Paper Citation Record · LEDGER

Self-composing neural operators for high-frequency and multiscale PDE surrogates

As of 19 August 2026, this Paper Citation Record lists 55 of 55 outbound references and 4 inbound Pith citation observations for arXiv:2508.20650.

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

pith.paper-citation-record.v1
2508.20650 v2

Coverage vector

measured 55 of 55 reference resolution

Typed states for the displayed outbound observations.

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measured 59 of 59 standing notices

One-hop event checks from named stored sources.

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measured 4 of 4 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-07-03T22:32:58.936039Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-03T22:39:01.268430Z

Reference resolution

55 of 55 outbound references displayed

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External citation measurements

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Outbound references

Observation b8aeb877-b19f-4375-9724-93e423b849ca · outbound

This paper cites an unresolved cited work.

Self-composing neural operators for high-frequency and multiscale PDE surrogates Unresolved cited work

Reference 1

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Self-composing neural operators for high-frequency and multiscale PDE surrogates Unresolved cited work

Reference 2

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Observation 021e3b52-ba8a-45a1-b7e9-62a00b1ace0e · outbound

This paper cites Cao, Choose a transformer: Fourier or galerkin, Advances in Neural Information Processing Systems, 34 (2021).

Self-composing neural operators for high-frequency and multiscale PDE surrogates Cao, Choose a transformer: Fourier or galerkin, Advances in Neural Information Processing Systems, 34 (2021)

Reference 3

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This paper cites Learning Neural Operators on Riemannian Manifolds.

Self-composing neural operators for high-frequency and multiscale PDE surrogates Learning Neural Operators on Riemannian Manifolds

Reference 4

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Self-composing neural operators for high-frequency and multiscale PDE surrogates Unresolved cited work

Reference 5

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Self-composing neural operators for high-frequency and multiscale PDE surrogates Unresolved cited work

Reference 6

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Self-composing neural operators for high-frequency and multiscale PDE surrogates Unresolved cited work

Reference 7

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Self-composing neural operators for high-frequency and multiscale PDE surrogates Unresolved cited work

Reference 8

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Self-composing neural operators for high-frequency and multiscale PDE surrogates Unresolved cited work

Reference 9

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Self-composing neural operators for high-frequency and multiscale PDE surrogates Unresolved cited work

Reference 10

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Observation 50c97496-dcac-4bbd-abd8-739ce5767704 · outbound

This paper cites E , A Proposal on Machine Learning via Dynamical Systems , Communications in Mathe- matics and Statistics, 5 (2017), pp.

Self-composing neural operators for high-frequency and multiscale PDE surrogates E , A Proposal on Machine Learning via Dynamical Systems , Communications in Mathe- matics and Statistics, 5 (2017), pp

Reference 11

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Self-composing neural operators for high-frequency and multiscale PDE surrogates Unresolved cited work

Reference 12

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This paper cites Geng, X.-Y.

Self-composing neural operators for high-frequency and multiscale PDE surrogates Geng, X.-Y

Reference 13

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Self-composing neural operators for high-frequency and multiscale PDE surrogates Gregor and Y

Reference 14

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This paper cites Adaptive Fourier Neural Operators: Efficient Token Mixers for Transformers.

Self-composing neural operators for high-frequency and multiscale PDE surrogates Adaptive Fourier Neural Operators: Efficient Token Mixers for Transformers

Reference 15

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This paper cites Gupta, X.

Self-composing neural operators for high-frequency and multiscale PDE surrogates Gupta, X

Reference 16

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Observation 768fb264-4236-4f57-8316-9df66bf0a4da · outbound

This paper cites Haber, L.

Self-composing neural operators for high-frequency and multiscale PDE surrogates Haber, L

Reference 17

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Observation bb481455-4405-41f4-8b28-537d5ab535d5 · outbound

This paper cites Hackbusch , Multi-grid methods and applications , vol.

Self-composing neural operators for high-frequency and multiscale PDE surrogates Hackbusch , Multi-grid methods and applications , vol

Reference 18

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Self-composing neural operators for high-frequency and multiscale PDE surrogates Unresolved cited work

Reference 19

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Self-composing neural operators for high-frequency and multiscale PDE surrogates Unresolved cited work

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Self-composing neural operators for high-frequency and multiscale PDE surrogates Unresolved cited work

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Self-composing neural operators for high-frequency and multiscale PDE surrogates He and J

Reference 22

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This paper cites an unresolved cited work.

Self-composing neural operators for high-frequency and multiscale PDE surrogates Unresolved cited work

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Self-composing neural operators for high-frequency and multiscale PDE surrogates Unresolved cited work

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Self-composing neural operators for high-frequency and multiscale PDE surrogates Unresolved cited work

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Self-composing neural operators for high-frequency and multiscale PDE surrogates Hu and P

Reference 26

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Self-composing neural operators for high-frequency and multiscale PDE surrogates Unresolved cited work

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Self-composing neural operators for high-frequency and multiscale PDE surrogates Unresolved cited work

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Self-composing neural operators for high-frequency and multiscale PDE surrogates Neural Operator: Learning Maps Between Function Spaces

Reference 29

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Self-composing neural operators for high-frequency and multiscale PDE surrogates Kovachki, Z

Reference 30

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Self-composing neural operators for high-frequency and multiscale PDE surrogates Nonlocality and Nonlinearity Implies Universality in Operator Learning

Reference 31

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Self-composing neural operators for high-frequency and multiscale PDE surrogates Fourier Neural Operator with Learned Deformations for PDEs on General Geometries

Reference 32

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Self-composing neural operators for high-frequency and multiscale PDE surrogates Unresolved cited work

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Self-composing neural operators for high-frequency and multiscale PDE surrogates Unresolved cited work

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Self-composing neural operators for high-frequency and multiscale PDE surrogates Unresolved cited work

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Self-composing neural operators for high-frequency and multiscale PDE surrogates Unresolved cited work

Reference 36

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This paper cites Transolver++: An Accurate Neural Solver for PDEs on Million-Scale Geometries.

Self-composing neural operators for high-frequency and multiscale PDE surrogates Transolver++: An Accurate Neural Solver for PDEs on Million-Scale Geometries

Reference 37

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Self-composing neural operators for high-frequency and multiscale PDE surrogates Marwah, A

Reference 38

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Self-composing neural operators for high-frequency and multiscale PDE surrogates Osnabrugge, S

Reference 39

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Observation af477472-46aa-48ed-b945-14fbc7a4accb · outbound

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Self-composing neural operators for high-frequency and multiscale PDE surrogates FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators

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Self-composing neural operators for high-frequency and multiscale PDE surrogates Unresolved cited work

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Self-composing neural operators for high-frequency and multiscale PDE surrogates Raonic, R

Reference 42

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Observation 0af66b0d-d930-4cf8-8a93-6361c46bf50b · outbound

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Self-composing neural operators for high-frequency and multiscale PDE surrogates Ronneberger, P

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:49:50.221834Z

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Self-composing neural operators for high-frequency and multiscale PDE surrogates Trottenberg, C

Reference 44

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Self-composing neural operators for high-frequency and multiscale PDE surrogates V aswani, N

Reference 45

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Self-composing neural operators for high-frequency and multiscale PDE surrogates Solving High-Dimensional PDEs with Latent Spectral Models

Reference 46

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This paper cites Xu , Theory of multilevel methods , vol.

Self-composing neural operators for high-frequency and multiscale PDE surrogates Xu , Theory of multilevel methods , vol

Reference 47

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:49:50.169677Z

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Observation 91529543-918f-4c8f-ae47-38d34bd2d806 · outbound

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Self-composing neural operators for high-frequency and multiscale PDE surrogates Unresolved cited work

Reference 48

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Observation 8d3a6dd8-a379-472f-9e84-f9b9c8bf5f94 · outbound

This paper cites A Physics-Guided Neural Operator Learning Approach to Model Biological Tissues from Digital Image Correlation Measurements.

Self-composing neural operators for high-frequency and multiscale PDE surrogates A Physics-Guided Neural Operator Learning Approach to Model Biological Tissues from Digital Image Correlation Measurements

Reference 49

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Self-composing neural operators for high-frequency and multiscale PDE surrogates Point Cloud Neural Operator for Parametric PDEs on Complex and Variable Geometries

Reference 50

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Observation 5c8e27bf-89dc-484f-a977-a31988e71ade · outbound

This paper cites OpenBreastUS: Benchmarking Neural Operators for Wave Imaging Using Breast Ultrasound Computed Tomography.

Self-composing neural operators for high-frequency and multiscale PDE surrogates OpenBreastUS: Benchmarking Neural Operators for Wave Imaging Using Breast Ultrasound Computed Tomography

Reference 51

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Self-composing neural operators for high-frequency and multiscale PDE surrogates Zhang, J

Reference 52

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:49:50.133199Z

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Observation 5564adea-9a22-4a83-a3c8-f669ffa185f4 · outbound

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Self-composing neural operators for high-frequency and multiscale PDE surrogates Unresolved cited work

Reference 53

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 10e6ded1-64bf-4467-95a9-9d842974203d · outbound

This paper cites an unresolved cited work.

Self-composing neural operators for high-frequency and multiscale PDE surrogates Unresolved cited work

Reference 54

Resolution: unresolved; raw_fallback, observed 2026-08-15T16:49:50.103399Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation afdd4d46-dd76-4647-aaf9-44720ffc2492 · outbound

This paper cites an unresolved cited work.

Self-composing neural operators for high-frequency and multiscale PDE surrogates Unresolved cited work

Reference 55

Resolution: unresolved; raw_fallback, observed 2026-08-15T16:49:50.088400Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Pith citing papers

Observation ab0f15e5-9250-459c-8057-6997fefe52a2 · inbound

Neural Flow Operators can Approximate any Operator: Abstract Frameworks and Universal Approximations cites this paper.

Neural Flow Operators can Approximate any Operator: Abstract Frameworks and Universal Approximations Self-composing neural operators for high-frequency and multiscale PDE surrogates

Reference 126

Resolution: verified exact; arxiv_id, observed 2026-08-04T01:51:47.953126Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 3ddf92b3-306d-4230-99c2-31c54eba051e · inbound

Neural Flow Operators can Approximate any Operator: Abstract Frameworks and Universal Approximations cites this paper.

Neural Flow Operators can Approximate any Operator: Abstract Frameworks and Universal Approximations Self-composing neural operators for high-frequency and multiscale PDE surrogates

Reference 30

Resolution: verified exact; arxiv_id, observed 2026-08-04T01:51:47.953126Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 4c4b0598-1264-471c-ab53-ca9e005b507f · inbound

McMg: A Learned Phase-Space Multi-channel Multigrid Preconditioner for Helmholtz Equation cites this paper.

McMg: A Learned Phase-Space Multi-channel Multigrid Preconditioner for Helmholtz Equation Self-composing neural operators for high-frequency and multiscale PDE surrogates

Reference 72

Resolution: verified exact; arxiv_id, observed 2026-08-04T01:51:47.953126Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 2f90de52-c80e-4151-8097-3116bac45d65 · inbound

McMg: A Learned Phase-Space Multi-channel Multigrid Preconditioner for Helmholtz Equation cites this paper.

McMg: A Learned Phase-Space Multi-channel Multigrid Preconditioner for Helmholtz Equation Self-composing neural operators for high-frequency and multiscale PDE surrogates

Reference 72

Resolution: verified exact; arxiv_id, observed 2026-08-04T01:51:47.953126Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.