Paper Citation Record · LEDGER

GITO: Graph-Informed Transformer Operator for Learning Complex Partial Differential Equations

As of 7 August 2026, this Paper Citation Record lists 37 of 37 outbound references and 1 inbound Pith citation observation for arXiv:2506.13906.

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

pith.paper-citation-record.v1
2506.13906 v1

Coverage vector

measured 37 of 37 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T00:29:34.371251Z

measured 38 of 38 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-07T06:34:17.273281+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-05T15:53:00.193734Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-05T15:53:00.260765Z

Reference resolution

37 of 37 outbound references displayed

verified exact0
verified fuzzy10
unresolved27
parse uncertain0
malformed identifier0
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External citation measurements

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Outbound references

Observation d88f8622-081d-49ea-8e1e-b4c49a78c1a8 · outbound

This paper cites Springer, 2014.

GITO: Graph-Informed Transformer Operator for Learning Complex Partial Differential Equations Springer, 2014

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T00:29:37.280273Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 38174ec9-e432-48ca-8e8a-cb065b4e41ac · outbound

This paper cites Bayesian deep convolutional encoder–decoder networks for surrogate modeling and uncertainty quantification.Journal of Computational Physics, 366:415–447, 2018.

GITO: Graph-Informed Transformer Operator for Learning Complex Partial Differential Equations Bayesian deep convolutional encoder–decoder networks for surrogate modeling and uncertainty quantification.Journal of Computational Physics, 366:415–447, 2018

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T00:29:37.074508Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 0dbe1429-5149-4b02-87a9-0ec97bd928e4 · outbound

This paper cites Prediction of aerodynamic flow fields using convolutional neural networks.Computational Mechanics, 64:525–545, 2019.

GITO: Graph-Informed Transformer Operator for Learning Complex Partial Differential Equations Prediction of aerodynamic flow fields using convolutional neural networks.Computational Mechanics, 64:525–545, 2019

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T00:29:36.825410Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation db1af5ab-0f12-4872-815e-2b851185555d · outbound

This paper cites an unresolved cited work.

GITO: Graph-Informed Transformer Operator for Learning Complex Partial Differential Equations Unresolved cited work

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-07T00:29:31.554729Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4b94d56e-392b-4bd5-937d-be8cb4fc338d · outbound

This paper cites Gpt-pinn: Generative pre-trained physics-informed neural networks toward non-intrusive meta-learning of parametric pdes.Finite Elements in Analysis and Design, 228:104047, 2024.

GITO: Graph-Informed Transformer Operator for Learning Complex Partial Differential Equations Gpt-pinn: Generative pre-trained physics-informed neural networks toward non-intrusive meta-learning of parametric pdes.Finite Elements in Analysis and Design, 228:104047, 2024

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T00:29:36.568045Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 5eebc7bd-480d-456c-80d4-92373fb8b3a2 · outbound

This paper cites an unresolved cited work.

GITO: Graph-Informed Transformer Operator for Learning Complex Partial Differential Equations Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-08-07T00:29:36.301946Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 915cc7eb-3456-40bc-87d3-6343d5af57a0 · outbound

This paper cites Learning nonlinear operators via deeponet based on the universal approximation theorem of operators.Nature machine intelligence, 3(3): 218–229, 2021.

GITO: Graph-Informed Transformer Operator for Learning Complex Partial Differential Equations Learning nonlinear operators via deeponet based on the universal approximation theorem of operators.Nature machine intelligence, 3(3): 218–229, 2021

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-07T00:29:31.883578Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2658423f-296b-4d86-b347-301ccc2c5528 · outbound

This paper cites Fourier Neural Operator for Parametric Partial Differential Equations.

GITO: Graph-Informed Transformer Operator for Learning Complex Partial Differential Equations Fourier Neural Operator for Parametric Partial Differential Equations

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-07T00:29:31.997258Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4621ae6e-bb33-4094-ac5d-d9296e6fc54c · outbound

This paper cites Attention is all you need.Advances in neural information processing systems, 30, 2017.

GITO: Graph-Informed Transformer Operator for Learning Complex Partial Differential Equations Attention is all you need.Advances in neural information processing systems, 30, 2017

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-07T00:29:32.082356Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9ab57e0f-617c-4cfe-ab11-54f07a788851 · outbound

This paper cites Choose a transformer: Fourier or galerkin.Advances in neural information processing systems, 34: 24924–24940, 2021.

GITO: Graph-Informed Transformer Operator for Learning Complex Partial Differential Equations Choose a transformer: Fourier or galerkin.Advances in neural information processing systems, 34: 24924–24940, 2021

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T00:29:36.061746Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 88e65926-bf98-4c6d-a23f-c4af83830046 · outbound

This paper cites Predicting Physics in Mesh-reduced Space with Temporal Attention.

GITO: Graph-Informed Transformer Operator for Learning Complex Partial Differential Equations Predicting Physics in Mesh-reduced Space with Temporal Attention

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-07T00:29:32.193921Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fbd164d8-3686-4a0e-ab64-ace3eefaf6f3 · outbound

This paper cites Transformer for Partial Differential Equations' Operator Learning.

GITO: Graph-Informed Transformer Operator for Learning Complex Partial Differential Equations Transformer for Partial Differential Equations' Operator Learning

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-07T00:29:32.247990Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bea72011-870f-4808-9c51-38bb7222e277 · outbound

This paper cites Gnot: A general neural operator transformer for operator learning.

GITO: Graph-Informed Transformer Operator for Learning Complex Partial Differential Equations Gnot: A general neural operator transformer for operator learning

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-07T00:29:32.332973Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 48681d2a-f73f-4cda-a0dc-4408ae89b680 · outbound

This paper cites Universal physics transformers: A framework for efficiently scaling neural operators.Advances in Neural Information Processing Systems, 37:25152–25194, 2024.

GITO: Graph-Informed Transformer Operator for Learning Complex Partial Differential Equations Universal physics transformers: A framework for efficiently scaling neural operators.Advances in Neural Information Processing Systems, 37:25152–25194, 2024

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-07T00:29:32.444877Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f03ead74-9f2d-4e5f-bae4-10847196986e · outbound

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

GITO: Graph-Informed Transformer Operator for Learning Complex Partial Differential Equations Transolver: A Fast Transformer Solver for PDEs on General Geometries

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-07T00:29:32.524857Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation dc562d79-c6f7-4cae-b1ab-24de2a98ee66 · outbound

This paper cites HAMLET: Graph Transformer Neural Operator for Partial Differential Equations.

GITO: Graph-Informed Transformer Operator for Learning Complex Partial Differential Equations HAMLET: Graph Transformer Neural Operator for Partial Differential Equations

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-07T00:29:32.613048Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7c784cec-8a13-42f7-85b0-e6dfb8594c8c · outbound

This paper cites Transformers for modeling physical systems.Neural Networks, 146: 272–289, 2022.

GITO: Graph-Informed Transformer Operator for Learning Complex Partial Differential Equations Transformers for modeling physical systems.Neural Networks, 146: 272–289, 2022

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T00:29:35.775517Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 6ac08c9c-63c1-4afa-902e-d656be3abaac · outbound

This paper cites Continuous Spatiotemporal Transformers.

GITO: Graph-Informed Transformer Operator for Learning Complex Partial Differential Equations Continuous Spatiotemporal Transformers

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-07T00:29:32.812874Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fe0f1db8-64ed-4d95-8ad0-40d60d024a0f · outbound

This paper cites Scalable transformer for pde surrogate modeling.Advances in Neural Information Processing Systems, 36:28010–28039, 2023.

GITO: Graph-Informed Transformer Operator for Learning Complex Partial Differential Equations Scalable transformer for pde surrogate modeling.Advances in Neural Information Processing Systems, 36:28010–28039, 2023

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T00:29:35.525934Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 831d3145-3489-4f17-8495-538375eac13c · outbound

This paper cites Positional Knowledge is All You Need: Position-induced Transformer (PiT) for Operator Learning.

GITO: Graph-Informed Transformer Operator for Learning Complex Partial Differential Equations Positional Knowledge is All You Need: Position-induced Transformer (PiT) for Operator Learning

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-07T00:29:32.958311Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 746943c1-c68b-4a12-a19a-f79a3bd6b5fe · outbound

This paper cites Message Passing Neural PDE Solvers.

GITO: Graph-Informed Transformer Operator for Learning Complex Partial Differential Equations Message Passing Neural PDE Solvers

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-07T00:29:33.032066Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c3a8eaf3-7a96-461f-ab7d-79aea7ad6fab · outbound

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

GITO: Graph-Informed Transformer Operator for Learning Complex Partial Differential Equations Neural Operator: Graph Kernel Network for Partial Differential Equations

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-07T00:29:33.094158Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d69c0fbc-1d10-4612-b2c7-ee55692ad1fb · outbound

This paper cites Graph networks as learnable physics engines for inference and control.

GITO: Graph-Informed Transformer Operator for Learning Complex Partial Differential Equations Graph networks as learnable physics engines for inference and control

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T00:29:35.315768Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation e554990f-e25c-43e2-a8ee-119cc269a82e · outbound

This paper cites Learning skillful medium-range global weather forecasting.Science, 382(6677):1416–1421, 2023.

GITO: Graph-Informed Transformer Operator for Learning Complex Partial Differential Equations Learning skillful medium-range global weather forecasting.Science, 382(6677):1416–1421, 2023

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-07T00:29:33.205729Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a24592a4-98f9-43ad-b380-3fc4b485e629 · outbound

This paper cites Graph Neural Networks Exponentially Lose Expressive Power for Node Classification.

GITO: Graph-Informed Transformer Operator for Learning Complex Partial Differential Equations Graph Neural Networks Exponentially Lose Expressive Power for Node Classification

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-07T00:29:33.289341Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 60a764d4-4f29-4db7-8ab7-baba5c953e92 · outbound

This paper cites On the Bottleneck of Graph Neural Networks and its Practical Implications.

GITO: Graph-Informed Transformer Operator for Learning Complex Partial Differential Equations On the Bottleneck of Graph Neural Networks and its Practical Implications

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-07T00:29:33.364660Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 837c1ea1-70cd-4213-8510-0822c3912fef · outbound

This paper cites A Generalization of Transformer Networks to Graphs.

GITO: Graph-Informed Transformer Operator for Learning Complex Partial Differential Equations A Generalization of Transformer Networks to Graphs

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-07T00:29:33.432823Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 41c557aa-07cd-46a2-a787-c08fd1917ca2 · outbound

This paper cites Do transformers really perform badly for graph representation?Advances in neural information processing systems, 34:28877–28888, 2021.

GITO: Graph-Informed Transformer Operator for Learning Complex Partial Differential Equations Do transformers really perform badly for graph representation?Advances in neural information processing systems, 34:28877–28888, 2021

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-07T00:29:33.517985Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 18ea0ae0-ee5c-4491-b1f4-99404d38d970 · outbound

This paper cites GraphiT: Encoding Graph Structure in Transformers.

GITO: Graph-Informed Transformer Operator for Learning Complex Partial Differential Equations GraphiT: Encoding Graph Structure in Transformers

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-07T00:29:33.580126Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 02b8cc60-b3a2-4d11-a338-a77f2814e92e · outbound

This paper cites Recipe for a general, powerful, scalable graph transformer.Advances in Neural Information Processing Systems, 35:14501–14515, 2022.

GITO: Graph-Informed Transformer Operator for Learning Complex Partial Differential Equations Recipe for a general, powerful, scalable graph transformer.Advances in Neural Information Processing Systems, 35:14501–14515, 2022

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-07T00:29:33.661519Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d66b8911-6822-43c9-92df-971e56e1622d · outbound

This paper cites Exphormer: Sparse transformers for graphs.

GITO: Graph-Informed Transformer Operator for Learning Complex Partial Differential Equations Exphormer: Sparse transformers for graphs

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T00:29:35.069178Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 6b2529ca-e820-4049-b1e0-c99bc9893ba8 · outbound

This paper cites Scaling physics-informed hard constraints with mixture-of-experts.

GITO: Graph-Informed Transformer Operator for Learning Complex Partial Differential Equations Scaling physics-informed hard constraints with mixture-of-experts

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-07T00:29:33.777167Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 48fdb0a2-6b00-494b-a4d1-d8aeef4afa40 · outbound

This paper cites How Attentive are Graph Attention Networks?.

GITO: Graph-Informed Transformer Operator for Learning Complex Partial Differential Equations How Attentive are Graph Attention Networks?

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-07T00:29:33.884601Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fd78b97f-5764-4675-a6f7-af4e67301674 · outbound

This paper cites Fourier Neural Operator with Learned Deformations for PDEs on General Geometries.

GITO: Graph-Informed Transformer Operator for Learning Complex Partial Differential Equations Fourier Neural Operator with Learned Deformations for PDEs on General Geometries

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-07T00:29:33.966479Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9a29d156-f354-4e08-b013-430b57b0e253 · outbound

This paper cites MIONet: Learning multiple-input operators via tensor product.

GITO: Graph-Informed Transformer Operator for Learning Complex Partial Differential Equations MIONet: Learning multiple-input operators via tensor product

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-07T00:29:34.066103Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 847cdae7-a81d-476c-84b3-827f3cb59ecd · outbound

This paper cites Pointnet++: Deep hierarchical feature learning on point sets in a metric space.Advances in neural information processing systems, 30, 2017.

GITO: Graph-Informed Transformer Operator for Learning Complex Partial Differential Equations Pointnet++: Deep hierarchical feature learning on point sets in a metric space.Advances in neural information processing systems, 30, 2017

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-07T00:29:34.218178Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation aad4636f-96c2-4776-87d9-3ff72dea0c29 · outbound

This paper cites Elsevier, 2014.

GITO: Graph-Informed Transformer Operator for Learning Complex Partial Differential Equations Elsevier, 2014

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T00:29:34.796961Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Pith citing papers

Observation f4c66dd6-d217-44af-ae3e-4e882b86d6ba · inbound

DETNO: A Diffusion-Enhanced Transformer Neural Operator for Long-Term Traffic Forecasting cites this paper.

DETNO: A Diffusion-Enhanced Transformer Neural Operator for Long-Term Traffic Forecasting GITO: Graph-Informed Transformer Operator for Learning Complex Partial Differential Equations

Reference 29

Resolution: verified exact; local_arxiv, observed 2026-08-05T15:53:00.264879Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.