Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-15T19:11:56.793977Z
Paper Citation Record · LEDGER
LFR-PINO: A Layered Fourier Reduced Physics-Informed Neural Operator for Parametric PDEs
As of 20 August 2026, this Paper Citation Record lists 32 of 32 outbound references and 0 inbound Pith citation observations for arXiv:2506.17582.
A citation records a reference. It does not transfer a finding from one paper to another.
Coverage vector
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-20T06:33:59.587034+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links
A source-named dated measurement, never combined with another source.
Source: cited_works
Reference resolution
32 of 32 outbound references displayed
- verified exact2
- verified fuzzy11
- unresolved17
- parse uncertain0
- malformed identifier2
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 3f022929-154d-4d34-a00f-3e0c0a55f5b8 · outbound
This paper cites an unresolved cited work.
LFR-PINO: A Layered Fourier Reduced Physics-Informed Neural Operator for Parametric PDEs Unresolved cited work
Reference 1
- Resolution
- unresolved
- raw_fallback, observed 2026-08-15T19:11:57.119011Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 131281d3-9fce-43d5-be1a-eaf3062c9050 · outbound
This paper cites an unresolved cited work.
LFR-PINO: A Layered Fourier Reduced Physics-Informed Neural Operator for Parametric PDEs Unresolved cited work
Reference 2
- Resolution
- unresolved
- raw_fallback, observed 2026-08-15T19:11:57.110785Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation c74a4cbc-69eb-49dd-9351-5baf9af04c1c · outbound
This paper cites Zienkiewicz, R.
LFR-PINO: A Layered Fourier Reduced Physics-Informed Neural Operator for Parametric PDEs Zienkiewicz, R
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T19:11:57.103145Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 1ab49e87-7a76-4438-8ff7-4f2e4439cbae · outbound
This paper cites Godunov and I.
LFR-PINO: A Layered Fourier Reduced Physics-Informed Neural Operator for Parametric PDEs Godunov and I
Reference 4
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T19:11:57.093370Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 6c189fe2-5254-4219-9423-560ce6d45482 · outbound
This paper cites Eymard, T.
LFR-PINO: A Layered Fourier Reduced Physics-Informed Neural Operator for Parametric PDEs Eymard, T
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T19:11:57.085699Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation b3fa2936-084b-46f3-8932-3b61444038dc · outbound
This paper cites an unresolved cited work.
LFR-PINO: A Layered Fourier Reduced Physics-Informed Neural Operator for Parametric PDEs Unresolved cited work
Reference 6
- Resolution
- unresolved
- raw_fallback, observed 2026-08-15T19:11:57.077370Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 881ec914-b394-4468-9403-df1896ba123b · outbound
This paper cites an unresolved cited work.
LFR-PINO: A Layered Fourier Reduced Physics-Informed Neural Operator for Parametric PDEs Unresolved cited work
Reference 7
- Resolution
- unresolved
- raw_fallback, observed 2026-08-15T19:11:57.067870Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation e36e7f52-50bd-4a3a-863e-18fe39559412 · outbound
This paper cites Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets.
LFR-PINO: A Layered Fourier Reduced Physics-Informed Neural Operator for Parametric PDEs Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets
Reference 8
- Resolution
- unresolved
- no resolver link, observed 2026-08-15T19:11:56.717464Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 2f8a00ac-3e74-4bf0-9b8f-96dda81738e2 · outbound
This paper cites Meta-Auto-Decoder for Solving Parametric Partial Differential Equations.
LFR-PINO: A Layered Fourier Reduced Physics-Informed Neural Operator for Parametric PDEs Meta-Auto-Decoder for Solving Parametric Partial Differential Equations
Reference 9
- Resolution
- verified exact
- local_arxiv, observed 2026-08-15T19:11:56.910003Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation de819b62-000a-421a-8f60-5ee6ad53f550 · outbound
This paper cites Belbute-Peres, F.
LFR-PINO: A Layered Fourier Reduced Physics-Informed Neural Operator for Parametric PDEs Belbute-Peres, F
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T19:11:57.060469Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation a636db74-f3fd-4d82-803c-8fdfeecf8e36 · outbound
This paper cites an unresolved cited work.
LFR-PINO: A Layered Fourier Reduced Physics-Informed Neural Operator for Parametric PDEs Unresolved cited work
Reference 11
- Resolution
- unresolved
- raw_fallback, observed 2026-08-15T19:11:57.051623Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 1c5661f3-ffbc-4f0b-a347-f62f2737dc74 · outbound
This paper cites Understanding training and generalization in deep learning by Fourier analysis.
LFR-PINO: A Layered Fourier Reduced Physics-Informed Neural Operator for Parametric PDEs Understanding training and generalization in deep learning by Fourier analysis
Reference 12
- Resolution
- unresolved
- no resolver link, observed 2026-08-15T19:11:56.732531Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation e967798d-8ba5-412a-bf3d-26f411ca8a64 · outbound
This paper cites LeCun, Y.
LFR-PINO: A Layered Fourier Reduced Physics-Informed Neural Operator for Parametric PDEs LeCun, Y
Reference 13
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T19:11:57.043507Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 6d115a96-bd06-460e-8439-41eb1f3d6828 · outbound
This paper cites Raissi, P.
LFR-PINO: A Layered Fourier Reduced Physics-Informed Neural Operator for Parametric PDEs Raissi, P
Reference 14
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T19:11:57.035333Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation dbd5399c-6590-4241-b1f0-1b51bdf70b0c · outbound
This paper cites Sirignano and K.
LFR-PINO: A Layered Fourier Reduced Physics-Informed Neural Operator for Parametric PDEs Sirignano and K
Reference 15
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T19:11:57.026737Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation dc3d40c2-c73d-4c16-8ab6-e3787b760e18 · outbound
This paper cites Yu,et al.,The deep ritz method: a deep learning-based numerical algorithm for solving variational problems, Communications in Mathematics and Statistics 6 (2018), pp.
LFR-PINO: A Layered Fourier Reduced Physics-Informed Neural Operator for Parametric PDEs Yu,et al.,The deep ritz method: a deep learning-based numerical algorithm for solving variational problems, Communications in Mathematics and Statistics 6 (2018), pp
Reference 16
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T19:11:57.018851Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 551f0b87-41b2-4a63-bddb-c55dea2d5b78 · outbound
This paper cites an unresolved cited work.
LFR-PINO: A Layered Fourier Reduced Physics-Informed Neural Operator for Parametric PDEs Unresolved cited work
Reference 17
- Resolution
- unresolved
- raw_fallback, observed 2026-08-15T19:11:57.009742Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation e957f737-d050-4a57-9354-6dce8901a4b0 · outbound
This paper cites Raissi, A.
LFR-PINO: A Layered Fourier Reduced Physics-Informed Neural Operator for Parametric PDEs Raissi, A
Reference 18
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T19:11:57.001654Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 78e0de77-8567-4d6c-a227-0d7b788cfecd · outbound
This paper cites an unresolved cited work.
LFR-PINO: A Layered Fourier Reduced Physics-Informed Neural Operator for Parametric PDEs Unresolved cited work
Reference 19
- Resolution
- unresolved
- raw_fallback, observed 2026-08-15T19:11:56.993246Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation a1229dba-a834-4ac8-bca9-f36589668669 · outbound
This paper cites an unresolved cited work.
LFR-PINO: A Layered Fourier Reduced Physics-Informed Neural Operator for Parametric PDEs Unresolved cited work
Reference 20
- Resolution
- unresolved
- raw_fallback, observed 2026-08-15T19:11:56.984416Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation b60ca831-241a-44cf-bd5a-c99e7c5a759e · outbound
This paper cites Neural Operator: Graph Kernel Network for Partial Differential Equations.
LFR-PINO: A Layered Fourier Reduced Physics-Informed Neural Operator for Parametric PDEs Neural Operator: Graph Kernel Network for Partial Differential Equations
Reference 21
- Resolution
- unresolved
- no resolver link, observed 2026-08-15T19:11:56.763344Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation f01ee33d-cf7c-4082-80f5-dd972a644999 · outbound
This paper cites an unresolved cited work.
LFR-PINO: A Layered Fourier Reduced Physics-Informed Neural Operator for Parametric PDEs Unresolved cited work
Reference 22
- Resolution
- unresolved
- raw_fallback, observed 2026-08-15T19:11:56.976052Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 4c6c164d-9855-4c18-a394-fa362425c5a6 · outbound
This paper cites Penwarden, S.
LFR-PINO: A Layered Fourier Reduced Physics-Informed Neural Operator for Parametric PDEs Penwarden, S
Reference 23
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T19:11:56.967811Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation a78bbfbc-88b7-43cb-826c-5f42177e8b48 · outbound
This paper cites an unresolved cited work.
LFR-PINO: A Layered Fourier Reduced Physics-Informed Neural Operator for Parametric PDEs Unresolved cited work
Reference 24
- Resolution
- unresolved
- no resolver link, observed 2026-08-15T19:11:56.772276Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 967c107a-18aa-49bc-ae37-8ccbf708aac0 · outbound
This paper cites an unresolved cited work.
LFR-PINO: A Layered Fourier Reduced Physics-Informed Neural Operator for Parametric PDEs Unresolved cited work
Reference 25
- Resolution
- verified exact
- doi, observed 2026-08-06T23:36:19.416689Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 3dc6ff8c-5919-40ca-85e0-c8dfaf764d33 · outbound
This paper cites Zou and G.E.
LFR-PINO: A Layered Fourier Reduced Physics-Informed Neural Operator for Parametric PDEs Zou and G.E
Reference 26
- Resolution
- unresolved
- no resolver link, observed 2026-08-15T19:11:56.777931Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 345a8d4f-2090-421e-a865-7bb5939d2d06 · outbound
This paper cites HyperNetworks.
LFR-PINO: A Layered Fourier Reduced Physics-Informed Neural Operator for Parametric PDEs HyperNetworks
Reference 27
- Resolution
- unresolved
- no resolver link, observed 2026-08-15T19:11:56.780379Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 690cfc24-e6df-41b9-9d7c-2218d25c98c6 · outbound
This paper cites an unresolved cited work.
LFR-PINO: A Layered Fourier Reduced Physics-Informed Neural Operator for Parametric PDEs Unresolved cited work
Reference 28
- Resolution
- unresolved
- raw_fallback, observed 2026-08-15T19:11:56.958756Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 02ed87ec-9148-4de1-94ad-dd90b7d80ea4 · outbound
This paper cites Xiang, W.
LFR-PINO: A Layered Fourier Reduced Physics-Informed Neural Operator for Parametric PDEs Xiang, W
Reference 29
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T19:11:56.949763Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation a72139ed-41a4-40b6-ba9c-b86b6b4c98d0 · outbound
This paper cites an unresolved cited work.
LFR-PINO: A Layered Fourier Reduced Physics-Informed Neural Operator for Parametric PDEs Unresolved cited work
Reference 30
- Resolution
- unresolved
- raw_fallback, observed 2026-08-15T19:11:56.942349Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 26326323-6e54-4b47-b0db-f190b99dda5c · outbound
This paper cites Iserles,A first course in the numerical analysis of differential equations, 44, Cambridge university press, 2009.
LFR-PINO: A Layered Fourier Reduced Physics-Informed Neural Operator for Parametric PDEs Iserles,A first course in the numerical analysis of differential equations, 44, Cambridge university press, 2009
Reference 31
- Resolution
- malformed identifier
- raw_fallback, observed 2026-08-15T19:11:56.934267Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation a22814ba-665b-45e9-8fce-de16ae5a8764 · outbound
This paper cites Iserles,A first course in the numerical analysis of differential equations, 44, Cambridge university press, 2009.
LFR-PINO: A Layered Fourier Reduced Physics-Informed Neural Operator for Parametric PDEs Iserles,A first course in the numerical analysis of differential equations, 44, Cambridge university press, 2009
Reference 31
- Resolution
- malformed identifier
- raw_fallback, observed 2026-08-15T19:11:56.925229Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Pith citing papers
No inbound Pith citation observations are available.