Paper Citation Record · LEDGER

MscaleFNO: Multi-scale Fourier Neural Operator Learning for Oscillatory Function Spaces

As of 14 August 2026, this Paper Citation Record lists 17 of 17 outbound references and 4 inbound Pith citation observations for arXiv:2412.20183.

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

pith.paper-citation-record.v1
2412.20183 v1

Coverage vector

measured 17 of 17 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-10T23:32:57.373671Z

measured 21 of 21 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-14T06:32:32.682623+00:00

measured 4 of 4 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-10T19:32:41.811028Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-02T02:06:27.754353Z

Reference resolution

17 of 17 outbound references displayed

verified exact0
verified fuzzy5
unresolved12
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 1e439a18-da30-40b1-a826-6773ba3f3ed4 · outbound

This paper cites Boull´ e, C.

MscaleFNO: Multi-scale Fourier Neural Operator Learning for Oscillatory Function Spaces Boull´ e, C

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:32:57.611593Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 8674bff5-64ed-49aa-b6cc-2828beafdbf9 · outbound

This paper cites Boull´ e and A.

MscaleFNO: Multi-scale Fourier Neural Operator Learning for Oscillatory Function Spaces Boull´ e and A

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:32:57.600378Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation adbcf2ed-8fa1-4d3d-a89c-ffd67adbfab2 · outbound

This paper cites an unresolved cited work.

MscaleFNO: Multi-scale Fourier Neural Operator Learning for Oscillatory Function Spaces Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-08-10T23:32:57.589023Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 11ac1011-b28e-4036-a05d-f9b19ee57958 · outbound

This paper cites an unresolved cited work.

MscaleFNO: Multi-scale Fourier Neural Operator Learning for Oscillatory Function Spaces Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-08-10T23:32:57.577609Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 2f16614f-a4e5-41c9-b736-d997fc62d189 · outbound

This paper cites an unresolved cited work.

MscaleFNO: Multi-scale Fourier Neural Operator Learning for Oscillatory Function Spaces Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-08-10T23:32:57.563130Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 37802d81-43ea-4655-8c9a-89c12b2203de · outbound

This paper cites an unresolved cited work.

MscaleFNO: Multi-scale Fourier Neural Operator Learning for Oscillatory Function Spaces Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-08-10T23:32:57.550864Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 0ead081a-b27e-41b9-ad65-55d7743adb72 · outbound

This paper cites an unresolved cited work.

MscaleFNO: Multi-scale Fourier Neural Operator Learning for Oscillatory Function Spaces Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-10T23:32:57.538801Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 5cb7019b-7fb9-4be4-808c-380101695951 · outbound

This paper cites an unresolved cited work.

MscaleFNO: Multi-scale Fourier Neural Operator Learning for Oscillatory Function Spaces Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-10T23:32:57.526470Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation d1389d6a-9073-47b6-a82e-ecae50caece7 · outbound

This paper cites Mitigating spectral bias for the multiscale operator learning.

MscaleFNO: Multi-scale Fourier Neural Operator Learning for Oscillatory Function Spaces Mitigating spectral bias for the multiscale operator learning

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-10T23:32:57.335908Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5a1e9cb2-1e52-4dd8-8222-e6a48b7552a0 · outbound

This paper cites an unresolved cited work.

MscaleFNO: Multi-scale Fourier Neural Operator Learning for Oscillatory Function Spaces Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-10T23:32:57.511534Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 2f5defb3-3b82-44da-9dff-a64df5299a36 · outbound

This paper cites an unresolved cited work.

MscaleFNO: Multi-scale Fourier Neural Operator Learning for Oscillatory Function Spaces Unresolved cited work

Reference 11

Resolution: unresolved; raw_fallback, observed 2026-08-10T23:32:57.499350Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation b1dd858b-990f-475c-9c5e-7bbff280e302 · outbound

This paper cites Integrating Neural Operators with Diffusion Models Improves Spectral Representation in Turbulence Modeling.

MscaleFNO: Multi-scale Fourier Neural Operator Learning for Oscillatory Function Spaces Integrating Neural Operators with Diffusion Models Improves Spectral Representation in Turbulence Modeling

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-10T23:32:57.350901Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5a48e88b-0086-4f5a-a055-cc29d58d4d3d · outbound

This paper cites Rahaman, A.

MscaleFNO: Multi-scale Fourier Neural Operator Learning for Oscillatory Function Spaces Rahaman, A

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:32:57.486737Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation b36ad373-953e-4557-9798-2b8d6c92d52c · outbound

This paper cites Ronneberger, P.

MscaleFNO: Multi-scale Fourier Neural Operator Learning for Oscillatory Function Spaces Ronneberger, P

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:32:57.475017Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 3bc0ee69-426b-482e-b722-5bc1b54efa67 · outbound

This paper cites an unresolved cited work.

MscaleFNO: Multi-scale Fourier Neural Operator Learning for Oscillatory Function Spaces Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-08-10T23:32:57.462199Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation ce390347-c88b-417f-9eb2-c7a2ad2598d2 · outbound

This paper cites an unresolved cited work.

MscaleFNO: Multi-scale Fourier Neural Operator Learning for Oscillatory Function Spaces Unresolved cited work

Reference 16

Resolution: unresolved; raw_fallback, observed 2026-08-10T23:32:57.449749Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 47f1cc6c-f8c0-4353-8b8f-61d409bd1916 · outbound

This paper cites Zhang, W.

MscaleFNO: Multi-scale Fourier Neural Operator Learning for Oscillatory Function Spaces Zhang, W

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:32:57.436025Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Pith citing papers

Observation 02e0c6f9-570d-43aa-898d-1d0eb3fa0d8e · inbound

On understanding and overcoming spectral biases of deep neural network learning methods for solving PDEs cites this paper.

On understanding and overcoming spectral biases of deep neural network learning methods for solving PDEs MscaleFNO: Multi-scale Fourier Neural Operator Learning for Oscillatory Function Spaces

Reference 124

Resolution: unresolved; no resolver link, observed 2026-08-10T19:32:41.811028Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 577803ec-18d6-4f58-9dd2-73dfcbef53a1 · inbound

A Greedy PDE Router for Blending Neural Operators and Classical Methods cites this paper.

A Greedy PDE Router for Blending Neural Operators and Classical Methods MscaleFNO: Multi-scale Fourier Neural Operator Learning for Oscillatory Function Spaces

Reference 19

Resolution: verified exact; arxiv_id, observed 2026-05-18T12:32:36.228002Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation a027da67-ac21-459a-b38a-979c881ff182 · inbound

Generalized Spherical Neural Operators: Green's Function Formulation cites this paper.

Generalized Spherical Neural Operators: Green's Function Formulation MscaleFNO: Multi-scale Fourier Neural Operator Learning for Oscillatory Function Spaces

Reference 23

Resolution: verified exact; arxiv_id, observed 2026-05-16T23:08:40.073154Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation f0e4e2f2-34a3-48ca-a465-ecc893ce2fb5 · inbound

Correcting Neural Operator Spectral Bias via Diffusion Posterior Sampling with Sparse Observations cites this paper.

Correcting Neural Operator Spectral Bias via Diffusion Posterior Sampling with Sparse Observations MscaleFNO: Multi-scale Fourier Neural Operator Learning for Oscillatory Function Spaces

Reference 17

Resolution: verified exact; arxiv_id, observed 2026-07-02T02:06:27.757130Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.