Paper Citation Record · LEDGER

PG-KINN: A Physics-Informed Petrov-Galerkin Kolmogorov-Arnold Network for Solving Forward and Inverse PDEs

As of 3 August 2026, this Paper Citation Record lists 48 of 48 outbound references and 0 inbound Pith citation observations for arXiv:2607.20378.

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

pith.paper-citation-record.v1
2607.20378 v1

Coverage vector

measured 48 of 48 reference resolution

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Source: paper_references, paper_reference_links, observed 2026-08-01T10:04:24.105307Z

measured 48 of 48 standing notices

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Source: scholarly_work_events, retraction_status_cache, observed 2026-08-03T06:30:56.289259+00:00

measured 0 of 0 inbound itemization

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measured 0 of 1 external citation measurements

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Reference resolution

48 of 48 outbound references displayed

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Outbound references

Observation a553190e-b1a2-4113-86b9-b5085f270d0a · outbound

This paper cites an unresolved cited work.

PG-KINN: A Physics-Informed Petrov-Galerkin Kolmogorov-Arnold Network for Solving Forward and Inverse PDEs Unresolved cited work

Reference 1

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Observation 29045a46-6f0a-47c1-a1e7-95483b99ba3a · outbound

This paper cites an unresolved cited work.

PG-KINN: A Physics-Informed Petrov-Galerkin Kolmogorov-Arnold Network for Solving Forward and Inverse PDEs Unresolved cited work

Reference 2

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Observation aff9faec-f165-40f5-bca4-82e0ec498f44 · outbound

This paper cites Bathe, Finite element procedures, Klaus-Jurgen Bathe, 2006.

PG-KINN: A Physics-Informed Petrov-Galerkin Kolmogorov-Arnold Network for Solving Forward and Inverse PDEs Bathe, Finite element procedures, Klaus-Jurgen Bathe, 2006

Reference 3

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Observation fb2b3acb-4172-427e-9762-bddd504d4357 · outbound

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PG-KINN: A Physics-Informed Petrov-Galerkin Kolmogorov-Arnold Network for Solving Forward and Inverse PDEs Unresolved cited work

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-01T10:04:18.297126Z

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PG-KINN: A Physics-Informed Petrov-Galerkin Kolmogorov-Arnold Network for Solving Forward and Inverse PDEs Unresolved cited work

Reference 5

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Observation 4c7bd0f3-410d-4ede-b782-eb1ff312d105 · outbound

This paper cites Rabczuk, T.

PG-KINN: A Physics-Informed Petrov-Galerkin Kolmogorov-Arnold Network for Solving Forward and Inverse PDEs Rabczuk, T

Reference 6

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Observation d4c6957b-c42d-4ca6-a250-dbe5d9537502 · outbound

This paper cites an unresolved cited work.

PG-KINN: A Physics-Informed Petrov-Galerkin Kolmogorov-Arnold Network for Solving Forward and Inverse PDEs Unresolved cited work

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-01T10:04:18.807308Z

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Observation b5ebebf3-7033-4195-8bf1-8d060c7584d7 · outbound

This paper cites an unresolved cited work.

PG-KINN: A Physics-Informed Petrov-Galerkin Kolmogorov-Arnold Network for Solving Forward and Inverse PDEs Unresolved cited work

Reference 8

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Observation f04792ab-4431-4824-8476-a4b9dd550f74 · outbound

This paper cites Darwish, F.

PG-KINN: A Physics-Informed Petrov-Galerkin Kolmogorov-Arnold Network for Solving Forward and Inverse PDEs Darwish, F

Reference 9

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Observation 3eb62c7c-3480-4559-9c1b-22296cbfba78 · outbound

This paper cites an unresolved cited work.

PG-KINN: A Physics-Informed Petrov-Galerkin Kolmogorov-Arnold Network for Solving Forward and Inverse PDEs Unresolved cited work

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-01T10:04:19.365764Z

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Observation 467dfc78-57d6-43c7-af45-b51776a69a99 · outbound

This paper cites Raissi, P.

PG-KINN: A Physics-Informed Petrov-Galerkin Kolmogorov-Arnold Network for Solving Forward and Inverse PDEs Raissi, P

Reference 11

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Observation 8dd7cd22-200f-42d8-b50d-3d48c57889d0 · outbound

This paper cites an unresolved cited work.

PG-KINN: A Physics-Informed Petrov-Galerkin Kolmogorov-Arnold Network for Solving Forward and Inverse PDEs Unresolved cited work

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-01T10:04:19.597749Z

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Observation 5fd71461-fc67-4511-8cdb-dde4dfd47fe4 · outbound

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

PG-KINN: A Physics-Informed Petrov-Galerkin Kolmogorov-Arnold Network for Solving Forward and Inverse PDEs Fourier Neural Operator for Parametric Partial Differential Equations

Reference 13

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Observation 51f8dbdf-8c10-4502-8309-0550d16eccc0 · outbound

This paper cites an unresolved cited work.

PG-KINN: A Physics-Informed Petrov-Galerkin Kolmogorov-Arnold Network for Solving Forward and Inverse PDEs Unresolved cited work

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-01T10:04:19.900611Z

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Observation 25410513-9760-41e5-98c7-5fa645c97256 · outbound

This paper cites Kharazmi, Z.

PG-KINN: A Physics-Informed Petrov-Galerkin Kolmogorov-Arnold Network for Solving Forward and Inverse PDEs Kharazmi, Z

Reference 15

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Observation c2858bbf-c8a9-46b0-b44c-4ec387935ca1 · outbound

This paper cites Variational Physics-Informed Neural Networks For Solving Partial Differential Equations.

PG-KINN: A Physics-Informed Petrov-Galerkin Kolmogorov-Arnold Network for Solving Forward and Inverse PDEs Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

Reference 16

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Observation f20ffd96-096b-4c79-a61c-40a4c82ebdc8 · outbound

This paper cites Khodayi-Mehr, M.

PG-KINN: A Physics-Informed Petrov-Galerkin Kolmogorov-Arnold Network for Solving Forward and Inverse PDEs Khodayi-Mehr, M

Reference 17

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Observation abf7cab1-35a6-4614-988e-97a321f3a1e9 · outbound

This paper cites Berrone, C.

PG-KINN: A Physics-Informed Petrov-Galerkin Kolmogorov-Arnold Network for Solving Forward and Inverse PDEs Berrone, C

Reference 18

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Observation a7b09562-9951-4e37-9a6d-1f5c976127b6 · outbound

This paper cites Samaniego, C.

PG-KINN: A Physics-Informed Petrov-Galerkin Kolmogorov-Arnold Network for Solving Forward and Inverse PDEs Samaniego, C

Reference 19

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Observation 94cc8ede-bd0d-4fe5-9450-b8e05123dc59 · 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.

PG-KINN: A Physics-Informed Petrov-Galerkin Kolmogorov-Arnold Network for Solving Forward and Inverse PDEs 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 20

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PG-KINN: A Physics-Informed Petrov-Galerkin Kolmogorov-Arnold Network for Solving Forward and Inverse PDEs Unresolved cited work

Reference 21

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Observation 551c995f-56cd-4ea3-b158-7d215e519d64 · outbound

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PG-KINN: A Physics-Informed Petrov-Galerkin Kolmogorov-Arnold Network for Solving Forward and Inverse PDEs Unresolved cited work

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-01T10:04:20.928129Z

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Observation c021c114-564c-4e9e-a229-7e4de18f06fc · outbound

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PG-KINN: A Physics-Informed Petrov-Galerkin Kolmogorov-Arnold Network for Solving Forward and Inverse PDEs Unresolved cited work

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-01T10:04:21.103486Z

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Observation 1e1312d7-a772-41ca-a3f5-ee1546c1a5ad · outbound

This paper cites Cybenko, Approximation by superpositions of a sigmoidal function, Mathematics of control, signals and systems 2 (4) (1989) 303–314.

PG-KINN: A Physics-Informed Petrov-Galerkin Kolmogorov-Arnold Network for Solving Forward and Inverse PDEs Cybenko, Approximation by superpositions of a sigmoidal function, Mathematics of control, signals and systems 2 (4) (1989) 303–314

Reference 25

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Observation 88fe9932-51e3-4e7f-907b-5b7d14d213bf · outbound

This paper cites Jacot, F.

PG-KINN: A Physics-Informed Petrov-Galerkin Kolmogorov-Arnold Network for Solving Forward and Inverse PDEs Jacot, F

Reference 26

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PG-KINN: A Physics-Informed Petrov-Galerkin Kolmogorov-Arnold Network for Solving Forward and Inverse PDEs Unresolved cited work

Reference 27

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Observation 13f8bbc4-2843-46cc-b32a-3a1918f62fa8 · outbound

This paper cites Rahaman, A.

PG-KINN: A Physics-Informed Petrov-Galerkin Kolmogorov-Arnold Network for Solving Forward and Inverse PDEs Rahaman, A

Reference 28

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This paper cites KAN: Kolmogorov-Arnold Networks.

PG-KINN: A Physics-Informed Petrov-Galerkin Kolmogorov-Arnold Network for Solving Forward and Inverse PDEs KAN: Kolmogorov-Arnold Networks

Reference 29

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PG-KINN: A Physics-Informed Petrov-Galerkin Kolmogorov-Arnold Network for Solving Forward and Inverse PDEs Unresolved cited work

Reference 30

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Observation e58cb73c-ed87-47f2-b10b-a03e4aa5d771 · outbound

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PG-KINN: A Physics-Informed Petrov-Galerkin Kolmogorov-Arnold Network for Solving Forward and Inverse PDEs Braun, M

Reference 31

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PG-KINN: A Physics-Informed Petrov-Galerkin Kolmogorov-Arnold Network for Solving Forward and Inverse PDEs Unresolved cited work

Reference 32

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Observation 464f531c-6fb6-48f1-89dc-882b9679e5f4 · outbound

This paper cites Chebyshev Polynomial-Based Kolmogorov-Arnold Networks: An Efficient Architecture for Nonlinear Function Approximation.

PG-KINN: A Physics-Informed Petrov-Galerkin Kolmogorov-Arnold Network for Solving Forward and Inverse PDEs Chebyshev Polynomial-Based Kolmogorov-Arnold Networks: An Efficient Architecture for Nonlinear Function Approximation

Reference 33

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This paper cites A comprehensive and FAIR comparison between MLP and KAN representations for differential equations and operator networks.

PG-KINN: A Physics-Informed Petrov-Galerkin Kolmogorov-Arnold Network for Solving Forward and Inverse PDEs A comprehensive and FAIR comparison between MLP and KAN representations for differential equations and operator networks

Reference 34

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Observation b8b1edd3-ab08-495b-932a-a7582dd874b4 · outbound

This paper cites Kolmogorov-Arnold Networks are Radial Basis Function Networks.

PG-KINN: A Physics-Informed Petrov-Galerkin Kolmogorov-Arnold Network for Solving Forward and Inverse PDEs Kolmogorov-Arnold Networks are Radial Basis Function Networks

Reference 35

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PG-KINN: A Physics-Informed Petrov-Galerkin Kolmogorov-Arnold Network for Solving Forward and Inverse PDEs Wav-KAN: Wavelet Kolmogorov-Arnold Networks

Reference 36

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PG-KINN: A Physics-Informed Petrov-Galerkin Kolmogorov-Arnold Network for Solving Forward and Inverse PDEs Rigas, M

Reference 37

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PG-KINN: A Physics-Informed Petrov-Galerkin Kolmogorov-Arnold Network for Solving Forward and Inverse PDEs On the expressiveness and spectral bias of KANs

Reference 38

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PG-KINN: A Physics-Informed Petrov-Galerkin Kolmogorov-Arnold Network for Solving Forward and Inverse PDEs Unresolved cited work

Reference 39

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PG-KINN: A Physics-Informed Petrov-Galerkin Kolmogorov-Arnold Network for Solving Forward and Inverse PDEs Unresolved cited work

Reference 40

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PG-KINN: A Physics-Informed Petrov-Galerkin Kolmogorov-Arnold Network for Solving Forward and Inverse PDEs Unresolved cited work

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PG-KINN: A Physics-Informed Petrov-Galerkin Kolmogorov-Arnold Network for Solving Forward and Inverse PDEs Adam: A Method for Stochastic Optimization

Reference 42

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PG-KINN: A Physics-Informed Petrov-Galerkin Kolmogorov-Arnold Network for Solving Forward and Inverse PDEs Bonet, R

Reference 43

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PG-KINN: A Physics-Informed Petrov-Galerkin Kolmogorov-Arnold Network for Solving Forward and Inverse PDEs Unresolved cited work

Reference 44

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PG-KINN: A Physics-Informed Petrov-Galerkin Kolmogorov-Arnold Network for Solving Forward and Inverse PDEs Quarteroni, R

Reference 45

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PG-KINN: A Physics-Informed Petrov-Galerkin Kolmogorov-Arnold Network for Solving Forward and Inverse PDEs Unresolved cited work

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PG-KINN: A Physics-Informed Petrov-Galerkin Kolmogorov-Arnold Network for Solving Forward and Inverse PDEs Unresolved cited work

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PG-KINN: A Physics-Informed Petrov-Galerkin Kolmogorov-Arnold Network for Solving Forward and Inverse PDEs Unresolved cited work

Reference 48

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PG-KINN: A Physics-Informed Petrov-Galerkin Kolmogorov-Arnold Network for Solving Forward and Inverse PDEs Unresolved cited work

Reference 49

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Pith citing papers

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