Paper Citation Record · LEDGER

A discontinuous Galerkin plane wave neural network method for Helmholtz equation and Maxwell's equations

As of 14 August 2026, this Paper Citation Record lists 37 of 37 outbound references and 0 inbound Pith citation observations for arXiv:2506.09309.

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

pith.paper-citation-record.v1
2506.09309 v1

Coverage vector

measured 37 of 37 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T05:01:21.651282Z

measured 37 of 37 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 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

37 of 37 outbound references displayed

verified exact0
verified fuzzy26
unresolved10
parse uncertain0
malformed identifier1
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 17038de9-cf49-4952-8020-4d5107c8c6d0 · outbound

This paper cites Ainsworth and J.

A discontinuous Galerkin plane wave neural network method for Helmholtz equation and Maxwell's equations Ainsworth and J

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:01:22.054308Z

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 d86678a9-d833-4a92-85ca-0f5fb30a8f20 · outbound

This paper cites Ammari, B.

A discontinuous Galerkin plane wave neural network method for Helmholtz equation and Maxwell's equations Ammari, B

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:01:22.044655Z

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 e8929124-bb0b-4eed-9603-9fe7248df7da · outbound

This paper cites an unresolved cited work.

A discontinuous Galerkin plane wave neural network method for Helmholtz equation and Maxwell's equations Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-08-07T05:01:22.034879Z

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 d89de45f-be7d-4f10-a775-34ef69c2ca05 · outbound

This paper cites Berg and K.

A discontinuous Galerkin plane wave neural network method for Helmholtz equation and Maxwell's equations Berg and K

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:01:22.026005Z

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 3f86fbb4-42bd-40a3-a683-a32ad9f6511c · outbound

This paper cites Cybenko, Approximation by superpositions of a sigmoidal function, Math.

A discontinuous Galerkin plane wave neural network method for Helmholtz equation and Maxwell's equations Cybenko, Approximation by superpositions of a sigmoidal function, Math

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:01:22.017283Z

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 bc5874fd-1a62-4734-a10e-87ae26723597 · outbound

This paper cites an unresolved cited work.

A discontinuous Galerkin plane wave neural network method for Helmholtz equation and Maxwell's equations Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-08-07T05:01:22.008204Z

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 dfc39e40-44a7-413e-9c60-4d2adb2f86e0 · outbound

This paper cites Folland, Real Analysis: Modern Techniques and Their Applications, Pure Appl.

A discontinuous Galerkin plane wave neural network method for Helmholtz equation and Maxwell's equations Folland, Real Analysis: Modern Techniques and Their Applications, Pure Appl

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:01:21.999488Z

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 dfed79f4-a8c2-43ae-bcf3-ff19be1af34f · outbound

This paper cites Gittelson, R.

A discontinuous Galerkin plane wave neural network method for Helmholtz equation and Maxwell's equations Gittelson, R

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:01:21.989962Z

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 834bc5ad-c41f-43fa-87b0-2a5654246739 · outbound

This paper cites an unresolved cited work.

A discontinuous Galerkin plane wave neural network method for Helmholtz equation and Maxwell's equations Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-07T05:01:21.980308Z

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 f5d55fce-8df5-46da-b6d7-6821d97a0532 · outbound

This paper cites Hiptmair, A.

A discontinuous Galerkin plane wave neural network method for Helmholtz equation and Maxwell's equations Hiptmair, A

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:01:21.970336Z

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 12e344dd-c035-4037-9ace-354e711d9178 · outbound

This paper cites Hiptmair, A.

A discontinuous Galerkin plane wave neural network method for Helmholtz equation and Maxwell's equations Hiptmair, A

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:01:21.959957Z

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 447e2e71-c164-42c9-9532-ad3b8933ad4d · outbound

This paper cites Hiptmair, A.

A discontinuous Galerkin plane wave neural network method for Helmholtz equation and Maxwell's equations Hiptmair, A

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:01:21.949542Z

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 f7902c21-6bc9-41a3-9389-d914ada9700b · outbound

This paper cites Hornik, Approximation capabilities of multilayer feedforward networks, Neural Netw., 4(1991), pp.

A discontinuous Galerkin plane wave neural network method for Helmholtz equation and Maxwell's equations Hornik, Approximation capabilities of multilayer feedforward networks, Neural Netw., 4(1991), pp

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:01:21.939789Z

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 77c25e0f-e48f-4c08-a774-3cde5a1b45e6 · outbound

This paper cites Hu and L.

A discontinuous Galerkin plane wave neural network method for Helmholtz equation and Maxwell's equations Hu and L

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:01:21.929750Z

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 b8360454-ccc8-47bd-b722-b255b51854ad · outbound

This paper cites Hu and L.

A discontinuous Galerkin plane wave neural network method for Helmholtz equation and Maxwell's equations Hu and L

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:01:21.920039Z

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 498b088e-8cf8-4e0d-a05c-ce1e93edd3d4 · outbound

This paper cites Hu and L.

A discontinuous Galerkin plane wave neural network method for Helmholtz equation and Maxwell's equations Hu and L

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:01:21.910321Z

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 56f472e1-9130-4b8c-ac77-d40738e3a8cd · outbound

This paper cites Huttunen, P.

A discontinuous Galerkin plane wave neural network method for Helmholtz equation and Maxwell's equations Huttunen, P

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:01:21.900084Z

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 f3995b91-b690-4e6d-aee5-9c44f2c45991 · outbound

This paper cites Huttunen, J.

A discontinuous Galerkin plane wave neural network method for Helmholtz equation and Maxwell's equations Huttunen, J

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:01:21.888917Z

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 c7490cfd-d97e-4e0d-a732-c32bfe39cee9 · outbound

This paper cites Variational Physics-Informed Neural Networks For Solving Partial Differential Equations.

A discontinuous Galerkin plane wave neural network method for Helmholtz equation and Maxwell's equations Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-07T05:01:21.584192Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 23cab569-2a43-48cf-932b-1089531743e4 · outbound

This paper cites Leshno, V.

A discontinuous Galerkin plane wave neural network method for Helmholtz equation and Maxwell's equations Leshno, V

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:01:21.878697Z

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 77327649-a3f5-4a2b-9633-fa7421f43ef6 · outbound

This paper cites an unresolved cited work.

A discontinuous Galerkin plane wave neural network method for Helmholtz equation and Maxwell's equations Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-08-07T05:01:21.868498Z

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 7be7e7d0-d6a3-4b6e-a501-3579e8b92973 · outbound

This paper cites Moiola and I.

A discontinuous Galerkin plane wave neural network method for Helmholtz equation and Maxwell's equations Moiola and I

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:01:21.857932Z

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 d4cc8bc3-25ec-4359-95f7-2f5c72922db6 · outbound

This paper cites Moiola, R.

A discontinuous Galerkin plane wave neural network method for Helmholtz equation and Maxwell's equations Moiola, R

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:01:21.848628Z

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 625468b8-f6f2-40c4-b291-b13bc1f47b2e · outbound

This paper cites Monk and D.

A discontinuous Galerkin plane wave neural network method for Helmholtz equation and Maxwell's equations Monk and D

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:01:21.839626Z

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 20cd512b-be56-49e2-bd18-c0492a5612ad · outbound

This paper cites Parolin, D.

A discontinuous Galerkin plane wave neural network method for Helmholtz equation and Maxwell's equations Parolin, D

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:01:21.830124Z

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 a4f709d4-507f-4288-b111-50f5d8f8f35e · outbound

This paper cites an unresolved cited work.

A discontinuous Galerkin plane wave neural network method for Helmholtz equation and Maxwell's equations Unresolved cited work

Reference 26

Resolution: unresolved; raw_fallback, observed 2026-08-07T05:01:21.820120Z

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 142daac9-4274-4d06-94ff-fa9006b9c206 · outbound

This paper cites an unresolved cited work.

A discontinuous Galerkin plane wave neural network method for Helmholtz equation and Maxwell's equations Unresolved cited work

Reference 27

Resolution: unresolved; raw_fallback, observed 2026-08-07T05:01:21.810102Z

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 1cdf3eff-9ab4-401f-be6c-9c3785d465a6 · outbound

This paper cites Petersen, M.

A discontinuous Galerkin plane wave neural network method for Helmholtz equation and Maxwell's equations Petersen, M

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:01:21.800299Z

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 4492e86f-cfc3-4bb4-9b41-bbbb75cb7f61 · outbound

This paper cites Raissi, P.

A discontinuous Galerkin plane wave neural network method for Helmholtz equation and Maxwell's equations Raissi, P

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:01:21.790421Z

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 434414ae-1173-4aef-8726-d383f859389c · outbound

This paper cites Error estimates of residual minimization using neural networks for linear PDEs.

A discontinuous Galerkin plane wave neural network method for Helmholtz equation and Maxwell's equations Error estimates of residual minimization using neural networks for linear PDEs

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-07T05:01:21.624675Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 91d4410f-e58e-4ee4-b7f3-465288b0292a · outbound

This paper cites Yeung, K.

A discontinuous Galerkin plane wave neural network method for Helmholtz equation and Maxwell's equations Yeung, K

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:01:21.780311Z

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 64a24508-8270-409f-a6c7-53e702698450 · outbound

This paper cites Yuan and Q.

A discontinuous Galerkin plane wave neural network method for Helmholtz equation and Maxwell's equations Yuan and Q

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:01:21.767934Z

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 69e58470-824a-4fa4-86b0-1edf9d8f2101 · outbound

This paper cites an unresolved cited work.

A discontinuous Galerkin plane wave neural network method for Helmholtz equation and Maxwell's equations Unresolved cited work

Reference 33

Resolution: malformed identifier; raw_fallback, observed 2026-08-07T05:01:21.756885Z

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 d4b00613-7c30-40be-b663-da09696c24a1 · outbound

This paper cites Yuan and Q.

A discontinuous Galerkin plane wave neural network method for Helmholtz equation and Maxwell's equations Yuan and Q

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:01:21.746831Z

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 74943f1c-9f8a-4f12-bf57-ee635c4e123c · outbound

This paper cites an unresolved cited work.

A discontinuous Galerkin plane wave neural network method for Helmholtz equation and Maxwell's equations Unresolved cited work

Reference 35

Resolution: unresolved; raw_fallback, observed 2026-08-07T05:01:21.735501Z

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 9a8aae5d-a64d-4e9c-a31b-9d543b8fd2fc · outbound

This paper cites Zhang, C.

A discontinuous Galerkin plane wave neural network method for Helmholtz equation and Maxwell's equations Zhang, C

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:01:21.724920Z

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 fbef3a18-9b70-479a-a5cf-3b18221cb17b · outbound

This paper cites an unresolved cited work.

A discontinuous Galerkin plane wave neural network method for Helmholtz equation and Maxwell's equations Unresolved cited work

Reference 37

Resolution: unresolved; raw_fallback, observed 2026-08-07T05:01:21.713176Z

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

No inbound Pith citation observations are available.