Paper Citation Record · LEDGER

Multi-Resolution Training-Enhanced Kolmogorov-Arnold Networks for Multi-Scale PDE Problems

As of 8 August 2026, this Paper Citation Record lists 53 of 53 outbound references and 3 inbound Pith citation observations for arXiv:2507.19888.

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pith.paper-citation-record.v1
2507.19888 v1

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Reference resolution

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Outbound references

Observation 8a2c6917-33f6-48ab-993b-db1971fe4721 · outbound

This paper cites Communications in Numerical Methods in Engineering 10(3), 195–201 (1994) https://doi.org/10.1002/cnm.1640100303.

Multi-Resolution Training-Enhanced Kolmogorov-Arnold Networks for Multi-Scale PDE Problems Communications in Numerical Methods in Engineering 10(3), 195–201 (1994) https://doi.org/10.1002/cnm.1640100303

Reference 1

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This paper cites IEEE Transactions on Neural Networks 9(5), 987–1000 (1998) https://doi.org/10.1109/72.712178.

Multi-Resolution Training-Enhanced Kolmogorov-Arnold Networks for Multi-Scale PDE Problems IEEE Transactions on Neural Networks 9(5), 987–1000 (1998) https://doi.org/10.1109/72.712178

Reference 2

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This paper cites Communications in Mathematics and Statistics 6(1), 1–12 (2018) https://doi.org/10.1007/s40304-018-0127-z.

Multi-Resolution Training-Enhanced Kolmogorov-Arnold Networks for Multi-Scale PDE Problems Communications in Mathematics and Statistics 6(1), 1–12 (2018) https://doi.org/10.1007/s40304-018-0127-z

Reference 3

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This paper cites Nature Reviews Physics 3(6), 422–440 (2021) https://doi.org/10.1038/s42254-021-00314-5.

Multi-Resolution Training-Enhanced Kolmogorov-Arnold Networks for Multi-Scale PDE Problems Nature Reviews Physics 3(6), 422–440 (2021) https://doi.org/10.1038/s42254-021-00314-5

Reference 4

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Observation 2ed85a3d-966a-4aea-bb70-7415ed3ddc2f · outbound

This paper cites Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations.

Multi-Resolution Training-Enhanced Kolmogorov-Arnold Networks for Multi-Scale PDE Problems Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations

Reference 5

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This paper cites Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations.

Multi-Resolution Training-Enhanced Kolmogorov-Arnold Networks for Multi-Scale PDE Problems Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations

Reference 6

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

Multi-Resolution Training-Enhanced Kolmogorov-Arnold Networks for Multi-Scale PDE Problems Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

Reference 7

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This paper cites Computer Methods in Applied Mechanics and Engineering 362, 112790 (2020) https://doi.org/10.1016/j.cma.2019.112790.

Multi-Resolution Training-Enhanced Kolmogorov-Arnold Networks for Multi-Scale PDE Problems Computer Methods in Applied Mechanics and Engineering 362, 112790 (2020) https://doi.org/10.1016/j.cma.2019.112790

Reference 8

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This paper cites IEEE Transactions on Neural Networks 4(6), 910–918 (1993) https://doi.org/10.1109/72.286886.

Multi-Resolution Training-Enhanced Kolmogorov-Arnold Networks for Multi-Scale PDE Problems IEEE Transactions on Neural Networks 4(6), 910–918 (1993) https://doi.org/10.1109/72.286886

Reference 9

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This paper cites In: Proceedings of the 36th International Conference on Machine Learning, vol.

Multi-Resolution Training-Enhanced Kolmogorov-Arnold Networks for Multi-Scale PDE Problems In: Proceedings of the 36th International Conference on Machine Learning, vol

Reference 10

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This paper cites Computer Methods in Applied Mechanics and Engineering384, 113938 (2021) https://doi.org/10.1016/j.cma.2021.113938.

Multi-Resolution Training-Enhanced Kolmogorov-Arnold Networks for Multi-Scale PDE Problems Computer Methods in Applied Mechanics and Engineering384, 113938 (2021) https://doi.org/10.1016/j.cma.2021.113938

Reference 11

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This paper cites Journal of Computational Physics 404, 109136 (2020) https://doi.org/10.1016/j.jcp.2019.

Multi-Resolution Training-Enhanced Kolmogorov-Arnold Networks for Multi-Scale PDE Problems Journal of Computational Physics 404, 109136 (2020) https://doi.org/10.1016/j.jcp.2019

Reference 12

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This paper cites A multi-scale DNN algorithm for nonlinear elliptic equations with multiple scales.

Multi-Resolution Training-Enhanced Kolmogorov-Arnold Networks for Multi-Scale PDE Problems A multi-scale DNN algorithm for nonlinear elliptic equations with multiple scales

Reference 13

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This paper cites Frequency-adaptive Multi-scale Deep Neural Networks.

Multi-Resolution Training-Enhanced Kolmogorov-Arnold Networks for Multi-Scale PDE Problems Frequency-adaptive Multi-scale Deep Neural Networks

Reference 14

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This paper cites KAN: Kolmogorov-Arnold Networks.

Multi-Resolution Training-Enhanced Kolmogorov-Arnold Networks for Multi-Scale PDE Problems KAN: Kolmogorov-Arnold Networks

Reference 15

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This paper cites KAN 2.0: Kolmogorov-Arnold Networks Meet Science.

Multi-Resolution Training-Enhanced Kolmogorov-Arnold Networks for Multi-Scale PDE Problems KAN 2.0: Kolmogorov-Arnold Networks Meet Science

Reference 16

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This paper cites Computer Methods in Applied Mechanics and Engineering 431, 117290 (2024) https://doi.org/10.1016/j.cma.2024.117290.

Multi-Resolution Training-Enhanced Kolmogorov-Arnold Networks for Multi-Scale PDE Problems Computer Methods in Applied Mechanics and Engineering 431, 117290 (2024) https://doi.org/10.1016/j.cma.2024.117290

Reference 17

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

Multi-Resolution Training-Enhanced Kolmogorov-Arnold Networks for Multi-Scale PDE Problems Chebyshev Polynomial-Based Kolmogorov-Arnold Networks: An Efficient Architecture for Nonlinear Function Approximation

Reference 18

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

Multi-Resolution Training-Enhanced Kolmogorov-Arnold Networks for Multi-Scale PDE Problems Kolmogorov-Arnold Networks are Radial Basis Function Networks

Reference 19

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This paper cites Wav-KAN: Wavelet Kolmogorov-Arnold Networks.

Multi-Resolution Training-Enhanced Kolmogorov-Arnold Networks for Multi-Scale PDE Problems Wav-KAN: Wavelet Kolmogorov-Arnold Networks

Reference 20

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This paper cites Kolmogorov Arnold Informed neural network: A physics-informed deep learning framework for solving forward and inverse problems based on Kolmogorov Arnold Networks.

Multi-Resolution Training-Enhanced Kolmogorov-Arnold Networks for Multi-Scale PDE Problems Kolmogorov Arnold Informed neural network: A physics-informed deep learning framework for solving forward and inverse problems based on Kolmogorov Arnold Networks

Reference 21

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This paper cites SIAM Review 63(1), 208–228 (2021) https:// doi.org/10.1137/19M1274067.

Multi-Resolution Training-Enhanced Kolmogorov-Arnold Networks for Multi-Scale PDE Problems SIAM Review 63(1), 208–228 (2021) https:// doi.org/10.1137/19M1274067

Reference 22

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Multi-Resolution Training-Enhanced Kolmogorov-Arnold Networks for Multi-Scale PDE Problems Computer Methods in Applied Mechanics and Engineering403, 115671 (2023) https://doi.org/10.1016/j.cma.2022.115671

Reference 23

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This paper cites Applied Mathematics and Mechanics 44(7), 1069–1084 (2023) https://doi.org/10.1007/s10483-023-2994-7.

Multi-Resolution Training-Enhanced Kolmogorov-Arnold Networks for Multi-Scale PDE Problems Applied Mathematics and Mechanics 44(7), 1069–1084 (2023) https://doi.org/10.1007/s10483-023-2994-7

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Multi-Resolution Training-Enhanced Kolmogorov-Arnold Networks for Multi-Scale PDE Problems SIAM Journal on Scientific Computing 45(4), 1971–1994 (2023) https://doi.org/10

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This paper cites Adaptive Training of Grid-Dependent Physics-Informed Kolmogorov-Arnold Networks.

Multi-Resolution Training-Enhanced Kolmogorov-Arnold Networks for Multi-Scale PDE Problems Adaptive Training of Grid-Dependent Physics-Informed Kolmogorov-Arnold Networks

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Multi-Resolution Training-Enhanced Kolmogorov-Arnold Networks for Multi-Scale PDE Problems Computer-Aided Civil and Infrastruc- ture Engineering 36(8), 962–977 (2021) https://doi.org/10.1111/mice.12685

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Multi-Resolution Training-Enhanced Kolmogorov-Arnold Networks for Multi-Scale PDE Problems Journal of Computational Physics 476, 111868 (2023) https://doi.org/10.1016/j.jcp.2022.111868

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Multi-Resolution Training-Enhanced Kolmogorov-Arnold Networks for Multi-Scale PDE Problems Computer Methods in Applied Mechanics and Engineering 419, 116666 (2024) https://doi.org/10.1016/ j.cma.2023.116666

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Multi-Resolution Training-Enhanced Kolmogorov-Arnold Networks for Multi-Scale PDE Problems Journal of Computational Physics 504, 112865 (2024) https: //doi.org/10.1016/j.jcp.2024.112865

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Multi-Resolution Training-Enhanced Kolmogorov-Arnold Networks for Multi-Scale PDE Problems Journal of Computational Physics 520, 113438 (2025) https://doi.org/10.1016/j.jcp.2024.113438

Reference 31

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Multi-Resolution Training-Enhanced Kolmogorov-Arnold Networks for Multi-Scale PDE Problems In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pp

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Multi-Resolution Training-Enhanced Kolmogorov-Arnold Networks for Multi-Scale PDE Problems In: Proceedings of the AAAI Conference on Artificial Intelligence, vol

Reference 33

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Multi-Resolution Training-Enhanced Kolmogorov-Arnold Networks for Multi-Scale PDE Problems SIAM Journal on Scientific Computing 43(5), 3055–3081 (2021) https://doi.org/10.1137/20M1318043

Reference 34

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Multi-Resolution Training-Enhanced Kolmogorov-Arnold Networks for Multi-Scale PDE Problems Journal of Computational Physics 449 (2022) https: //doi.org/10.1016/j.jcp.2021.110768

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Multi-Resolution Training-Enhanced Kolmogorov-Arnold Networks for Multi-Scale PDE Problems Journal of Computational Physics 474, 111722 (2023) https://doi.org/10

Reference 36

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Multi-Resolution Training-Enhanced Kolmogorov-Arnold Networks for Multi-Scale PDE Problems Computer Meth- ods in Applied Mechanics and Engineering 421, 116805 (2024) https://doi.org/ 10.1016/j.cma.2024.116805

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Multi-Resolution Training-Enhanced Kolmogorov-Arnold Networks for Multi-Scale PDE Problems In: Doklady Akademii Nauk SSSR, vol

Reference 38

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Multi-Resolution Training-Enhanced Kolmogorov-Arnold Networks for Multi-Scale PDE Problems Learning in PINNs: Phase transition, total diffusion, and generalization

Reference 39

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Multi-Resolution Training-Enhanced Kolmogorov-Arnold Networks for Multi-Scale PDE Problems Springer Series in Com- putational Mathematics, vol

Reference 40

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Multi-Resolution Training-Enhanced Kolmogorov-Arnold Networks for Multi-Scale PDE Problems In: Teh, Y.W., Titterington, M

Reference 41

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Multi-Resolution Training-Enhanced Kolmogorov-Arnold Networks for Multi-Scale PDE Problems In: Advances in Neural Information Processing Systems, vol

Reference 42

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Multi-Resolution Training-Enhanced Kolmogorov-Arnold Networks for Multi-Scale PDE Problems In: Inter- national Conference on Learning Representations (ICLR2015)

Reference 43

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Multi-Resolution Training-Enhanced Kolmogorov-Arnold Networks for Multi-Scale PDE Problems Oxford University Press, (1990)

Reference 44

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This paper cites Pafnuty Publications, Oxford (2014).

Multi-Resolution Training-Enhanced Kolmogorov-Arnold Networks for Multi-Scale PDE Problems Pafnuty Publications, Oxford (2014)

Reference 45

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T13:58:39.024441Z

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Observation 19ab2dcd-617f-47e6-8743-cb1d41e265a6 · outbound

This paper cites Journal of Computational Physics 176(2), 430–455 (2002).

Multi-Resolution Training-Enhanced Kolmogorov-Arnold Networks for Multi-Scale PDE Problems Journal of Computational Physics 176(2), 430–455 (2002)

Reference 46

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T13:58:38.845648Z

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 50f92ac9-b614-40d3-a36c-af7937c68d57 · outbound

This paper cites Renewable Energy 220, 119565 (2024) https://doi.org/10.1016/j.renene.2023.119565.

Multi-Resolution Training-Enhanced Kolmogorov-Arnold Networks for Multi-Scale PDE Problems Renewable Energy 220, 119565 (2024) https://doi.org/10.1016/j.renene.2023.119565

Reference 47

Resolution: metadata mismatch; raw_fallback, observed 2026-08-06T13:58:36.249749Z

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 414b9b19-8f2c-4f35-8d97-d61aca2029a9 · outbound

This paper cites Annual Review of Materials Research 45(1), 391–431 (2015) https://doi.org/10.1146/annurev-matsci-070214-021103.

Multi-Resolution Training-Enhanced Kolmogorov-Arnold Networks for Multi-Scale PDE Problems Annual Review of Materials Research 45(1), 391–431 (2015) https://doi.org/10.1146/annurev-matsci-070214-021103

Reference 48

Resolution: verified exact; doi, observed 2026-08-06T13:58:35.769567Z

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 1710e1aa-49e0-48a0-bba1-624c5bc39068 · outbound

This paper cites In: International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, vol.

Multi-Resolution Training-Enhanced Kolmogorov-Arnold Networks for Multi-Scale PDE Problems In: International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, vol

Reference 49

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T13:58:38.758154Z

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 69e51486-9649-4218-8860-0a2d68c1c327 · outbound

This paper cites Engineering Applications of Artificial Intelligence 127 (2024) https://doi.org/10.1016/j.engappai.2023.

Multi-Resolution Training-Enhanced Kolmogorov-Arnold Networks for Multi-Scale PDE Problems Engineering Applications of Artificial Intelligence 127 (2024) https://doi.org/10.1016/j.engappai.2023

Reference 50

Resolution: unresolved; no resolver link, observed 2026-08-06T13:58:35.103284Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cf6a625b-6047-4f86-8761-c58be8ea88b4 · outbound

This paper cites Experimental Mechanics 55(6), 1105–1122 (2015) https: //doi.org/10.1007/s11340-015-0009-1.

Multi-Resolution Training-Enhanced Kolmogorov-Arnold Networks for Multi-Scale PDE Problems Experimental Mechanics 55(6), 1105–1122 (2015) https: //doi.org/10.1007/s11340-015-0009-1

Reference 51

Resolution: verified exact; doi, observed 2026-08-06T13:58:35.582200Z

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 2147b250-de1a-498b-8c0b-9d01b6abc29c · outbound

This paper cites Proceedings of the National Academy of Sciences 118(31), 2102721118 (2021) 31 https://doi.org/10.1073/pnas.2102721118.

Multi-Resolution Training-Enhanced Kolmogorov-Arnold Networks for Multi-Scale PDE Problems Proceedings of the National Academy of Sciences 118(31), 2102721118 (2021) 31 https://doi.org/10.1073/pnas.2102721118

Reference 52

Resolution: unresolved; no resolver link, observed 2026-08-06T13:58:35.279439Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6c65895f-ff97-4b0d-91cc-3ffc1366bc16 · outbound

This paper cites Springer, (2016) 32.

Multi-Resolution Training-Enhanced Kolmogorov-Arnold Networks for Multi-Scale PDE Problems Springer, (2016) 32

Reference 53

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T13:58:38.587790Z

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 cc00ee0c-a7cf-4e66-b145-2bccd9615a7d · inbound

A Practitioner's Guide to Kolmogorov-Arnold Networks cites this paper.

A Practitioner's Guide to Kolmogorov-Arnold Networks Multi-Resolution Training-Enhanced Kolmogorov-Arnold Networks for Multi-Scale PDE Problems

Reference 75

Resolution: verified exact; arxiv_id, observed 2026-05-18T03:30:50.497889Z

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 729bb144-4249-4f64-b185-ec18fced14ad · inbound

Faster by Design: Interactive Aerodynamics via Neural Surrogates Trained on Expert-Validated CFD cites this paper.

Faster by Design: Interactive Aerodynamics via Neural Surrogates Trained on Expert-Validated CFD Multi-Resolution Training-Enhanced Kolmogorov-Arnold Networks for Multi-Scale PDE Problems

Reference 48

Resolution: metadata mismatch; arxiv_id, observed 2026-05-10T06:11:20.655780Z

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 46274677-3060-4ba1-99dc-3dee1a824684 · inbound

PILIR: Physics-Informed Local Implicit Representation cites this paper.

PILIR: Physics-Informed Local Implicit Representation Multi-Resolution Training-Enhanced Kolmogorov-Arnold Networks for Multi-Scale PDE Problems

Reference 24

Resolution: verified exact; arxiv_id, observed 2026-05-11T15:42:02.420134Z

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.