Paper Citation Record · LEDGER

A Kolmogorov High Order Deep Neural Network for High Frequency Partial Differential Equations in High Dimensions

As of 13 August 2026, this Paper Citation Record lists 37 of 37 outbound references and 0 inbound Pith citation observations for arXiv:2502.01938.

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

pith.paper-citation-record.v1
2502.01938 v1

Coverage vector

measured 37 of 37 reference resolution

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Source: paper_references, paper_reference_links, observed 2026-08-09T14:04:34.206416Z

measured 37 of 37 standing notices

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Reference resolution

37 of 37 outbound references displayed

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External citation measurements

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Outbound references

Observation 50951952-071f-4fae-89e2-24e96450c1d7 · outbound

This paper cites an unresolved cited work.

A Kolmogorov High Order Deep Neural Network for High Frequency Partial Differential Equations in High Dimensions Unresolved cited work

Reference 1

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Observation 8284950a-808f-4281-a96c-6b0bc54370de · outbound

This paper cites Yu, et al., The deep ritz method: a deep learning-based numerical algorithm for solving variational problems, Communications in Mathematics and Statistics 6 (1) (2018) 1–12.

A Kolmogorov High Order Deep Neural Network for High Frequency Partial Differential Equations in High Dimensions Yu, et al., The deep ritz method: a deep learning-based numerical algorithm for solving variational problems, Communications in Mathematics and Statistics 6 (1) (2018) 1–12

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-09T14:04:34.105832Z

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Observation 88c5a0dc-746b-4853-bca4-e54b436b7290 · outbound

This paper cites Raissi, P.

A Kolmogorov High Order Deep Neural Network for High Frequency Partial Differential Equations in High Dimensions Raissi, P

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T14:04:34.747690Z

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Observation 6bd4dc36-d778-4ee2-ae64-a387efc79e5a · outbound

This paper cites an unresolved cited work.

A Kolmogorov High Order Deep Neural Network for High Frequency Partial Differential Equations in High Dimensions Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-08-09T14:04:34.740141Z

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Observation 654ddc68-7e2b-4463-b0f9-36ec5aae4b12 · outbound

This paper cites Sirignano, K.

A Kolmogorov High Order Deep Neural Network for High Frequency Partial Differential Equations in High Dimensions Sirignano, K

Reference 5

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Observation bcff1afc-542d-4f02-860f-9e4cb67ded5b · outbound

This paper cites an unresolved cited work.

A Kolmogorov High Order Deep Neural Network for High Frequency Partial Differential Equations in High Dimensions Unresolved cited work

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-09T14:04:34.116651Z

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Observation 5dc961af-8681-42cc-874e-18d15f475b26 · outbound

This paper cites Understanding training and generalization in deep learning by Fourier analysis.

A Kolmogorov High Order Deep Neural Network for High Frequency Partial Differential Equations in High Dimensions Understanding training and generalization in deep learning by Fourier analysis

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-09T14:04:34.119460Z

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Observation 64d79519-257b-4eae-acdf-60b7a0d5db1a · outbound

This paper cites an unresolved cited work.

A Kolmogorov High Order Deep Neural Network for High Frequency Partial Differential Equations in High Dimensions Unresolved cited work

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-09T14:04:34.123034Z

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Observation a525ce2c-df3e-47dd-a41c-daf12ccb500a · outbound

This paper cites an unresolved cited work.

A Kolmogorov High Order Deep Neural Network for High Frequency Partial Differential Equations in High Dimensions Unresolved cited work

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-09T14:04:34.126099Z

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Observation d5159da6-f14f-4167-a25a-4ed71e0f1dfd · outbound

This paper cites Multi-scale Deep Neural Networks for Solving High Dimensional PDEs.

A Kolmogorov High Order Deep Neural Network for High Frequency Partial Differential Equations in High Dimensions Multi-scale Deep Neural Networks for Solving High Dimensional PDEs

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-09T14:04:34.129063Z

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Observation 92c8567e-278e-466c-a6a0-b6229397eb9d · outbound

This paper cites Multi-scale Deep Neural Network (MscaleDNN) for Solving Poisson-Boltzmann Equation in Complex Domains.

A Kolmogorov High Order Deep Neural Network for High Frequency Partial Differential Equations in High Dimensions Multi-scale Deep Neural Network (MscaleDNN) for Solving Poisson-Boltzmann Equation in Complex Domains

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-09T14:04:34.132410Z

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Observation 49e960d7-9a74-40a6-8edf-d6fca282d334 · outbound

This paper cites Li, Z.-Q.

A Kolmogorov High Order Deep Neural Network for High Frequency Partial Differential Equations in High Dimensions Li, Z.-Q

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T14:04:34.715293Z

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Observation f0b9e5ed-23ef-436b-b112-36bc902f8db7 · outbound

This paper cites Bai, G.-R.

A Kolmogorov High Order Deep Neural Network for High Frequency Partial Differential Equations in High Dimensions Bai, G.-R

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-09T14:04:34.142204Z

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Observation a0dcfd74-7b89-4758-bc53-7ada3da527ac · outbound

This paper cites Chang, K.

A Kolmogorov High Order Deep Neural Network for High Frequency Partial Differential Equations in High Dimensions Chang, K

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T14:04:34.706028Z

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Observation 46500321-198e-40ff-827e-8fa02c4c6096 · outbound

This paper cites Chang, K.

A Kolmogorov High Order Deep Neural Network for High Frequency Partial Differential Equations in High Dimensions Chang, K

Reference 16

Resolution: verified exact; doi, observed 2026-08-09T14:04:34.282438Z

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Observation 02b055eb-ff06-4219-91a2-e9fd47fa35e5 · outbound

This paper cites an unresolved cited work.

A Kolmogorov High Order Deep Neural Network for High Frequency Partial Differential Equations in High Dimensions Unresolved cited work

Reference 17

Resolution: unresolved; raw_fallback, observed 2026-08-09T14:04:34.696935Z

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Observation 65c50b4f-dd3b-48ec-b416-1a4125e1e7db · outbound

This paper cites Lorentz, Metric entropy, widths, and superpositions of functions, The American Mathe- matical Monthly 69 (6) (1962) 469–485.

A Kolmogorov High Order Deep Neural Network for High Frequency Partial Differential Equations in High Dimensions Lorentz, Metric entropy, widths, and superpositions of functions, The American Mathe- matical Monthly 69 (6) (1962) 469–485

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T14:04:34.687601Z

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Observation 4596f7e5-c5c0-4d7c-9bfb-09e0cb6dd87a · outbound

This paper cites Lorentz, Approximation of functions.-holt, rinehart and wilson, Inc., New York (1966).

A Kolmogorov High Order Deep Neural Network for High Frequency Partial Differential Equations in High Dimensions Lorentz, Approximation of functions.-holt, rinehart and wilson, Inc., New York (1966)

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-09T14:04:34.155663Z

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Observation 7a795a4d-4fde-42b4-a101-0cd209ea4670 · outbound

This paper cites Doss, On the representation of the continuous functions of two variables by mean of addition and continuous functions of one variable, Colloquium Mathematicum 10 (2) (2017) 249–259.

A Kolmogorov High Order Deep Neural Network for High Frequency Partial Differential Equations in High Dimensions Doss, On the representation of the continuous functions of two variables by mean of addition and continuous functions of one variable, Colloquium Mathematicum 10 (2) (2017) 249–259

Reference 20

Resolution: verified exact; doi, observed 2026-08-09T14:04:34.272381Z

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Observation b2ca7700-2c00-489f-ba67-715058ac0d01 · outbound

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A Kolmogorov High Order Deep Neural Network for High Frequency Partial Differential Equations in High Dimensions Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-08-09T14:04:34.673648Z

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Observation 04767792-c13a-43e1-9a05-6a7a32bb1fe1 · outbound

This paper cites an unresolved cited work.

A Kolmogorov High Order Deep Neural Network for High Frequency Partial Differential Equations in High Dimensions Unresolved cited work

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-09T14:04:34.163232Z

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Observation 4085569b-dfc8-454b-bcf1-914cac90d1f4 · outbound

This paper cites Braun, M.

A Kolmogorov High Order Deep Neural Network for High Frequency Partial Differential Equations in High Dimensions Braun, M

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-09T14:04:34.165702Z

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Observation 9b5758bc-1af7-4aac-b7e0-fbed347e76b5 · outbound

This paper cites an unresolved cited work.

A Kolmogorov High Order Deep Neural Network for High Frequency Partial Differential Equations in High Dimensions Unresolved cited work

Reference 24

Resolution: verified exact; doi, observed 2026-08-09T14:04:34.252692Z

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Observation 988dff58-4856-494f-b94b-adce37e48f55 · outbound

This paper cites Igelnik, N.

A Kolmogorov High Order Deep Neural Network for High Frequency Partial Differential Equations in High Dimensions Igelnik, N

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T14:04:34.665462Z

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Observation 251b77ac-7c5b-4aa0-acde-5a853b84284f · outbound

This paper cites an unresolved cited work.

A Kolmogorov High Order Deep Neural Network for High Frequency Partial Differential Equations in High Dimensions Unresolved cited work

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-09T14:04:34.173717Z

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Observation 8cd18c4c-1e21-484d-ac62-4d1dfb1502af · outbound

This paper cites K ˚urkov´a, Kolmogorov’s theorem is relevant, Neural Computation (1991) 617–622 doi: 10.1162/neco.1991.3.4.617.

A Kolmogorov High Order Deep Neural Network for High Frequency Partial Differential Equations in High Dimensions K ˚urkov´a, Kolmogorov’s theorem is relevant, Neural Computation (1991) 617–622 doi: 10.1162/neco.1991.3.4.617

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-09T14:04:34.176349Z

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Observation e372383f-d6a2-45b2-8995-d3f27e6bf91c · outbound

This paper cites K ˚urkov´a, Kolmogorov’s theorem and multilayer neural networks, Neural Networks (1992) 501–506doi:10.1016/0893-6080(92)90012-8.

A Kolmogorov High Order Deep Neural Network for High Frequency Partial Differential Equations in High Dimensions K ˚urkov´a, Kolmogorov’s theorem and multilayer neural networks, Neural Networks (1992) 501–506doi:10.1016/0893-6080(92)90012-8

Reference 28

Resolution: verified exact; doi, observed 2026-08-09T14:04:34.236501Z

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Observation 4a2d324a-8cc4-4be3-96c1-481f152d0837 · outbound

This paper cites Schmidt-Hieber, The kolmogorov-arnold representation theorem revisited, Neural net- works 137 (2021) 119–126.

A Kolmogorov High Order Deep Neural Network for High Frequency Partial Differential Equations in High Dimensions Schmidt-Hieber, The kolmogorov-arnold representation theorem revisited, Neural net- works 137 (2021) 119–126

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T14:04:34.656441Z

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Observation 9c2ddc31-8792-4496-aa96-d98ad2f85486 · outbound

This paper cites Montanelli, H.

A Kolmogorov High Order Deep Neural Network for High Frequency Partial Differential Equations in High Dimensions Montanelli, H

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T14:04:34.538803Z

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Observation deaee495-05cf-4907-8117-9609d27a84b2 · outbound

This paper cites Wang, Numerical Approximation, 2nd Edition, Beijing Higher Education Press, Beijing, 2012.

A Kolmogorov High Order Deep Neural Network for High Frequency Partial Differential Equations in High Dimensions Wang, Numerical Approximation, 2nd Edition, Beijing Higher Education Press, Beijing, 2012

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T14:04:34.529903Z

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Observation 590fd191-0d1f-4594-a7d2-3e6a19f08e13 · outbound

This paper cites Maczuga, M.

A Kolmogorov High Order Deep Neural Network for High Frequency Partial Differential Equations in High Dimensions Maczuga, M

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T14:04:34.520416Z

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Observation 939a3d70-4e6f-4351-b894-13df2337a0fa · outbound

This paper cites an unresolved cited work.

A Kolmogorov High Order Deep Neural Network for High Frequency Partial Differential Equations in High Dimensions Unresolved cited work

Reference 33

Resolution: unresolved; raw_fallback, observed 2026-08-09T14:04:34.511732Z

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Observation 395a3f81-458c-4b98-9b99-301ed4e28e2d · outbound

This paper cites an unresolved cited work.

A Kolmogorov High Order Deep Neural Network for High Frequency Partial Differential Equations in High Dimensions Unresolved cited work

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-09T14:04:34.195858Z

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Observation 60f99e41-31bc-4a18-bcf1-05e7489c7c6a · outbound

This paper cites an unresolved cited work.

A Kolmogorov High Order Deep Neural Network for High Frequency Partial Differential Equations in High Dimensions Unresolved cited work

Reference 35

Resolution: unresolved; raw_fallback, observed 2026-08-09T14:04:34.497651Z

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Observation 7db97cdb-dd5e-40be-894e-9c9d5d10fe3f · outbound

This paper cites KAN: Kolmogorov-Arnold Networks.

A Kolmogorov High Order Deep Neural Network for High Frequency Partial Differential Equations in High Dimensions KAN: Kolmogorov-Arnold Networks

Reference 36

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Observation 2402d3d1-4772-4cf7-a940-5f2c0705cef3 · outbound

This paper cites Tensor Neural Network Interpolation and Its Applications.

A Kolmogorov High Order Deep Neural Network for High Frequency Partial Differential Equations in High Dimensions Tensor Neural Network Interpolation and Its Applications

Reference 37

Resolution: unresolved; no resolver link, observed 2026-08-09T14:04:34.203668Z

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Observation 12a44fcf-14b0-4243-9059-6bc995686dfc · outbound

This paper cites De Ryck, S.

A Kolmogorov High Order Deep Neural Network for High Frequency Partial Differential Equations in High Dimensions De Ryck, S

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T14:04:34.489357Z

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