Paper Citation Record · LEDGER

Regularized Random Fourier Features and Finite Element Reconstruction for Operator Learning in Sobolev Space

As of 8 August 2026, this Paper Citation Record lists 37 of 37 outbound references and 1 inbound Pith citation observation for arXiv:2512.17884.

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

pith.paper-citation-record.v1
2512.17884 v1

Coverage vector

measured 37 of 37 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-03T15:14:43.460736Z

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 2026-05-13T22:45:53.377753Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-13T22:48:23.001267Z

Reference resolution

37 of 37 outbound references displayed

verified exact0
verified fuzzy0
unresolved37
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 723e1abf-6435-4f4e-9dd5-d0ebc5309ad0 · outbound

This paper cites Representation equivalent neural operators: A framework for alias-free operator learning.

Regularized Random Fourier Features and Finite Element Reconstruction for Operator Learning in Sobolev Space Representation equivalent neural operators: A framework for alias-free operator learning

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-03T15:14:41.173945Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b3653313-6424-4d11-87d5-ac3e1b872ecd · outbound

This paper cites Kernel methods are competitive for operator learning.Journal of Computational Physics, 2023.

Regularized Random Fourier Features and Finite Element Reconstruction for Operator Learning in Sobolev Space Kernel methods are competitive for operator learning.Journal of Computational Physics, 2023

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-03T15:14:41.222890Z

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Observation 023438ac-644a-474a-a624-e0e71d234d7d · outbound

This paper cites Approximations of continuous functionals by neural networks with application to dynamic systems.IEEE Transactions on Neural networks, 4(6):910–918, 1993.

Regularized Random Fourier Features and Finite Element Reconstruction for Operator Learning in Sobolev Space Approximations of continuous functionals by neural networks with application to dynamic systems.IEEE Transactions on Neural networks, 4(6):910–918, 1993

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-03T15:14:41.289247Z

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Observation c12de6e9-e32c-4ab1-97da-7b258a5f2c7c · outbound

This paper cites an unresolved cited work.

Regularized Random Fourier Features and Finite Element Reconstruction for Operator Learning in Sobolev Space Unresolved cited work

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-03T15:14:41.332233Z

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Observation 72cece45-fd91-4ffd-8ea8-245facea1cfd · outbound

This paper cites Conditioning of random Fourier feature matrices: Dou- ble descent and generalization error.Information and Inference: A Journal of the IMA, 13(2):iaad054, 2024.

Regularized Random Fourier Features and Finite Element Reconstruction for Operator Learning in Sobolev Space Conditioning of random Fourier feature matrices: Dou- ble descent and generalization error.Information and Inference: A Journal of the IMA, 13(2):iaad054, 2024

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-03T15:14:41.404128Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7612b0ee-03ca-4111-ba5e-3a02a7193db7 · outbound

This paper cites Concentration of random feature matrices in high-dimensions.

Regularized Random Fourier Features and Finite Element Reconstruction for Operator Learning in Sobolev Space Concentration of random feature matrices in high-dimensions

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-03T15:14:41.501983Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 87d193d1-3ac3-41dc-a314-de83b48e37dc · outbound

This paper cites de Hoop, Daniel Zhengyu Huang, Elizabeth Qian, and Andrew M.

Regularized Random Fourier Features and Finite Element Reconstruction for Operator Learning in Sobolev Space de Hoop, Daniel Zhengyu Huang, Elizabeth Qian, and Andrew M

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-03T15:14:41.563500Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0a2fdf8e-c42e-4e6a-a604-2bfbdcf4074c · outbound

This paper cites Approximation rates of DeepONets for learning operators arising from advection-diffusion equations.Neural Networks, 153:411–426, 2022.

Regularized Random Fourier Features and Finite Element Reconstruction for Operator Learning in Sobolev Space Approximation rates of DeepONets for learning operators arising from advection-diffusion equations.Neural Networks, 153:411–426, 2022

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-03T15:14:41.623615Z

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Unavailable: canonical work link unavailable.

Observation eeccfef4-4d4e-449a-828c-047686b46420 · outbound

This paper cites Evans.Partial differential equations.

Regularized Random Fourier Features and Finite Element Reconstruction for Operator Learning in Sobolev Space Evans.Partial differential equations

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-03T15:14:41.673103Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5eb41078-a660-4b0a-a003-00bb22ab21fe · outbound

This paper cites Learning from non-random data in Hilbert spaces: An optimal recovery perspective.Sampling Theory, Signal Processing, and Data Analysis, 20, 2022.

Regularized Random Fourier Features and Finite Element Reconstruction for Operator Learning in Sobolev Space Learning from non-random data in Hilbert spaces: An optimal recovery perspective.Sampling Theory, Signal Processing, and Data Analysis, 20, 2022

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-03T15:14:41.715318Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 61d02f69-d5d0-429f-891c-54e15f32ccd4 · outbound

This paper cites Gin, Daniel E.

Regularized Random Fourier Features and Finite Element Reconstruction for Operator Learning in Sobolev Space Gin, Daniel E

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-03T15:14:41.775366Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4df42504-33b7-4b7a-8b7c-e56dc1410a0d · outbound

This paper cites Generalization bounds for sparse random feature expansions.Applied and Computational Harmonic Analysis, 62:310–330, 2023.

Regularized Random Fourier Features and Finite Element Reconstruction for Operator Learning in Sobolev Space Generalization bounds for sparse random feature expansions.Applied and Computational Harmonic Analysis, 62:310–330, 2023

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-03T15:14:41.842864Z

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Observation 786ec44f-c20e-423f-b295-2ced4e433504 · outbound

This paper cites Huang, Kailai Xu, Charbel Farhat, and Eric Darve.

Regularized Random Fourier Features and Finite Element Reconstruction for Operator Learning in Sobolev Space Huang, Kailai Xu, Charbel Farhat, and Eric Darve

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-03T15:14:41.944818Z

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Unavailable: canonical work link unavailable.

Observation 8377f730-24e1-42fc-8c24-6a9c2454e819 · outbound

This paper cites Bridging traditional and machine learning-based algorithms for solving PDEs: The random feature method.Journal of Machine Learning, 1(3):268–298, 2022.

Regularized Random Fourier Features and Finite Element Reconstruction for Operator Learning in Sobolev Space Bridging traditional and machine learning-based algorithms for solving PDEs: The random feature method.Journal of Machine Learning, 1(3):268–298, 2022

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-03T15:14:42.010005Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0423fb34-e6ff-4b20-b116-f6052df80bbd · outbound

This paper cites On universal approximation and error bounds for Fourier Neural Operators.

Regularized Random Fourier Features and Finite Element Reconstruction for Operator Learning in Sobolev Space On universal approximation and error bounds for Fourier Neural Operators

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-03T15:14:42.079321Z

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Unavailable: canonical work link unavailable.

Observation 015db971-d70a-49d0-9c35-a88cdf54a0bb · outbound

This paper cites an unresolved cited work.

Regularized Random Fourier Features and Finite Element Reconstruction for Operator Learning in Sobolev Space Unresolved cited work

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-03T15:14:42.169653Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a4c13c25-8a69-4755-adae-68b95f056722 · outbound

This paper cites Fourier neural operator for parametric partial differential equations.

Regularized Random Fourier Features and Finite Element Reconstruction for Operator Learning in Sobolev Space Fourier neural operator for parametric partial differential equations

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-03T15:14:42.218229Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 86276466-1eb8-42e3-b09c-ba1a5c48d9da · outbound

This paper cites Cauchy Random Features for Operator Learning in Sobolev Space.

Regularized Random Fourier Features and Finite Element Reconstruction for Operator Learning in Sobolev Space Cauchy Random Features for Operator Learning in Sobolev Space

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-03T15:14:42.278933Z

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Observation 6233369a-04db-46a0-a4c6-60d491dde7cc · outbound

This paper cites Differentially Private Random Feature Model.

Regularized Random Fourier Features and Finite Element Reconstruction for Operator Learning in Sobolev Space Differentially Private Random Feature Model

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-03T15:14:42.378501Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 504b8653-45d5-4829-a321-cd39fc434bd7 · outbound

This paper cites Generalization error guaranteed auto- encoder-based nonlinear model reduction for operator learning.Applied and Computational Harmonic Analysis, 74:101717, 2025.

Regularized Random Fourier Features and Finite Element Reconstruction for Operator Learning in Sobolev Space Generalization error guaranteed auto- encoder-based nonlinear model reduction for operator learning.Applied and Computational Harmonic Analysis, 74:101717, 2025

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-03T15:14:42.443027Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 435e7078-e3cb-4ef4-9ac0-4d3a29167656 · outbound

This paper cites Neural scaling laws of deep ReLU and deep operator network: A theoretical study, 2024.

Regularized Random Fourier Features and Finite Element Reconstruction for Operator Learning in Sobolev Space Neural scaling laws of deep ReLU and deep operator network: A theoretical study, 2024

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-03T15:14:42.510170Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 08e8a78b-2c1f-404f-b119-811be5f621f0 · outbound

This paper cites Random feature models for learning interacting dynamical systems.Proceedings of the Royal Society A, 479(2275):20220835, 2023.

Regularized Random Fourier Features and Finite Element Reconstruction for Operator Learning in Sobolev Space Random feature models for learning interacting dynamical systems.Proceedings of the Royal Society A, 479(2275):20220835, 2023

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-03T15:14:42.567978Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d79c9408-392d-4314-8756-927c74d787a0 · outbound

This paper cites Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators.

Regularized Random Fourier Features and Finite Element Reconstruction for Operator Learning in Sobolev Space Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-03T15:14:42.610092Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 648a7b9c-c38d-492a-9b9f-5b75dd598287 · outbound

This paper cites A comprehensive and fair comparison of two neural operators (with practical extensions) based on fair data.Computer Methods in Applied Mechanics and Engineering, 393:114778, 2022.

Regularized Random Fourier Features and Finite Element Reconstruction for Operator Learning in Sobolev Space A comprehensive and fair comparison of two neural operators (with practical extensions) based on fair data.Computer Methods in Applied Mechanics and Engineering, 393:114778, 2022

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-03T15:14:42.666106Z

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Observation 57ce5224-6b28-4f37-9baa-b73f6df7cb0d · outbound

This paper cites an unresolved cited work.

Regularized Random Fourier Features and Finite Element Reconstruction for Operator Learning in Sobolev Space Unresolved cited work

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-03T15:14:42.746762Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 94236954-100c-4e14-bc7b-4d607dc24b27 · outbound

This paper cites Operator learning with Gaussian processes.Computer Methods in Applied Mechanics and Engineering, 434:117581, 2025.

Regularized Random Fourier Features and Finite Element Reconstruction for Operator Learning in Sobolev Space Operator learning with Gaussian processes.Computer Methods in Applied Mechanics and Engineering, 434:117581, 2025

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-03T15:14:42.816877Z

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Unavailable: canonical work link unavailable.

Observation 29c993fe-7cac-407c-a9a5-ab982f040def · outbound

This paper cites Nelsen and Andrew M.

Regularized Random Fourier Features and Finite Element Reconstruction for Operator Learning in Sobolev Space Nelsen and Andrew M

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-03T15:14:42.898842Z

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Observation 7566126e-ddef-4506-9763-fbe5bad5892a · outbound

This paper cites Nelsen and Andrew M.

Regularized Random Fourier Features and Finite Element Reconstruction for Operator Learning in Sobolev Space Nelsen and Andrew M

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-03T15:14:42.947340Z

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Observation d0d2e768-a504-4fd0-baf8-a725bedc4356 · outbound

This paper cites The Mat´ ern model: A journey through statistics, numerical analysis and machine learning.Statistical Science, 39, 08 2024.

Regularized Random Fourier Features and Finite Element Reconstruction for Operator Learning in Sobolev Space The Mat´ ern model: A journey through statistics, numerical analysis and machine learning.Statistical Science, 39, 08 2024

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-03T15:14:42.998482Z

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Unavailable: canonical work link unavailable.

Observation d8f15a0f-097c-443f-8aa4-f6a99ee9c20c · outbound

This paper cites Random features for large-scale kernel machines.

Regularized Random Fourier Features and Finite Element Reconstruction for Operator Learning in Sobolev Space Random features for large-scale kernel machines

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-03T15:14:43.051904Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d5c9a58c-c1c2-4255-9900-3dff68a3ece3 · outbound

This paper cites Uniform approximation of functions with random bases.

Regularized Random Fourier Features and Finite Element Reconstruction for Operator Learning in Sobolev Space Uniform approximation of functions with random bases

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-03T15:14:43.089424Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b762ce58-2a14-4a6d-83fa-693b5a0c8c42 · outbound

This paper cites Raissi, P.

Regularized Random Fourier Features and Finite Element Reconstruction for Operator Learning in Sobolev Space Raissi, P

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-03T15:14:43.187509Z

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Observation e4a7d4e9-28f0-4ba7-be31-be9b30fcecfd · outbound

This paper cites HARFE: hard-ridge random feature expansion.

Regularized Random Fourier Features and Finite Element Reconstruction for Operator Learning in Sobolev Space HARFE: hard-ridge random feature expansion

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-03T15:14:43.245433Z

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Observation 312fc033-e48b-4c0d-932d-90ed57bd5094 · outbound

This paper cites an unresolved cited work.

Regularized Random Fourier Features and Finite Element Reconstruction for Operator Learning in Sobolev Space Unresolved cited work

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-03T15:14:43.300715Z

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Unavailable: canonical work link unavailable.

Observation 686cede3-0b14-4237-9fc8-8d8b1ebeb62e · outbound

This paper cites A deep learning frame- work for multi-operator learning: Architectures and approximation theory.arXiv preprint arXiv:2510.25379, 2025.

Regularized Random Fourier Features and Finite Element Reconstruction for Operator Learning in Sobolev Space A deep learning frame- work for multi-operator learning: Architectures and approximation theory.arXiv preprint arXiv:2510.25379, 2025

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-03T15:14:43.346175Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation eb8e5af3-4861-4cc0-a162-d5227bd164fe · outbound

This paper cites Huang, and Eric Darve.

Regularized Random Fourier Features and Finite Element Reconstruction for Operator Learning in Sobolev Space Huang, and Eric Darve

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-03T15:14:43.398323Z

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Observation bb655c53-fe19-41ef-8ffe-38708c7f6ad0 · outbound

This paper cites BelNet: basis enhanced learning, a mesh- free neural operator.Proceedings of the Royal Society A, 479, 08 2023.

Regularized Random Fourier Features and Finite Element Reconstruction for Operator Learning in Sobolev Space BelNet: basis enhanced learning, a mesh- free neural operator.Proceedings of the Royal Society A, 479, 08 2023

Reference 37

Resolution: unresolved; no resolver link, observed 2026-08-03T15:14:43.460736Z

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Pith citing papers

Observation 3dc94ff9-cd5d-4c9f-86e3-1bfdf932d53a · inbound

MVNN: A Measure-Valued Neural Network for Learning McKean-Vlasov Dynamics from Particle Data cites this paper.

MVNN: A Measure-Valued Neural Network for Learning McKean-Vlasov Dynamics from Particle Data Regularized Random Fourier Features and Finite Element Reconstruction for Operator Learning in Sobolev Space

Reference 53

Resolution: verified exact; arxiv_id, observed 2026-06-30T03:17:26.093741Z

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.