Paper Citation Record · LEDGER

Breaking the Precision Ceiling in Physics-Informed Neural Networks: A Hybrid Fourier-Neural Architecture for Ultra-High Accuracy

As of 11 August 2026, this Paper Citation Record lists 38 of 38 outbound references and 0 inbound Pith citation observations for arXiv:2507.20929.

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

pith.paper-citation-record.v1
2507.20929 v1

Coverage vector

measured 38 of 38 reference resolution

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Pith citing papers itemized under the disclosed page cap.

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measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

38 of 38 outbound references displayed

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External citation measurements

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Outbound references

Observation 9790f1e4-fc2f-4fe5-976b-76615e27654c · outbound

This paper cites Journal of Computational Physics 378, 686–707 (2019) https://doi.org/10.1016/j.jcp.

Breaking the Precision Ceiling in Physics-Informed Neural Networks: A Hybrid Fourier-Neural Architecture for Ultra-High Accuracy Journal of Computational Physics 378, 686–707 (2019) https://doi.org/10.1016/j.jcp

Reference 1

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Observation e9cd6cf5-39ba-4686-b650-6086d21e3038 · outbound

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

Breaking the Precision Ceiling in Physics-Informed Neural Networks: A Hybrid Fourier-Neural Architecture for Ultra-High Accuracy Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations

Reference 2

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Observation c57294e7-4ae1-4d98-8793-415670d7f443 · outbound

This paper cites Nature Reviews Physics 3(6), 422–440 (2021) https://doi.org/10.

Breaking the Precision Ceiling in Physics-Informed Neural Networks: A Hybrid Fourier-Neural Architecture for Ultra-High Accuracy Nature Reviews Physics 3(6), 422–440 (2021) https://doi.org/10

Reference 3

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Observation 3da595fe-418b-41d4-aa04-9808e4abacc1 · outbound

This paper cites Journal of Scientific Computing 92(3), 88 (2022) https://doi.org/10.1007/s10915-022-01939-z.

Breaking the Precision Ceiling in Physics-Informed Neural Networks: A Hybrid Fourier-Neural Architecture for Ultra-High Accuracy Journal of Scientific Computing 92(3), 88 (2022) https://doi.org/10.1007/s10915-022-01939-z

Reference 4

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Observation b5b1c162-adf7-4712-9e63-abb3135c2f86 · outbound

This paper cites Nature Communications 12(1), 6136 (2021) https://doi.org/10.1038/s41467-021-26434-1.

Breaking the Precision Ceiling in Physics-Informed Neural Networks: A Hybrid Fourier-Neural Architecture for Ultra-High Accuracy Nature Communications 12(1), 6136 (2021) https://doi.org/10.1038/s41467-021-26434-1

Reference 5

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Observation 654adb52-14e6-491c-912d-2df7ed100eed · outbound

This paper cites SIAM Journal on Scientific Computing 41(4), 2603–2626 (2019) https://doi.org/10.1137/18M1229845.

Breaking the Precision Ceiling in Physics-Informed Neural Networks: A Hybrid Fourier-Neural Architecture for Ultra-High Accuracy SIAM Journal on Scientific Computing 41(4), 2603–2626 (2019) https://doi.org/10.1137/18M1229845

Reference 6

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Observation e8edb2e3-aa28-4b1d-9bf7-e099ac0eb1e2 · outbound

This paper cites IEEE Transactions on Neural Networks and Learning Systems (2023) https://doi.org/10.1109/TNNLS.2023.3310585.

Breaking the Precision Ceiling in Physics-Informed Neural Networks: A Hybrid Fourier-Neural Architecture for Ultra-High Accuracy IEEE Transactions on Neural Networks and Learning Systems (2023) https://doi.org/10.1109/TNNLS.2023.3310585

Reference 7

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Observation 9de1034c-b441-4411-bedf-5e753c6cf8b0 · outbound

This paper cites Mechanical Systems and Signal Processing 200, 110575 (2023) https://doi.org/10.1016/j.ymssp.

Breaking the Precision Ceiling in Physics-Informed Neural Networks: A Hybrid Fourier-Neural Architecture for Ultra-High Accuracy Mechanical Systems and Signal Processing 200, 110575 (2023) https://doi.org/10.1016/j.ymssp

Reference 8

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Observation 1d9aaae0-aceb-4d76-8316-b662a6f3afbd · outbound

This paper cites Engineering Applications of Artificial Intelligence 133, 108085 (2024) https://doi.org/10.1016/j.engappai.2024.108085.

Breaking the Precision Ceiling in Physics-Informed Neural Networks: A Hybrid Fourier-Neural Architecture for Ultra-High Accuracy Engineering Applications of Artificial Intelligence 133, 108085 (2024) https://doi.org/10.1016/j.engappai.2024.108085

Reference 9

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Observation f76c0ca9-7ddc-4a52-a60d-a7d7d50c523e · outbound

This paper cites Journal of Engineering Mechanics 148(2), 04021139 (2022) https://doi.org/10.1061/(ASCE)EM.1943-7889.0002062.

Breaking the Precision Ceiling in Physics-Informed Neural Networks: A Hybrid Fourier-Neural Architecture for Ultra-High Accuracy Journal of Engineering Mechanics 148(2), 04021139 (2022) https://doi.org/10.1061/(ASCE)EM.1943-7889.0002062

Reference 10

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Observation 3f0d8664-5843-41d8-b361-bddab59060eb · outbound

This paper cites High Precision Differentiation Techniques for Data-Driven Solution of Nonlinear PDEs by Physics-Informed Neural Networks.

Breaking the Precision Ceiling in Physics-Informed Neural Networks: A Hybrid Fourier-Neural Architecture for Ultra-High Accuracy High Precision Differentiation Techniques for Data-Driven Solution of Nonlinear PDEs by Physics-Informed Neural Networks

Reference 11

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Observation ecac2351-211c-4535-8df1-65703af592e8 · outbound

This paper cites IEEE Transactions on Artificial Intelligence 5(6), 2547–2557 (2024) https:// doi.org/10.1109/TAI.2022.3192362.

Breaking the Precision Ceiling in Physics-Informed Neural Networks: A Hybrid Fourier-Neural Architecture for Ultra-High Accuracy IEEE Transactions on Artificial Intelligence 5(6), 2547–2557 (2024) https:// doi.org/10.1109/TAI.2022.3192362

Reference 12

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Observation b741d24d-670c-4be3-be3b-369ee0427b9a · outbound

This paper cites Com- puter Methods in Applied Mechanics and Engineering 365, 113028 (2020) https://doi.org/10.

Breaking the Precision Ceiling in Physics-Informed Neural Networks: A Hybrid Fourier-Neural Architecture for Ultra-High Accuracy Com- puter Methods in Applied Mechanics and Engineering 365, 113028 (2020) https://doi.org/10

Reference 13

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Observation 6c880882-00b9-465c-9f03-6d11a52b83c3 · outbound

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

Breaking the Precision Ceiling in Physics-Informed Neural Networks: A Hybrid Fourier-Neural Architecture for Ultra-High Accuracy SIAM Review 63(1), 208–228 (2021) https://doi.org/10.1137/19M1274067

Reference 14

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Observation e4cf3032-c811-455a-8434-1cae19b85e46 · outbound

This paper cites Nature Computational Science 4(7), 483–494 (2024) https://doi.org/10.1038/ s43588-024-00643-2.

Breaking the Precision Ceiling in Physics-Informed Neural Networks: A Hybrid Fourier-Neural Architecture for Ultra-High Accuracy Nature Computational Science 4(7), 483–494 (2024) https://doi.org/10.1038/ s43588-024-00643-2

Reference 15

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Observation 15065b35-1aa4-4af9-a01a-46a5276814f1 · outbound

This paper cites Physics of Fluids 36(10), 101301 (2024) https://doi.org/10.1063/5.0226562.

Breaking the Precision Ceiling in Physics-Informed Neural Networks: A Hybrid Fourier-Neural Architecture for Ultra-High Accuracy Physics of Fluids 36(10), 101301 (2024) https://doi.org/10.1063/5.0226562

Reference 16

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Observation af4af0fb-5cca-48b7-94a5-91239c0c489f · outbound

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

Breaking the Precision Ceiling in Physics-Informed Neural Networks: A Hybrid Fourier-Neural Architecture for Ultra-High Accuracy Fourier Neural Operator for Parametric Partial Differential Equations

Reference 17

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Observation bd8c0192-b00a-4528-811f-8f37db7ca294 · outbound

This paper cites Communications in Computational Physics 28(5), 2002–2041 (2020) https://doi.org/10.4208/cicp.OA-2020-0164.

Breaking the Precision Ceiling in Physics-Informed Neural Networks: A Hybrid Fourier-Neural Architecture for Ultra-High Accuracy Communications in Computational Physics 28(5), 2002–2041 (2020) https://doi.org/10.4208/cicp.OA-2020-0164

Reference 18

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Observation 6de0f9bb-24f6-4e2d-aa35-9443ba386ef4 · outbound

This paper cites Computer Methods in Applied Mechanics and Engineering 374, 113547 (2021) https://doi.org/10.1016/j.cma.2020.113547.

Breaking the Precision Ceiling in Physics-Informed Neural Networks: A Hybrid Fourier-Neural Architecture for Ultra-High Accuracy Computer Methods in Applied Mechanics and Engineering 374, 113547 (2021) https://doi.org/10.1016/j.cma.2020.113547

Reference 19

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Observation 562f2a8e-50dd-4ba4-b98c-b26b2a294106 · outbound

This paper cites Journal of Computational Physics 496, 112603 (2024) https://doi.org/10.

Breaking the Precision Ceiling in Physics-Informed Neural Networks: A Hybrid Fourier-Neural Architecture for Ultra-High Accuracy Journal of Computational Physics 496, 112603 (2024) https://doi.org/10

Reference 20

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Observation bd4d5f85-f5f8-4bd1-b05c-d3ec7e796a33 · outbound

This paper cites Dual Cone Gradient Descent for Training Physics-Informed Neural Networks.

Breaking the Precision Ceiling in Physics-Informed Neural Networks: A Hybrid Fourier-Neural Architecture for Ultra-High Accuracy Dual Cone Gradient Descent for Training Physics-Informed Neural Networks

Reference 21

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Observation 1ae2cd42-051c-44ec-ba5a-3938fe465837 · outbound

This paper cites Journal of Computational Physics 457, 111053 (2022) https://doi.org/10.1016/j.jcp.2022.111053.

Breaking the Precision Ceiling in Physics-Informed Neural Networks: A Hybrid Fourier-Neural Architecture for Ultra-High Accuracy Journal of Computational Physics 457, 111053 (2022) https://doi.org/10.1016/j.jcp.2022.111053

Reference 22

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Observation 79e4036c-5630-4f3d-85ea-6afda1db4f1b · outbound

This paper cites Journal of Computational Physics 375, 1339–1364 (2018) https://doi.org/10.1016/j.

Breaking the Precision Ceiling in Physics-Informed Neural Networks: A Hybrid Fourier-Neural Architecture for Ultra-High Accuracy Journal of Computational Physics 375, 1339–1364 (2018) https://doi.org/10.1016/j

Reference 23

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Observation 3b0456b3-8812-4d2f-97ed-d2ac64aa099e · outbound

This paper cites Computer Methods in Applied Mechanics and Engineering 397, 115141 (2022) https://doi.org/10.1016/j.cma.2022.115141.

Breaking the Precision Ceiling in Physics-Informed Neural Networks: A Hybrid Fourier-Neural Architecture for Ultra-High Accuracy Computer Methods in Applied Mechanics and Engineering 397, 115141 (2022) https://doi.org/10.1016/j.cma.2022.115141

Reference 24

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Observation e54df2a5-26ef-4ba5-91d3-9fc761f08f99 · outbound

This paper cites Computer Methods in Applied Mechanics and Engineering 424, 116883 (2024) https://doi.org/10.1016/j.cma.2024.116883.

Breaking the Precision Ceiling in Physics-Informed Neural Networks: A Hybrid Fourier-Neural Architecture for Ultra-High Accuracy Computer Methods in Applied Mechanics and Engineering 424, 116883 (2024) https://doi.org/10.1016/j.cma.2024.116883

Reference 25

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This paper cites SIAM Journal on Scientific Computing 43(5), 3055–3081 (2021) https://doi.org/10.1137/20M1318043.

Breaking the Precision Ceiling in Physics-Informed Neural Networks: A Hybrid Fourier-Neural Architecture for Ultra-High Accuracy SIAM Journal on Scientific Computing 43(5), 3055–3081 (2021) https://doi.org/10.1137/20M1318043

Reference 26

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Observation af2510ae-92fc-415e-9f2b-da50efe072eb · outbound

This paper cites Characterizing possible failure modes in physics-informed neural networks.

Breaking the Precision Ceiling in Physics-Informed Neural Networks: A Hybrid Fourier-Neural Architecture for Ultra-High Accuracy Characterizing possible failure modes in physics-informed neural networks

Reference 27

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This paper cites Journal of Computational Physics 474, 111722 (2023) https://doi.org/10.1016/j.jcp.2022.111722.

Breaking the Precision Ceiling in Physics-Informed Neural Networks: A Hybrid Fourier-Neural Architecture for Ultra-High Accuracy Journal of Computational Physics 474, 111722 (2023) https://doi.org/10.1016/j.jcp.2022.111722

Reference 28

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This paper cites Journal of Computational Physics 473, 111768 (2023) https://doi.org/10.1016/j.jcp.2022.111768.

Breaking the Precision Ceiling in Physics-Informed Neural Networks: A Hybrid Fourier-Neural Architecture for Ultra-High Accuracy Journal of Computational Physics 473, 111768 (2023) https://doi.org/10.1016/j.jcp.2022.111768

Reference 29

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Observation f72ce411-5f11-42f8-9498-3cf1fd57e039 · outbound

This paper cites Separable Physics-Informed Neural Networks.

Breaking the Precision Ceiling in Physics-Informed Neural Networks: A Hybrid Fourier-Neural Architecture for Ultra-High Accuracy Separable Physics-Informed Neural Networks

Reference 30

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This paper cites Journal of Computational Physics 493, 112464 (2023) https: //doi.org/10.1016/j.jcp.2023.112464.

Breaking the Precision Ceiling in Physics-Informed Neural Networks: A Hybrid Fourier-Neural Architecture for Ultra-High Accuracy Journal of Computational Physics 493, 112464 (2023) https: //doi.org/10.1016/j.jcp.2023.112464

Reference 31

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This paper cites Journal of Sound and Vibration 225(5), 935–988 (1999) https://doi.org/10.1006/ jsvi.1999.2257.

Breaking the Precision Ceiling in Physics-Informed Neural Networks: A Hybrid Fourier-Neural Architecture for Ultra-High Accuracy Journal of Sound and Vibration 225(5), 935–988 (1999) https://doi.org/10.1006/ jsvi.1999.2257

Reference 32

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This paper cites Self-Adaptive Physics-Informed Neural Networks using a Soft Attention Mechanism.

Breaking the Precision Ceiling in Physics-Informed Neural Networks: A Hybrid Fourier-Neural Architecture for Ultra-High Accuracy Self-Adaptive Physics-Informed Neural Networks using a Soft Attention Mechanism

Reference 33

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Breaking the Precision Ceiling in Physics-Informed Neural Networks: A Hybrid Fourier-Neural Architecture for Ultra-High Accuracy Adam: A Method for Stochastic Optimization

Reference 34

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This paper cites Mathematical programming 45(1-3), 503–528 (1989).

Breaking the Precision Ceiling in Physics-Informed Neural Networks: A Hybrid Fourier-Neural Architecture for Ultra-High Accuracy Mathematical programming 45(1-3), 503–528 (1989)

Reference 35

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This paper cites Journal of Computational Physics 477, 111902 (2023).

Breaking the Precision Ceiling in Physics-Informed Neural Networks: A Hybrid Fourier-Neural Architecture for Ultra-High Accuracy Journal of Computational Physics 477, 111902 (2023)

Reference 36

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This paper cites https://arxiv.org/abs/2410.19843.

Breaking the Precision Ceiling in Physics-Informed Neural Networks: A Hybrid Fourier-Neural Architecture for Ultra-High Accuracy https://arxiv.org/abs/2410.19843

Reference 37

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Breaking the Precision Ceiling in Physics-Informed Neural Networks: A Hybrid Fourier-Neural Architecture for Ultra-High Accuracy GitHub (2025) 15 Fig

Reference 38

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Pith citing papers

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