Paper Citation Record · LEDGER

Hybrid Least Squares/Gradient Descent Methods for DeepONets

As of 8 August 2026, this Paper Citation Record lists 37 of 37 outbound references and 1 inbound Pith citation observation for arXiv:2508.15394.

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

pith.paper-citation-record.v1
2508.15394 v1

Coverage vector

measured 37 of 37 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-05T18:02:33.460580Z

measured 38 of 38 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-05T17:58:14.919609Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-05T17:58:15.059011Z

Reference resolution

37 of 37 outbound references displayed

verified exact0
verified fuzzy14
unresolved23
parse uncertain0
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 3323c1b9-c3d9-4c21-9252-b89c3f1bdd76 · outbound

This paper cites A Survey on Universal Approximation Theorems.

Hybrid Least Squares/Gradient Descent Methods for DeepONets A Survey on Universal Approximation Theorems

Reference 1

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Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 98a28db1-bbd0-4a64-a545-92d327ac6780 · outbound

This paper cites an unresolved cited work.

Hybrid Least Squares/Gradient Descent Methods for DeepONets Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-08-05T18:02:40.276712Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 0ef7d4b8-3ed0-4cde-b37f-f74a783b9585 · outbound

This paper cites an unresolved cited work.

Hybrid Least Squares/Gradient Descent Methods for DeepONets Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-08-05T18:02:40.030536Z

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Observation be1a4661-1110-40cd-be66-c3345049e8f4 · outbound

This paper cites an unresolved cited work.

Hybrid Least Squares/Gradient Descent Methods for DeepONets Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-08-05T18:02:39.817529Z

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Observation 3652e21a-9106-416e-94ae-8b0d627baabd · outbound

This paper cites Bradbury, R.

Hybrid Least Squares/Gradient Descent Methods for DeepONets Bradbury, R

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:02:39.615844Z

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Observation b26e3a93-1e98-4d5f-b92d-56845530b973 · outbound

This paper cites Chen and H.

Hybrid Least Squares/Gradient Descent Methods for DeepONets Chen and H

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:02:39.373397Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation c7a6d66c-b8de-4e9e-9f62-9b0d31f01e64 · outbound

This paper cites an unresolved cited work.

Hybrid Least Squares/Gradient Descent Methods for DeepONets Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-05T18:02:39.163576Z

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Observation 6a724d75-2077-4ab9-82e6-11ba368c5159 · outbound

This paper cites Cybenko, Approximation by superpositions of a sigmoidal function , Mathematics of Control, Signals and Systems, 2 (1989), pp.

Hybrid Least Squares/Gradient Descent Methods for DeepONets Cybenko, Approximation by superpositions of a sigmoidal function , Mathematics of Control, Signals and Systems, 2 (1989), pp

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:02:38.989731Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation c54dccf8-fc47-4f4c-939d-9f9b8337014b · outbound

This paper cites an unresolved cited work.

Hybrid Least Squares/Gradient Descent Methods for DeepONets Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-05T18:02:38.790537Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 4d0450fb-c953-4cc6-b83f-f79876816ae7 · outbound

This paper cites Sparse Networks from Scratch: Faster Training without Losing Performance.

Hybrid Least Squares/Gradient Descent Methods for DeepONets Sparse Networks from Scratch: Faster Training without Losing Performance

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-05T18:02:29.743385Z

Source-reported events for the cited work

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Observation a5d548d6-31cb-46f0-b259-23f8805133f6 · outbound

This paper cites an unresolved cited work.

Hybrid Least Squares/Gradient Descent Methods for DeepONets Unresolved cited work

Reference 11

Resolution: unresolved; raw_fallback, observed 2026-08-05T18:02:38.594014Z

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No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation b6688705-1086-4b59-b1b6-056bb6ea0ca8 · outbound

This paper cites an unresolved cited work.

Hybrid Least Squares/Gradient Descent Methods for DeepONets Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-08-05T18:02:38.401633Z

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Observation 5a4603fa-4e39-4c42-b049-7d6eebf4b32a · outbound

This paper cites Heinecke, J.

Hybrid Least Squares/Gradient Descent Methods for DeepONets Heinecke, J

Reference 13

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Source-reported events for the cited work

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Observation c9757214-4109-42fa-8bef-7898f8aeafa3 · outbound

This paper cites Hornik, M.

Hybrid Least Squares/Gradient Descent Methods for DeepONets Hornik, M

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:02:37.838413Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 0733edb8-7356-4154-b3aa-383d165349b3 · outbound

This paper cites an unresolved cited work.

Hybrid Least Squares/Gradient Descent Methods for DeepONets Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-08-05T18:02:37.576140Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 5a779b5f-22a7-40f4-80e6-96e734787b15 · outbound

This paper cites an unresolved cited work.

Hybrid Least Squares/Gradient Descent Methods for DeepONets Unresolved cited work

Reference 16

Resolution: unresolved; raw_fallback, observed 2026-08-05T18:02:37.268660Z

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Observation 62802a80-e848-4efc-accf-2e36c13b5c5e · outbound

This paper cites Adam: A Method for Stochastic Optimization.

Hybrid Least Squares/Gradient Descent Methods for DeepONets Adam: A Method for Stochastic Optimization

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-05T18:02:30.844837Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 231ac2a1-ff27-4fa7-bcd2-08dc53c182b2 · outbound

This paper cites an unresolved cited work.

Hybrid Least Squares/Gradient Descent Methods for DeepONets Unresolved cited work

Reference 18

Resolution: unresolved; raw_fallback, observed 2026-08-05T18:02:37.057143Z

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No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation b6a31c7e-9ef7-4909-95bb-e8a1327dc3d0 · outbound

This paper cites , IEEE Transactions on Neural Networks and Learning Systems, 35 (2024), pp.

Hybrid Least Squares/Gradient Descent Methods for DeepONets , IEEE Transactions on Neural Networks and Learning Systems, 35 (2024), pp

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:02:36.752962Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation dc6227fc-5def-41cd-ae30-0acded8f62a2 · outbound

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

Hybrid Least Squares/Gradient Descent Methods for DeepONets Fourier Neural Operator for Parametric Partial Differential Equations

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-05T18:02:31.251203Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4c17eab3-7acd-47bc-b704-65ca0705b37d · outbound

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

Hybrid Least Squares/Gradient Descent Methods for DeepONets Neural Operator: Graph Kernel Network for Partial Differential Equations

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-05T18:02:31.386164Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8eae6930-8fd8-4e77-9dc9-3b0da358998f · outbound

This paper cites Lin and S.

Hybrid Least Squares/Gradient Descent Methods for DeepONets Lin and S

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:02:36.489037Z

Source-reported events for the cited work

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Observation 9753d140-a2ff-4422-9c24-3d89ed957632 · outbound

This paper cites an unresolved cited work.

Hybrid Least Squares/Gradient Descent Methods for DeepONets Unresolved cited work

Reference 23

Resolution: unresolved; raw_fallback, observed 2026-08-05T18:02:36.293789Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 80062ec6-1915-4deb-8445-6396c7881c8c · outbound

This paper cites an unresolved cited work.

Hybrid Least Squares/Gradient Descent Methods for DeepONets Unresolved cited work

Reference 24

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No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 61402daf-cb04-46e2-bf65-f49ba89720f6 · outbound

This paper cites an unresolved cited work.

Hybrid Least Squares/Gradient Descent Methods for DeepONets Unresolved cited work

Reference 25

Resolution: unresolved; raw_fallback, observed 2026-08-05T18:02:35.913787Z

Source-reported events for the cited work

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Observation 8d7f5aef-6633-49ca-ac35-b8ee74fead96 · outbound

This paper cites an unresolved cited work.

Hybrid Least Squares/Gradient Descent Methods for DeepONets Unresolved cited work

Reference 26

Resolution: unresolved; raw_fallback, observed 2026-08-05T18:02:35.694913Z

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Observation 2e60fc6a-dd0e-4209-85ae-cece122595c0 · outbound

This paper cites an unresolved cited work.

Hybrid Least Squares/Gradient Descent Methods for DeepONets Unresolved cited work

Reference 27

Resolution: unresolved; raw_fallback, observed 2026-08-05T18:02:35.439229Z

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No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 14c9f3a4-bc96-44c8-94ab-c960408a1e94 · outbound

This paper cites an unresolved cited work.

Hybrid Least Squares/Gradient Descent Methods for DeepONets Unresolved cited work

Reference 28

Resolution: unresolved; raw_fallback, observed 2026-08-05T18:02:35.221694Z

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Observation 951c9afb-9040-4afd-a334-aaa3f7aa02fe · outbound

This paper cites Neudecker, The Kronecker matrix product and some of its applications in econometrics, Statistica Neerlandica, 22 (1968), pp.

Hybrid Least Squares/Gradient Descent Methods for DeepONets Neudecker, The Kronecker matrix product and some of its applications in econometrics, Statistica Neerlandica, 22 (1968), pp

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:02:35.069783Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 1cc160fe-dff4-4505-b567-aa7683344404 · outbound

This paper cites Raissi, P.

Hybrid Least Squares/Gradient Descent Methods for DeepONets Raissi, P

Reference 30

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 322afa86-88f1-4f94-a253-e813c29ee3a9 · outbound

This paper cites Searching for Activation Functions.

Hybrid Least Squares/Gradient Descent Methods for DeepONets Searching for Activation Functions

Reference 31

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Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 69bfef52-ca6c-4ecd-909a-a5ef520b9996 · outbound

This paper cites Salimans and D.

Hybrid Least Squares/Gradient Descent Methods for DeepONets Salimans and D

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:02:34.664923Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation a6e241bb-a64e-4b09-b570-6a756002cdf9 · outbound

This paper cites Son, ELM-DeepONets: Backpropagation-free training of deep operator networks via extreme learning machines , IEEE Access, 13 (2025), pp.

Hybrid Least Squares/Gradient Descent Methods for DeepONets Son, ELM-DeepONets: Backpropagation-free training of deep operator networks via extreme learning machines , IEEE Access, 13 (2025), pp

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:02:34.497011Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation b17ba2f2-d730-406d-966e-edd9ce4c8238 · outbound

This paper cites an unresolved cited work.

Hybrid Least Squares/Gradient Descent Methods for DeepONets Unresolved cited work

Reference 34

Resolution: unresolved; raw_fallback, observed 2026-08-05T18:02:34.341851Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 0245c864-afc5-4577-8ede-66ea653c02f3 · outbound

This paper cites W ang, H.

Hybrid Least Squares/Gradient Descent Methods for DeepONets W ang, H

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:02:34.116649Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 2d986370-e50e-4bc0-9dd5-f0566db6d15d · outbound

This paper cites Zheng, A.

Hybrid Least Squares/Gradient Descent Methods for DeepONets Zheng, A

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:02:33.911227Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 532e2dc3-d1e3-450b-bfdb-c5b5cbd13c88 · outbound

This paper cites Zhou, Universality of deep convolutional neural networks , Applied and Computa- tional Harmonic Analysis, 48 (2020), pp.

Hybrid Least Squares/Gradient Descent Methods for DeepONets Zhou, Universality of deep convolutional neural networks , Applied and Computa- tional Harmonic Analysis, 48 (2020), pp

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:02:33.725671Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Pith citing papers

Observation 5a2ae720-4a7f-4dc7-8517-d4f769393522 · inbound

Multilateralism in the Global Governance of Artificial Intelligence cites this paper.

Multilateralism in the Global Governance of Artificial Intelligence Hybrid Least Squares/Gradient Descent Methods for DeepONets

Reference 1

Resolution: verified exact; local_arxiv, observed 2026-08-05T17:58:15.140532Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.