Paper Citation Record · LEDGER

Spectral-inspired Operator Learning with Limited Data and Unknown Physics

As of 7 August 2026, this Paper Citation Record lists 16 of 16 outbound references and 0 inbound Pith citation observations for arXiv:2505.21573.

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

pith.paper-citation-record.v1
2505.21573 v3

Coverage vector

measured 16 of 16 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-05-25T08:30:15.509880Z

measured 16 of 16 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-07T06:34:17.273281+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

16 of 16 outbound references displayed

verified exact3
verified fuzzy10
unresolved2
parse uncertain0
malformed identifier0
metadata mismatch1

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 8737ff09-c091-4595-9349-7c0ab923b5cb · outbound

This paper cites Physics-Guided, Physics-Informed, and Physics-Encoded Neural Networks in Scientific Computing.

Spectral-inspired Operator Learning with Limited Data and Unknown Physics Physics-Guided, Physics-Informed, and Physics-Encoded Neural Networks in Scientific Computing

Reference 1

Resolution: verified exact; arxiv_id, observed 2026-05-25T08:30:31.466693Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 73cca18f-da52-4a7c-a7a9-db2419cf1360 · outbound

This paper cites Unisolver: PDE-Conditional Transformers Towards Universal Neural PDE Solvers.

Spectral-inspired Operator Learning with Limited Data and Unknown Physics Unisolver: PDE-Conditional Transformers Towards Universal Neural PDE Solvers

Reference 2

Resolution: verified exact; arxiv_id, observed 2026-05-25T08:30:31.459826Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 92d5636b-7055-4ef2-9c7a-6f561af9d2ef · outbound

This paper cites Dmitrii Kochkov, Jamie A Smith, Ayya Alieva, Qing Wang, Michael P Brenner, and Stephan Hoyer.

Spectral-inspired Operator Learning with Limited Data and Unknown Physics Dmitrii Kochkov, Jamie A Smith, Ayya Alieva, Qing Wang, Michael P Brenner, and Stephan Hoyer

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-05-25T08:30:32.304553Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 5b46b1e5-9914-4fe4-9370-fd235a871715 · outbound

This paper cites doi:10.1016/j.jcp.2019.108925.

Spectral-inspired Operator Learning with Limited Data and Unknown Physics doi:10.1016/j.jcp.2019.108925

Reference 4

Resolution: metadata mismatch; arxiv_id, observed 2026-05-25T08:30:30.987279Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation d98c6009-0fa1-44a8-b6c2-e9c118578c6c · outbound

This paper cites Recent Advances on Machine Learning for Computational Fluid Dynamics: A Survey.

Spectral-inspired Operator Learning with Limited Data and Unknown Physics Recent Advances on Machine Learning for Computational Fluid Dynamics: A Survey

Reference 5

Resolution: verified exact; arxiv_id, observed 2026-05-25T08:30:31.472817Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation e344693b-3cb1-46f4-b5e5-9a1aff90806c · outbound

This paper cites Gen.” denotes the resolution/time step used for generating high-fidelity data with spectral solvers. “DOL.

Spectral-inspired Operator Learning with Limited Data and Unknown Physics Gen.” denotes the resolution/time step used for generating high-fidelity data with spectral solvers. “DOL

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-05-25T08:30:32.300094Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 15581d61-9020-4c1d-9288-087a10f95630 · outbound

This paper cites In particular, the NSE dataset was generated using an open-source implementation from (Li et al., 2021).

Spectral-inspired Operator Learning with Limited Data and Unknown Physics In particular, the NSE dataset was generated using an open-source implementation from (Li et al., 2021)

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-05-25T08:30:32.311606Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation a9163b1d-07a9-45e5-a028-1becedb4c3ac · outbound

This paper cites an unresolved cited work.

Spectral-inspired Operator Learning with Limited Data and Unknown Physics Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-05-25T08:30:32.307699Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 928c6b3a-3501-4d37-a97b-cbc6a84b9e98 · outbound

This paper cites Details of baseline models are provided as follows: Fourier Neural Operator (FNO)(Li et al., 2021).

Spectral-inspired Operator Learning with Limited Data and Unknown Physics Details of baseline models are provided as follows: Fourier Neural Operator (FNO)(Li et al., 2021)

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-05-25T08:30:32.269148Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation cacfebfa-9d41-45ac-a92b-3621993c8af6 · outbound

This paper cites Factorized Fourier Neural Operator (FFNO)(Tran et al., 2023).

Spectral-inspired Operator Learning with Limited Data and Unknown Physics Factorized Fourier Neural Operator (FFNO)(Tran et al., 2023)

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-05-25T08:30:32.289176Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation e96d984e-320a-4637-88e1-5e788490ed67 · outbound

This paper cites CNext(Liu et al., 2022; Ohana et al., 2024).

Spectral-inspired Operator Learning with Limited Data and Unknown Physics CNext(Liu et al., 2022; Ohana et al., 2024)

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-05-25T08:30:32.292522Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 83a00cbd-0906-4dc2-9fff-9e304b560e10 · outbound

This paper cites Cross-Resolution Operator-learning Pipeline (CROP)(Gao et al., 2025).

Spectral-inspired Operator Learning with Limited Data and Unknown Physics Cross-Resolution Operator-learning Pipeline (CROP)(Gao et al., 2025)

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-05-25T08:30:32.280908Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 801326c8-21b4-4bb6-9f4f-6d42197da693 · outbound

This paper cites Physics-embedded Recurrent-Convolutional Neural Network (PeRCNN)(Rao et al., 2023).

Spectral-inspired Operator Learning with Limited Data and Unknown Physics Physics-embedded Recurrent-Convolutional Neural Network (PeRCNN)(Rao et al., 2023)

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-05-25T08:30:32.273149Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation eb3b26dd-7afb-4abd-92b1-ced7fc00ec44 · outbound

This paper cites Physics-encoded Spectral Attention Network (PeSANet)(Wan et al., 2025).

Spectral-inspired Operator Learning with Limited Data and Unknown Physics Physics-encoded Spectral Attention Network (PeSANet)(Wan et al., 2025)

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-05-25T08:30:32.277053Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 8efb9029-cd27-4201-ba57-fff2664cdcbe · outbound

This paper cites For hyperparameter tuning, we searched over the network width (32, 64.

Spectral-inspired Operator Learning with Limited Data and Unknown Physics For hyperparameter tuning, we searched over the network width (32, 64

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-05-25T08:30:32.285497Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 948eb151-8e2f-4571-970e-d7cd82389e37 · outbound

This paper cites an unresolved cited work.

Spectral-inspired Operator Learning with Limited Data and Unknown Physics Unresolved cited work

Reference 16

Resolution: unresolved; raw_fallback, observed 2026-05-25T08:30:32.295878Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Pith citing papers

No inbound Pith citation observations are available.