for Solving High-Dimensional PDEs De Ryck and S

Reference 5

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Source-reported events for the cited work

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Observation 0f05e10e-7800-4495-9700-88d02bb962eb · outbound

This paper cites De Ryck and S.

Approximation Theory and Applications of Randomized Neural Networks for Solving High-Dimensional PDEs De Ryck and S

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T17:42:26.079117Z

Source-reported events for the cited work

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Observation 95a48a14-fa6d-4667-8658-f063b86a05f8 · outbound

This paper cites Dong and Z.

Approximation Theory and Applications of Randomized Neural Networks for Solving High-Dimensional PDEs Dong and Z

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T17:42:26.064152Z

Source-reported events for the cited work

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Observation 02828d96-8519-4585-bd80-def042aac5dc · outbound

This paper cites Dwivedi and B.

Approximation Theory and Applications of Randomized Neural Networks for Solving High-Dimensional PDEs Dwivedi and B

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T17:42:26.048933Z

Source-reported events for the cited work

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Observation f8e3ff9b-a152-44e8-b574-4a93221c9243 · outbound

This paper cites an unresolved cited work.

Approximation Theory and Applications of Randomized Neural Networks for Solving High-Dimensional PDEs Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-10T17:42:26.032874Z

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Observation ac06b245-f956-4eb7-a4b7-3f2fc1fe7cd9 · outbound

This paper cites Gallicchio and S.

Approximation Theory and Applications of Randomized Neural Networks for Solving High-Dimensional PDEs Gallicchio and S

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T17:42:26.015783Z

Source-reported events for the cited work

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Observation 5d514c12-5c4c-4011-b08f-94ee3c09cdb9 · outbound

This paper cites an unresolved cited work.

Approximation Theory and Applications of Randomized Neural Networks for Solving High-Dimensional PDEs Unresolved cited work

Reference 11

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Source-reported events for the cited work

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Observation 54ab82f9-1cda-4f6c-b0b7-396d4b9a4c8a · outbound

This paper cites Gonon, L.

Approximation Theory and Applications of Randomized Neural Networks for Solving High-Dimensional PDEs Gonon, L

Reference 12

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Source-reported events for the cited work

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Observation c1dfb51e-a409-4ad3-a3e0-dcbcd26e396b · outbound

This paper cites Grohs, F.

Approximation Theory and Applications of Randomized Neural Networks for Solving High-Dimensional PDEs Grohs, F

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T17:42:25.968252Z

Source-reported events for the cited work

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Observation 4515af45-9ee2-47b2-ac80-c17cf9729857 · outbound

This paper cites Huang, Q.-Y.

Approximation Theory and Applications of Randomized Neural Networks for Solving High-Dimensional PDEs Huang, Q.-Y

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T17:42:25.952156Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation f1955c90-fd26-47aa-9fc9-bdd2c457dd75 · outbound

This paper cites Huang, Q.-Y.

Approximation Theory and Applications of Randomized Neural Networks for Solving High-Dimensional PDEs Huang, Q.-Y

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T17:42:25.935361Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 390f0733-183f-4b51-898b-86c2a2c6c22f · outbound

This paper cites Hutzenthaler, A.

Approximation Theory and Applications of Randomized Neural Networks for Solving High-Dimensional PDEs Hutzenthaler, A

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T17:42:25.920177Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation d6741d27-f1bd-4a9a-8634-c63b54788d18 · outbound

This paper cites A proof that deep artificial neural networks overcome the curse of dimensionality in the numerical approximation of Kolmogorov partial differential equations with constant diffusion and nonlinear drift coefficients.

Approximation Theory and Applications of Randomized Neural Networks for Solving High-Dimensional PDEs A proof that deep artificial neural networks overcome the curse of dimensionality in the numerical approximation of Kolmogorov partial differential equations with constant diffusion and nonlinear drift coefficients

Reference 17

Resolution: verified exact; local_arxiv, observed 2026-08-10T17:42:25.496559Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation f5b223c9-85c4-4ecf-a3dd-d65db6382640 · outbound

This paper cites Krishnapriyan, A.

Approximation Theory and Applications of Randomized Neural Networks for Solving High-Dimensional PDEs Krishnapriyan, A

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T17:42:25.905067Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 74a49810-d0e2-4882-8d67-38bc23aa6b66 · outbound

This paper cites Kutyniok, P.

Approximation Theory and Applications of Randomized Neural Networks for Solving High-Dimensional PDEs Kutyniok, P

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T17:42:25.888935Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 89f5dd6b-ac3e-4227-8a9b-cfab7dcbf922 · outbound

This paper cites an unresolved cited work.

Approximation Theory and Applications of Randomized Neural Networks for Solving High-Dimensional PDEs Unresolved cited work

Reference 20

Resolution: unresolved; raw_fallback, observed 2026-08-10T17:42:25.872297Z

Source-reported events for the cited work

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Observation 5bd73a21-0ce1-4ace-a9e3-6caec87be136 · outbound

This paper cites an unresolved cited work.

Approximation Theory and Applications of Randomized Neural Networks for Solving High-Dimensional PDEs Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-08-10T17:42:25.853780Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 35c6a896-9706-4b06-bff9-1fcb52c6dc2c · outbound

This paper cites an unresolved cited work.

Approximation Theory and Applications of Randomized Neural Networks for Solving High-Dimensional PDEs Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-08-10T17:42:25.837535Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation e55d7f65-235d-4c90-8df2-cb890a3c6cb8 · outbound

This paper cites an unresolved cited work.

Approximation Theory and Applications of Randomized Neural Networks for Solving High-Dimensional PDEs Unresolved cited work

Reference 23

Resolution: unresolved; raw_fallback, observed 2026-08-10T17:42:25.821903Z

Source-reported events for the cited work

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Observation 4e0e26eb-37af-449c-93de-992eef5c8591 · outbound

This paper cites Mishra and R.

Approximation Theory and Applications of Randomized Neural Networks for Solving High-Dimensional PDEs Mishra and R

Reference 24

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Observation b6d5ad96-3077-485c-b7c2-ac3773d5ca4f · outbound

This paper cites Mishra and R.

Approximation Theory and Applications of Randomized Neural Networks for Solving High-Dimensional PDEs Mishra and R

Reference 25

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Source-reported events for the cited work

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Observation 9e06eba8-ab99-4d9f-8681-a76d627efd3c · outbound

This paper cites Mishra and R.

Approximation Theory and Applications of Randomized Neural Networks for Solving High-Dimensional PDEs Mishra and R

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T17:42:25.773017Z

Source-reported events for the cited work

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Observation 8ce3787c-dfca-421d-a298-6261d571a8cb · outbound

This paper cites an unresolved cited work.

Approximation Theory and Applications of Randomized Neural Networks for Solving High-Dimensional PDEs Unresolved cited work

Reference 27

Resolution: unresolved; raw_fallback, observed 2026-08-10T17:42:25.756406Z

Source-reported events for the cited work

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Observation 668da11a-730e-44d0-bac7-a00f6b5e375b · outbound

This paper cites Pao and Y.

Approximation Theory and Applications of Randomized Neural Networks for Solving High-Dimensional PDEs Pao and Y

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T17:42:25.740226Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 6fbef876-4157-41ae-9cd2-2b7e1b2cc3ae · outbound

This paper cites Rahimi and B.

Approximation Theory and Applications of Randomized Neural Networks for Solving High-Dimensional PDEs Rahimi and B

Reference 29

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Source-reported events for the cited work

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Observation 7e3387dc-bd4b-402f-bb6a-a3aa715054ba · outbound

This paper cites Rahimi and B.

Approximation Theory and Applications of Randomized Neural Networks for Solving High-Dimensional PDEs Rahimi and B

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T17:42:25.713306Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 8716eab1-181a-4683-86f0-3279b1714eea · outbound

This paper cites Rahimi and B.

Approximation Theory and Applications of Randomized Neural Networks for Solving High-Dimensional PDEs Rahimi and B

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T17:42:25.696865Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 77428e3b-0718-4992-86df-9ea248213814 · outbound

This paper cites Raissi and G.

Approximation Theory and Applications of Randomized Neural Networks for Solving High-Dimensional PDEs Raissi and G

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T17:42:25.680645Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 09d12f5f-064f-48ac-95f1-33f34cd0878d · outbound

This paper cites Raissi, P.

Approximation Theory and Applications of Randomized Neural Networks for Solving High-Dimensional PDEs Raissi, P

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T17:42:25.664819Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation e49a5a70-7c58-4493-b11a-cead07afdb91 · outbound

This paper cites Schiassi, R.

Approximation Theory and Applications of Randomized Neural Networks for Solving High-Dimensional PDEs Schiassi, R

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T17:42:25.648603Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation bf159719-a594-4a71-b1ee-c9acd2459a68 · outbound

This paper cites Schwab and J.

Approximation Theory and Applications of Randomized Neural Networks for Solving High-Dimensional PDEs Schwab and J

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T17:42:25.631287Z

Source-reported events for the cited work

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Observation 62d83ef8-0be5-4539-956d-f39a84ed70c4 · outbound

This paper cites Shang and F.

Approximation Theory and Applications of Randomized Neural Networks for Solving High-Dimensional PDEs Shang and F

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T17:42:25.614503Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 0825db3b-d3b5-4033-bcda-c55050dbacd8 · outbound

This paper cites Shang, F.

Approximation Theory and Applications of Randomized Neural Networks for Solving High-Dimensional PDEs Shang, F

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T17:42:25.597516Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 9f7d010a-db7c-471c-9065-437582248250 · outbound

This paper cites an unresolved cited work.

Approximation Theory and Applications of Randomized Neural Networks for Solving High-Dimensional PDEs Unresolved cited work

Reference 38

Resolution: unresolved; raw_fallback, observed 2026-08-10T17:42:25.580186Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 3f5149e2-e05e-4c55-b35d-da008fe701c3 · outbound

This paper cites Sun and F.

Approximation Theory and Applications of Randomized Neural Networks for Solving High-Dimensional PDEs Sun and F

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T17:42:25.563341Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 1fc8a788-d0fd-4ee6-89c3-175cb6a118b0 · outbound

This paper cites On the Approximation Properties of Random ReLU Features.

Approximation Theory and Applications of Randomized Neural Networks for Solving High-Dimensional PDEs On the Approximation Properties of Random ReLU Features

Reference 40

Resolution: unresolved; no resolver link, observed 2026-08-10T17:42:25.416049Z

Source-reported events for the cited work

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Observation 071e2b2c-7593-40ac-b50b-2d5dc1348116 · outbound

This paper cites an unresolved cited work.

Approximation Theory and Applications of Randomized Neural Networks for Solving High-Dimensional PDEs Unresolved cited work

Reference 41

Resolution: unresolved; raw_fallback, observed 2026-08-10T17:42:25.547055Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 26263524-40c0-4ded-bf78-ef5015d71407 · outbound

This paper cites W ang, Y.

Approximation Theory and Applications of Randomized Neural Networks for Solving High-Dimensional PDEs W ang, Y

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T17:42:25.530232Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 9a460485-1dac-40b0-9fc8-a2f8812ed92b · outbound

This paper cites W ang, X.

Approximation Theory and Applications of Randomized Neural Networks for Solving High-Dimensional PDEs W ang, X

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T17:42:25.513434Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Pith citing papers

Observation 57db4a6d-468c-46d5-a697-9064e8c9d34a · inbound

Solving Inverse Parametrized Problems via Finite Elements and Extreme Learning Networks cites this paper.

Solving Inverse Parametrized Problems via Finite Elements and Extreme Learning Networks Approximation Theory and Applications of Randomized Neural Networks for Solving High-Dimensional PDEs

Reference 46

Resolution: verified exact; arxiv_id, observed 2026-05-15T22:00:20.914236Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 48baf74c-d7d5-49d9-840d-be67d4884a69 · inbound

Adaptive Randomized Neural Networks with Locally Activation Function: Theory and Algorithm for Solving PDEs cites this paper.

Adaptive Randomized Neural Networks with Locally Activation Function: Theory and Algorithm for Solving PDEs Approximation Theory and Applications of Randomized Neural Networks for Solving High-Dimensional PDEs

Reference 8

Resolution: verified exact; arxiv_id, observed 2026-05-11T05:41:00.025731Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 618fdfd8-46d5-4822-84b6-df4047fa5f5a · inbound

Adaptive-Distribution Randomized Neural Networks for PDEs: A Low-Dimensional Distribution-Learning Framework cites this paper.

Adaptive-Distribution Randomized Neural Networks for PDEs: A Low-Dimensional Distribution-Learning Framework Approximation Theory and Applications of Randomized Neural Networks for Solving High-Dimensional PDEs

Reference 6

Resolution: verified exact; arxiv_id, observed 2026-05-11T22:46:12.830381Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation c25b7f7f-5a97-4980-b6c5-817f56b8db33 · inbound

Random Neural Network Expressivity for Non-Linear Partial Differential Equations cites this paper.

Random Neural Network Expressivity for Non-Linear Partial Differential Equations Approximation Theory and Applications of Randomized Neural Networks for Solving High-Dimensional PDEs

Reference 21

Resolution: verified exact; arxiv_id, observed 2026-06-30T00:04:06.958946Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation af4c5f9f-ed55-4b62-b7be-5738facac502 · inbound

Learning universal approximations for partial differential equations with Physics-Informed Broad Learning System cites this paper.

Learning universal approximations for partial differential equations with Physics-Informed Broad Learning System Approximation Theory and Applications of Randomized Neural Networks for Solving High-Dimensional PDEs

Reference 46

Resolution: verified exact; arxiv_id, observed 2026-07-04T03:09:29.312582Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.