Paper Citation Record · LEDGER

A Geometry-Aware Message Passing Neural Network for Modeling Aerodynamics over Airfoils

As of 13 August 2026, this Paper Citation Record lists 28 of 28 outbound references and 2 inbound Pith citation observations for arXiv:2412.09399.

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

pith.paper-citation-record.v1
2412.09399 v2

Coverage vector

measured 28 of 28 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-11T17:10:51.643826Z

measured 30 of 30 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-13T06:32:02.005865+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-07T05:14:46.190904Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-19T10:22:14.694550Z

Reference resolution

28 of 28 outbound references displayed

verified exact0
verified fuzzy8
unresolved20
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 0942fdc2-00a2-46a6-a6e7-555e18063e6c · outbound

This paper cites Relational inductive biases, deep learning, and graph networks.

A Geometry-Aware Message Passing Neural Network for Modeling Aerodynamics over Airfoils Relational inductive biases, deep learning, and graph networks

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-11T17:10:51.547151Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8c967082-4291-4a45-ae33-86c65ea1de75 · outbound

This paper cites Bonnet, J.

A Geometry-Aware Message Passing Neural Network for Modeling Aerodynamics over Airfoils Bonnet, J

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T17:10:51.925809Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 243664c0-de48-4c5c-a2b7-f0ab68a424d8 · outbound

This paper cites an unresolved cited work.

A Geometry-Aware Message Passing Neural Network for Modeling Aerodynamics over Airfoils Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-08-11T17:10:51.916370Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 96ca364e-addd-49ef-8665-29493293be2d · outbound

This paper cites Casenave, B.

A Geometry-Aware Message Passing Neural Network for Modeling Aerodynamics over Airfoils Casenave, B

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T17:10:51.907535Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 3e5a806e-6d29-4478-bd83-3bd50c8e1f59 · outbound

This paper cites Fey and J.

A Geometry-Aware Message Passing Neural Network for Modeling Aerodynamics over Airfoils Fey and J

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-11T17:10:51.564523Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 050a1284-abaa-4d37-880b-4848dd018fe5 · outbound

This paper cites Gasteiger, J.

A Geometry-Aware Message Passing Neural Network for Modeling Aerodynamics over Airfoils Gasteiger, J

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T17:10:51.892658Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 05bd4b3e-1712-4157-861a-fa098e298ed9 · outbound

This paper cites Gilmer, S.

A Geometry-Aware Message Passing Neural Network for Modeling Aerodynamics over Airfoils Gilmer, S

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T17:10:51.884257Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 215dbe9c-dfc7-4982-a962-1a6d4f87e1ed · outbound

This paper cites an unresolved cited work.

A Geometry-Aware Message Passing Neural Network for Modeling Aerodynamics over Airfoils Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-11T17:10:51.875572Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 44f84b2d-a4d7-4142-891b-5264c730d451 · outbound

This paper cites an unresolved cited work.

A Geometry-Aware Message Passing Neural Network for Modeling Aerodynamics over Airfoils Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-11T17:10:51.864695Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation ba06dd98-5330-488c-9439-4b313f48600f · outbound

This paper cites Helwig, X.

A Geometry-Aware Message Passing Neural Network for Modeling Aerodynamics over Airfoils Helwig, X

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T17:10:51.854648Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation cbd9346a-090b-44be-914a-a9d98a94ca53 · outbound

This paper cites Adam: A Method for Stochastic Optimization.

A Geometry-Aware Message Passing Neural Network for Modeling Aerodynamics over Airfoils Adam: A Method for Stochastic Optimization

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-11T17:10:51.586125Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 40174850-c1c8-4559-ba10-6291825dd0dd · outbound

This paper cites Leyli Abadi, A.

A Geometry-Aware Message Passing Neural Network for Modeling Aerodynamics over Airfoils Leyli Abadi, A

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T17:10:51.844601Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 3983a502-d2cc-474e-a761-e648a7d03722 · outbound

This paper cites Neural Operator: Graph Kernel Network for Partial Differential Equations.

A Geometry-Aware Message Passing Neural Network for Modeling Aerodynamics over Airfoils Neural Operator: Graph Kernel Network for Partial Differential Equations

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-11T17:10:51.594157Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 774511f2-495b-4327-ade9-cb5b789b75e1 · outbound

This paper cites an unresolved cited work.

A Geometry-Aware Message Passing Neural Network for Modeling Aerodynamics over Airfoils Unresolved cited work

Reference 14

Resolution: unresolved; raw_fallback, observed 2026-08-11T17:10:51.834027Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 157e498e-9603-4c13-beff-f373ce48bca3 · outbound

This paper cites an unresolved cited work.

A Geometry-Aware Message Passing Neural Network for Modeling Aerodynamics over Airfoils Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-08-11T17:10:51.824379Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 345d3262-2bfa-465c-b3af-cd6a220bf8a3 · outbound

This paper cites an unresolved cited work.

A Geometry-Aware Message Passing Neural Network for Modeling Aerodynamics over Airfoils Unresolved cited work

Reference 16

Resolution: unresolved; raw_fallback, observed 2026-08-11T17:10:51.815417Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 75e5c6f7-c556-44b8-9f2b-6c0f01de3705 · outbound

This paper cites an unresolved cited work.

A Geometry-Aware Message Passing Neural Network for Modeling Aerodynamics over Airfoils Unresolved cited work

Reference 17

Resolution: unresolved; raw_fallback, observed 2026-08-11T17:10:51.806618Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 5bd51f24-dd6b-4474-afdf-682327eff1e4 · outbound

This paper cites an unresolved cited work.

A Geometry-Aware Message Passing Neural Network for Modeling Aerodynamics over Airfoils Unresolved cited work

Reference 18

Resolution: unresolved; raw_fallback, observed 2026-08-11T17:10:51.795930Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 86cd27f0-25c2-4d9a-af1a-029063605b9d · outbound

This paper cites an unresolved cited work.

A Geometry-Aware Message Passing Neural Network for Modeling Aerodynamics over Airfoils Unresolved cited work

Reference 19

Resolution: unresolved; raw_fallback, observed 2026-08-11T17:10:51.786509Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 4e77775a-091e-436c-bb71-ef522c4bfc8c · outbound

This paper cites Paszke, S.

A Geometry-Aware Message Passing Neural Network for Modeling Aerodynamics over Airfoils Paszke, S

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-11T17:10:51.620102Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d1fd0d9f-67e3-442f-9f1c-dcb97be662bc · outbound

This paper cites an unresolved cited work.

A Geometry-Aware Message Passing Neural Network for Modeling Aerodynamics over Airfoils Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-08-11T17:10:51.771573Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 0d485555-1388-480e-9af5-0239aa5daa27 · outbound

This paper cites an unresolved cited work.

A Geometry-Aware Message Passing Neural Network for Modeling Aerodynamics over Airfoils Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-08-11T17:10:51.760431Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 3cfec9b9-b666-4025-b54e-aef1e42b3e49 · outbound

This paper cites an unresolved cited work.

A Geometry-Aware Message Passing Neural Network for Modeling Aerodynamics over Airfoils Unresolved cited work

Reference 23

Resolution: unresolved; raw_fallback, observed 2026-08-11T17:10:51.750335Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 57693735-4087-48d0-972a-47db9c687b2d · outbound

This paper cites Vaswani, N.

A Geometry-Aware Message Passing Neural Network for Modeling Aerodynamics over Airfoils Vaswani, N

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T17:10:51.740135Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 8c58fb46-cad8-4471-90d8-005b6083bfdd · outbound

This paper cites an unresolved cited work.

A Geometry-Aware Message Passing Neural Network for Modeling Aerodynamics over Airfoils Unresolved cited work

Reference 25

Resolution: unresolved; raw_fallback, observed 2026-08-11T17:10:51.729330Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 5cb8d6e3-b4b2-4abb-9a6a-f1d1b42cbedb · outbound

This paper cites NeurIPS 2024 ML4CFD Competition: Harnessing Machine Learning for Computational Fluid Dynamics in Airfoil Design.

A Geometry-Aware Message Passing Neural Network for Modeling Aerodynamics over Airfoils NeurIPS 2024 ML4CFD Competition: Harnessing Machine Learning for Computational Fluid Dynamics in Airfoil Design

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-11T17:10:51.636841Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9965450f-ff19-4469-9ffb-2a9933461ec3 · outbound

This paper cites Artificial Intelligence for Science in Quantum, Atomistic, and Continuum Systems.

A Geometry-Aware Message Passing Neural Network for Modeling Aerodynamics over Airfoils Artificial Intelligence for Science in Quantum, Atomistic, and Continuum Systems

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-11T17:10:51.640771Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4247645a-50aa-4b51-851f-06de9236bd7b · outbound

This paper cites Zhang, J.

A Geometry-Aware Message Passing Neural Network for Modeling Aerodynamics over Airfoils Zhang, J

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T17:10:51.718222Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Pith citing papers

Observation b45a4dbe-3f77-490b-a68b-610ae8d103b1 · inbound

A Two-Phase Deep Learning Framework for Adaptive Time-Stepping in High-Speed Flow Modeling cites this paper.

A Two-Phase Deep Learning Framework for Adaptive Time-Stepping in High-Speed Flow Modeling A Geometry-Aware Message Passing Neural Network for Modeling Aerodynamics over Airfoils

Reference 36

Resolution: verified exact; arxiv_id, observed 2026-05-19T10:22:14.696306Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation a0d2fc15-0f3b-468d-9c2d-dc83db8bb50c · inbound

NeurIPS 2024 ML4CFD Competition: Results and Retrospective Analysis cites this paper.

NeurIPS 2024 ML4CFD Competition: Results and Retrospective Analysis A Geometry-Aware Message Passing Neural Network for Modeling Aerodynamics over Airfoils

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-07T05:14:46.190904Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.