Paper Citation Record · LEDGER

Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries

As of 22 August 2026, this Paper Citation Record lists 44 of 44 outbound references and 2 inbound Pith citation observations for arXiv:2411.15178.

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

pith.paper-citation-record.v1
2411.15178 v3

Coverage vector

measured 44 of 44 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-12T18:29:14.499710Z

measured 46 of 46 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-22T06:32:14.747728+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-09T15:42:31.757357Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-07T06:05:53.675825Z

Reference resolution

44 of 44 outbound references displayed

verified exact1
verified fuzzy9
unresolved33
parse uncertain0
malformed identifier1
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation a06aa44c-1786-4b68-9de8-e2c1d15c42b0 · outbound

This paper cites MAgNet: Mesh Agnostic Neural PDE Solver.

Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries MAgNet: Mesh Agnostic Neural PDE Solver

Reference 1

Resolution: verified exact; local_arxiv, observed 2026-08-12T18:29:14.783479Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 4f7159a7-75b2-43d0-b94b-aaa3834ead65 · outbound

This paper cites an unresolved cited work.

Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-08-12T18:29:15.319044Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 75a25189-8b9f-4261-b6eb-de0dd5e230b5 · outbound

This paper cites Bronstein, Joan Bruna, Yann LeCun, Arthur Szlam, and Pierre Van- dergheynst.

Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries Bronstein, Joan Bruna, Yann LeCun, Arthur Szlam, and Pierre Van- dergheynst

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T18:29:15.303914Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation bd161689-1226-4040-bb60-ad04096d739c · outbound

This paper cites an unresolved cited work.

Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-08-12T18:29:15.288623Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 3d449ff3-9a3c-4deb-a2fc-e2a37d410f5f · outbound

This paper cites an unresolved cited work.

Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-08-12T18:29:15.273103Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 3e2525d5-74b1-4f7c-b1e0-8beb28a1c6cf · outbound

This paper cites an unresolved cited work.

Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-08-12T18:29:15.258447Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation f89457c9-20ab-4f61-9f51-87acd38ece81 · outbound

This paper cites an unresolved cited work.

Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-12T18:29:15.242326Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 528d2607-34ea-41c6-96ab-ef70ae1be0cf · outbound

This paper cites Schoenholz, Patrick F.

Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries Schoenholz, Patrick F

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T18:29:15.227229Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation f3221af7-fd62-406b-ac05-666cdc459007 · outbound

This paper cites an unresolved cited work.

Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries Unresolved cited work

Reference 9

Resolution: malformed identifier; no resolver link, observed 2026-08-12T18:29:14.304289Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0931ea3a-356c-44f2-bf5c-14d6ac4ac26e · outbound

This paper cites an unresolved cited work.

Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-12T18:29:15.212127Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 5b910a79-4330-44b1-8f57-9ebba461831c · outbound

This paper cites an unresolved cited work.

Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries Unresolved cited work

Reference 11

Resolution: unresolved; raw_fallback, observed 2026-08-12T18:29:15.196026Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 202a9ea6-9f19-482b-8df0-cedb26f07fce · outbound

This paper cites Hamilton, Zhitao Ying, and Jure Leskovec.

Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries Hamilton, Zhitao Ying, and Jure Leskovec

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T18:29:15.180208Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 2758819e-1951-4218-b4f4-d8d90fdd5f0c · outbound

This paper cites GNOT: A General Neural Operator Transformer for Operator Learning.

Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries GNOT: A General Neural Operator Transformer for Operator Learning

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-12T18:29:14.325375Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 51844214-c8e7-4855-985e-e7c6642d1fa4 · outbound

This paper cites MgNO: Efficient Parameterization of Linear Operators via Multigrid.

Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries MgNO: Efficient Parameterization of Linear Operators via Multigrid

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-12T18:29:14.330942Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 450f3f30-dbd2-477f-a6cf-71f906d909e5 · outbound

This paper cites Kingma and Jimmy Ba.

Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries Kingma and Jimmy Ba

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T18:29:15.164326Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation a57aa467-1786-427b-962a-de3490c33aad · outbound

This paper cites Kovachki, Zongyi Li, Burigede Liu, Kamyar Azizzadenesheli, Kaushik Bhattacharya, Andrew M.

Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries Kovachki, Zongyi Li, Burigede Liu, Kamyar Azizzadenesheli, Kaushik Bhattacharya, Andrew M

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T18:29:15.146551Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation e5f928bd-8f29-4c4c-8e0c-2a3740a1612f · outbound

This paper cites an unresolved cited work.

Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries Unresolved cited work

Reference 17

Resolution: unresolved; raw_fallback, observed 2026-08-12T18:29:15.130348Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 82a05c58-1f82-464b-84f0-67498cec2572 · outbound

This paper cites Stuart, and Anima Anandkumar.

Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries Stuart, and Anima Anandkumar

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T18:29:15.113559Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation b053190b-0200-4504-8763-4163382d8394 · outbound

This paper cites Kovachki, Kamyar Azizzadenesheli, Burigede Liu, Andrew M.

Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries Kovachki, Kamyar Azizzadenesheli, Burigede Liu, Andrew M

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T18:29:15.096571Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 6880d4a3-687e-4229-8157-456806bf7d9b · outbound

This paper cites an unresolved cited work.

Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries Unresolved cited work

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-12T18:29:14.362467Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 15725c69-2d4c-499b-a077-d32f721e0e9a · outbound

This paper cites an unresolved cited work.

Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-08-12T18:29:15.079294Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation e6796525-f1cd-45ba-9d76-0586c53d6053 · outbound

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

Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries Neural Operator: Graph Kernel Network for Partial Differential Equations

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-12T18:29:14.373169Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 25aaed13-c39d-4ef6-b212-d10fd31c1a77 · outbound

This paper cites Geometry-Informed Neural Operator for Large-Scale 3D PDEs.

Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries Geometry-Informed Neural Operator for Large-Scale 3D PDEs

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-12T18:29:14.379042Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d050fc98-fa96-451b-a9a6-c01a864ed350 · outbound

This paper cites an unresolved cited work.

Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries Unresolved cited work

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-12T18:29:14.386322Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cb7ca429-93d1-4e2b-8a38-744e50726fc6 · outbound

This paper cites an unresolved cited work.

Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries Unresolved cited work

Reference 25

Resolution: unresolved; raw_fallback, observed 2026-08-12T18:29:15.052109Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation ad7a4fdd-abad-41e5-8618-6e6dbbdd91c5 · outbound

This paper cites an unresolved cited work.

Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries Unresolved cited work

Reference 26

Resolution: unresolved; raw_fallback, observed 2026-08-12T18:29:15.033986Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 16ef8533-171a-4276-a2cb-e1ecbabface1 · outbound

This paper cites an unresolved cited work.

Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries Unresolved cited work

Reference 27

Resolution: unresolved; raw_fallback, observed 2026-08-12T18:29:15.017848Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation b84aa9ee-b5af-4465-a127-312f44411935 · outbound

This paper cites Brunton, and J.

Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries Brunton, and J

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T18:29:15.000487Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation c824f1af-661c-404d-9d1b-4c3ca78fb014 · outbound

This paper cites an unresolved cited work.

Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries Unresolved cited work

Reference 29

Resolution: unresolved; raw_fallback, observed 2026-08-12T18:29:14.984034Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 60e0805c-3afe-4cd0-a5c6-6570a2ce52c3 · outbound

This paper cites Qi, Hao Su, Kaichun Mo, and Leonidas J.

Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries Qi, Hao Su, Kaichun Mo, and Leonidas J

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T18:29:14.969021Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation f829e309-0050-4148-b008-80b7ebff81d3 · outbound

This paper cites an unresolved cited work.

Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries Unresolved cited work

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-12T18:29:14.421742Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2ea941be-5583-482d-a66a-3df71b3566de · outbound

This paper cites an unresolved cited work.

Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries Unresolved cited work

Reference 32

Resolution: unresolved; raw_fallback, observed 2026-08-12T18:29:14.943258Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 7a240054-b040-44cf-835c-f1e9149302c9 · outbound

This paper cites Rumelhart, Geoffrey E.

Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries Rumelhart, Geoffrey E

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-12T18:29:14.431960Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f8911be7-0de8-4dd6-b996-8afa651abef3 · outbound

This paper cites an unresolved cited work.

Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries Unresolved cited work

Reference 34

Resolution: unresolved; raw_fallback, observed 2026-08-12T18:29:14.916071Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation d1abacd1-05b8-435a-8ac0-46b79e4e9423 · outbound

This paper cites an unresolved cited work.

Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries Unresolved cited work

Reference 35

Resolution: unresolved; raw_fallback, observed 2026-08-12T18:29:14.899259Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation b56c7d49-de5f-4a51-9cc6-d7f4e0e53091 · outbound

This paper cites an unresolved cited work.

Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries Unresolved cited work

Reference 36

Resolution: unresolved; raw_fallback, observed 2026-08-12T18:29:14.882006Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation d413e7b4-04f7-4d67-b3a0-cfd00fb74c00 · outbound

This paper cites an unresolved cited work.

Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries Unresolved cited work

Reference 37

Resolution: unresolved; raw_fallback, observed 2026-08-12T18:29:14.865706Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation cf800c40-9a3c-44b1-bd23-2bb5fb54d2c9 · outbound

This paper cites an unresolved cited work.

Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries Unresolved cited work

Reference 38

Resolution: unresolved; no resolver link, observed 2026-08-12T18:29:14.470136Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b1ec9ac8-6fe8-4dea-b03a-a046fc042324 · outbound

This paper cites Improved Operator Learning by Orthogonal Attention.

Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries Improved Operator Learning by Orthogonal Attention

Reference 39

Resolution: unresolved; no resolver link, observed 2026-08-12T18:29:14.483419Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7fc005db-b140-4244-8d43-d89541b3da12 · outbound

This paper cites an unresolved cited work.

Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries Unresolved cited work

Reference 40

Resolution: unresolved; raw_fallback, observed 2026-08-12T18:29:14.837169Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation ede481bb-efae-4c6c-baa2-9c49490c587e · outbound

This paper cites an unresolved cited work.

Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries Unresolved cited work

Reference 41

Resolution: unresolved; raw_fallback, observed 2026-08-12T18:29:14.816822Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 3b7d043e-60df-4e9d-8c9f-01c62af97086 · outbound

This paper cites an unresolved cited work.

Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries Unresolved cited work

Reference 42

Resolution: unresolved; raw_fallback, observed 2026-08-12T18:29:14.800354Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 131bca14-f8d3-4a04-8d1c-4bdebf0f7d34 · outbound

This paper cites Solving High-Dimensional PDEs with Latent Spectral Models.

Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries Solving High-Dimensional PDEs with Latent Spectral Models

Reference 2023

Resolution: unresolved; no resolver link, observed 2026-08-12T18:29:14.464477Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5ec920af-a4bd-4076-b063-cee2ce142e3f · outbound

This paper cites Transolver: A Fast Transformer Solver for PDEs on General Geometries.

Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries Transolver: A Fast Transformer Solver for PDEs on General Geometries

Reference 2024

Resolution: unresolved; no resolver link, observed 2026-08-12T18:29:14.475401Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation 5472448d-dd21-4962-9c47-5550ae9b0003 · inbound

Neural Preconditioning Operator for Efficient PDE Solves cites this paper.

Neural Preconditioning Operator for Efficient PDE Solves Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-09T15:42:31.757357Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ee4122de-0413-4506-a7eb-08419cee3dc4 · inbound

LaDEEP: A Deep Learning-based Surrogate Model for Large Deformation of Elastic-Plastic Solids cites this paper.

LaDEEP: A Deep Learning-based Surrogate Model for Large Deformation of Elastic-Plastic Solids Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries

Reference 36

Resolution: verified exact; local_arxiv, observed 2026-08-07T06:05:53.681741Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.