Paper Citation Record · LEDGER

Extending Fourier Neural Operators for Modeling Parameterized and Coupled PDEs

As of 9 August 2026, this Paper Citation Record lists 23 of 23 outbound references and 0 inbound Pith citation observations for arXiv:2607.23466.

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

pith.paper-citation-record.v1
2607.23466 v1

Coverage vector

measured 23 of 23 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-07-30T21:35:27.316706Z

measured 23 of 23 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-09T06:31:02.800959+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

23 of 23 outbound references displayed

verified exact0
verified fuzzy0
unresolved22
parse uncertain0
malformed identifier1
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 38b1c34d-2d96-415f-994e-a6e2ec5a66ee · outbound

This paper cites HyperFNO: Improving the general- ization behavior of Fourier neural operators.

Extending Fourier Neural Operators for Modeling Parameterized and Coupled PDEs HyperFNO: Improving the general- ization behavior of Fourier neural operators

Reference 1

Resolution: unresolved; no resolver link, observed 2026-07-30T21:35:25.868530Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 22e7e15e-0dad-431c-b5b0-bf8abd4a674a · outbound

This paper cites Sharing main- tains parameter efficiency, while separating allows each variable to evolve differently in latent space.

Extending Fourier Neural Operators for Modeling Parameterized and Coupled PDEs Sharing main- tains parameter efficiency, while separating allows each variable to evolve differently in latent space

Reference 2

Resolution: unresolved; no resolver link, observed 2026-07-30T21:35:26.595637Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6fa27cef-2383-4fe9-ba41-82ddf40f3535 · outbound

This paper cites PDE-Transformer: Efficient and Versatile Transformers for Physics Simulations.

Extending Fourier Neural Operators for Modeling Parameterized and Coupled PDEs PDE-Transformer: Efficient and Versatile Transformers for Physics Simulations

Reference 3

Resolution: unresolved; no resolver link, observed 2026-07-30T21:35:26.002162Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 15e66cd7-2195-43cf-9e8f-edf66b3a70c5 · outbound

This paper cites Neural Operator: Graph Kernel Network for Partial Differential Equations.

Extending Fourier Neural Operators for Modeling Parameterized and Coupled PDEs Neural Operator: Graph Kernel Network for Partial Differential Equations

Reference 7

Resolution: unresolved; no resolver link, observed 2026-07-30T21:35:26.251335Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a13bd73d-05cf-4453-8c31-7329ca1543ac · outbound

This paper cites While the proposedhpFNO x exhibits a mild degradation at the largestν m, it still achieves the lowest overall errors (nRMSE≈0.015–0.018).

Extending Fourier Neural Operators for Modeling Parameterized and Coupled PDEs While the proposedhpFNO x exhibits a mild degradation at the largestν m, it still achieves the lowest overall errors (nRMSE≈0.015–0.018)

Reference 8

Resolution: malformed identifier; no resolver link, observed 2026-07-30T21:35:27.061835Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 11f9e412-e81f-44fc-8e39-d167c1507ed3 · outbound

This paper cites Detecting strange attractors in turbulence.

Extending Fourier Neural Operators for Modeling Parameterized and Coupled PDEs Detecting strange attractors in turbulence

Reference 9

Resolution: unresolved; no resolver link, observed 2026-07-30T21:35:26.393242Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 240d1e86-04ea-41a7-9489-fa0e9bbdfe7d · outbound

This paper cites Each variable is treated as an independent function,a(x) = (aα(x), aβ(x)), and discretized separately asa α,a β ∈R m.

Extending Fourier Neural Operators for Modeling Parameterized and Coupled PDEs Each variable is treated as an independent function,a(x) = (aα(x), aβ(x)), and discretized separately asa α,a β ∈R m

Reference 10

Resolution: unresolved; no resolver link, observed 2026-07-30T21:35:26.466017Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3a86e1c6-0347-4b17-817f-7fc33abc7c1a · outbound

This paper cites an unresolved cited work.

Extending Fourier Neural Operators for Modeling Parameterized and Coupled PDEs Unresolved cited work

Reference 11

Resolution: unresolved; no resolver link, observed 2026-07-30T21:35:26.539565Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c696c3ab-ee2c-41c2-a205-d143ba95ce7e · outbound

This paper cites an unresolved cited work.

Extending Fourier Neural Operators for Modeling Parameterized and Coupled PDEs Unresolved cited work

Reference 12

Resolution: unresolved; no resolver link, observed 2026-07-30T21:35:26.988568Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e13d11f9-48dd-493c-b13d-84e30831974e · outbound

This paper cites an unresolved cited work.

Extending Fourier Neural Operators for Modeling Parameterized and Coupled PDEs Unresolved cited work

Reference 14

Resolution: unresolved; no resolver link, observed 2026-07-30T21:35:26.711335Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7b7c8d65-ea6f-4bed-8cb4-9f98d07ac9e7 · outbound

This paper cites an unresolved cited work.

Extending Fourier Neural Operators for Modeling Parameterized and Coupled PDEs Unresolved cited work

Reference 15

Resolution: unresolved; no resolver link, observed 2026-07-30T21:35:26.783498Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 83065754-d57c-4560-bace-726bf29a48da · outbound

This paper cites an unresolved cited work.

Extending Fourier Neural Operators for Modeling Parameterized and Coupled PDEs Unresolved cited work

Reference 16

Resolution: unresolved; no resolver link, observed 2026-07-30T21:35:26.854891Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 48f7e377-37b2-4e8d-b039-2b97363ea88c · outbound

This paper cites All Figures present the two spatio-temporal fields, the electron densityn e(x, t)and the electric potentialϕ(x, t), in thet−xplane, in a heatmap format.

Extending Fourier Neural Operators for Modeling Parameterized and Coupled PDEs All Figures present the two spatio-temporal fields, the electron densityn e(x, t)and the electric potentialϕ(x, t), in thet−xplane, in a heatmap format

Reference 17

Resolution: unresolved; no resolver link, observed 2026-07-30T21:35:26.915101Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation eda6230b-c835-403d-948e-93e0ee3ceae7 · outbound

This paper cites Table 8 reports the performance of all considered models on ID test samples and OOD test samples.

Extending Fourier Neural Operators for Modeling Parameterized and Coupled PDEs Table 8 reports the performance of all considered models on ID test samples and OOD test samples

Reference 20

Resolution: unresolved; no resolver link, observed 2026-07-30T21:35:27.134099Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9497c580-4de5-4c16-ab96-085641ecd6e5 · outbound

This paper cites Table 11: Performance comparisons between the proposed methods and the baseline methods.

Extending Fourier Neural Operators for Modeling Parameterized and Coupled PDEs Table 11: Performance comparisons between the proposed methods and the baseline methods

Reference 23

Resolution: unresolved; no resolver link, observed 2026-07-30T21:35:27.316706Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 19cdfb43-1ab3-4ddf-b10f-d9bcd0ee22ee · outbound

This paper cites In the experiments described in the main body, we consider the Taylor variant; in the Appendix, we provide the results of both variants.

Extending Fourier Neural Operators for Modeling Parameterized and Coupled PDEs In the experiments described in the main body, we consider the Taylor variant; in the Appendix, we provide the results of both variants

Reference 128

Resolution: unresolved; no resolver link, observed 2026-07-30T21:35:26.637626Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b6d41dca-4d0b-49d8-8fbd-575d5a7dd050 · outbound

This paper cites Deeper or narrower configurations, such as a 3-layer network (width 256, nRMSE = 0.0200) or 3- layer network (width 32, nRMSE = 0.0230), show a mild degradation in performance.

Extending Fourier Neural Operators for Modeling Parameterized and Coupled PDEs Deeper or narrower configurations, such as a 3-layer network (width 256, nRMSE = 0.0200) or 3- layer network (width 32, nRMSE = 0.0230), show a mild degradation in performance

Reference 256

Resolution: unresolved; no resolver link, observed 2026-07-30T21:35:27.208267Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation feab0e22-939f-4319-ac83-f8bc24272238 · outbound

This paper cites an unresolved cited work.

Extending Fourier Neural Operators for Modeling Parameterized and Coupled PDEs Unresolved cited work

Reference 2014

Resolution: unresolved; no resolver link, observed 2026-07-30T21:35:27.269701Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 75dfa0a0-a793-4bcb-b34a-aa7cdc3068bd · outbound

This paper cites Adam: A Method for Stochastic Optimization.

Extending Fourier Neural Operators for Modeling Parameterized and Coupled PDEs Adam: A Method for Stochastic Optimization

Reference 2015

Resolution: unresolved; no resolver link, observed 2026-07-30T21:35:26.184495Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c7472d54-2583-4ef1-bf3a-53e1d88703bf · outbound

This paper cites Kingma and Jimmy Ba.

Extending Fourier Neural Operators for Modeling Parameterized and Coupled PDEs Kingma and Jimmy Ba

Reference 2021

Resolution: unresolved; no resolver link, observed 2026-07-30T21:35:26.147653Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0888e8ed-38a1-4378-b371-d039651e50a3 · outbound

This paper cites URLhttps: //openreview.net/forum?id=j3oQF9coJd.

Extending Fourier Neural Operators for Modeling Parameterized and Coupled PDEs URLhttps: //openreview.net/forum?id=j3oQF9coJd

Reference 2023

Resolution: unresolved; no resolver link, observed 2026-07-30T21:35:26.318444Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ee2a6f51-8e01-4f2b-99ac-3d9f66ffeb9f · outbound

This paper cites Projection-based model reduction for reacting flows.

Extending Fourier Neural Operators for Modeling Parameterized and Coupled PDEs Projection-based model reduction for reacting flows

Reference 2024

Resolution: unresolved; no resolver link, observed 2026-07-30T21:35:25.942271Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0afcb281-99c0-4764-9aaa-543f2a31f2f2 · outbound

This paper cites The Sol supercomputer at Arizona State University.

Extending Fourier Neural Operators for Modeling Parameterized and Coupled PDEs The Sol supercomputer at Arizona State University

Reference 2025

Resolution: unresolved; no resolver link, observed 2026-07-30T21:35:26.074420Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.