Paper Citation Record · LEDGER

Transformer for Partial Differential Equations' Operator Learning

As of 8 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 42 inbound Pith citation observations for arXiv:2205.13671.

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pith.paper-citation-record.v1
2205.13671 v3

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measured 42 of 42 standing notices

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Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+00:00

measured 42 of 42 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-07T21:49:41.411813Z

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Source: arxiv_reference, observed 2026-08-05T02:28:24.338817Z

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46
arxiv_reference, observed 2026-08-05T02:28:24.338817Z

Outbound references

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Pith citing papers

Observation eac5a3db-7eaf-47fb-a496-10f8fe9d13b8 · inbound

TAEN: A Model-Constrained Tikhonov Autoencoder Network for Forward and Inverse Problems cites this paper.

TAEN: A Model-Constrained Tikhonov Autoencoder Network for Forward and Inverse Problems Transformer for Partial Differential Equations' Operator Learning

Reference 48

Resolution: verified exact; arxiv_id, observed 2026-05-23T07:32:42.780217Z

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Observation c8bc9129-1b7d-41ff-b824-7ac5e0a8c213 · inbound

Machine learning for modelling unstructured grid data in computational physics: a review cites this paper.

Machine learning for modelling unstructured grid data in computational physics: a review Transformer for Partial Differential Equations' Operator Learning

Reference 232

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Observation 9a4d1f8e-115b-487a-a970-86c2ed023a40 · inbound

Learning High-dimensional Ionic Model Dynamics Using Fourier Neural Operators cites this paper.

Learning High-dimensional Ionic Model Dynamics Using Fourier Neural Operators Transformer for Partial Differential Equations' Operator Learning

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-07T15:42:54.944738Z

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Observation 3d506c59-4171-472d-b4ca-3eab4c5bb3a6 · inbound

Neural Interpretable PDEs: Harmonizing Fourier Insights with Attention for Scalable and Interpretable Physics Discovery cites this paper.

Neural Interpretable PDEs: Harmonizing Fourier Insights with Attention for Scalable and Interpretable Physics Discovery Transformer for Partial Differential Equations' Operator Learning

Reference 2021

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Observation db6de5bb-feeb-453f-89ba-65a9258c6fdb · inbound

FourierFlow: Frequency-aware Flow Matching for Generative Turbulence Modeling cites this paper.

FourierFlow: Frequency-aware Flow Matching for Generative Turbulence Modeling Transformer for Partial Differential Equations' Operator Learning

Reference 27

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Observation d028e873-0e98-4473-bee1-5091cb8b77f2 · 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 Transformer for Partial Differential Equations' Operator Learning

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-07T06:05:53.385068Z

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Observation ae24f956-d4e9-4767-8601-7bcc46c153d1 · inbound

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning cites this paper.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Transformer for Partial Differential Equations' Operator Learning

Reference 61

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Observation ef1a6721-663f-4444-8b22-3676a5e29a2d · inbound

Learning Mappings in Mesh-based Simulations cites this paper.

Learning Mappings in Mesh-based Simulations Transformer for Partial Differential Equations' Operator Learning

Reference 43

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Observation 00031610-2122-43bd-8e6a-b0468ea6e71e · inbound

Accelerating PDE-Constrained Optimization by the Derivative of Neural Operators cites this paper.

Accelerating PDE-Constrained Optimization by the Derivative of Neural Operators Transformer for Partial Differential Equations' Operator Learning

Reference 2020

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

GITO: Graph-Informed Transformer Operator for Learning Complex Partial Differential Equations cites this paper.

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

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Observation 0227d9c1-c850-4db4-b88b-a06cb591db59 · inbound

Sequential Neural Operator Transformer for High-Fidelity Surrogates of Time-Dependent Non-linear Partial Differential Equations cites this paper.

Sequential Neural Operator Transformer for High-Fidelity Surrogates of Time-Dependent Non-linear Partial Differential Equations Transformer for Partial Differential Equations' Operator Learning

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-06T20:18:48.906392Z

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Observation eb44b415-88d0-442e-89b1-fb52e62912f8 · inbound

Efficient Transformer-Inspired Variants of Physics-Informed Deep Operator Networks cites this paper.

Efficient Transformer-Inspired Variants of Physics-Informed Deep Operator Networks Transformer for Partial Differential Equations' Operator Learning

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-05T12:22:09.710124Z

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Observation e60634e1-aaf7-43b2-bc1e-3a394910f281 · inbound

FEDONet : Fourier-Embedded DeepONet for Spectrally Accurate Operator Learning cites this paper.

FEDONet : Fourier-Embedded DeepONet for Spectrally Accurate Operator Learning Transformer for Partial Differential Equations' Operator Learning

Reference 43

Resolution: verified exact; arxiv_id, observed 2026-05-18T16:06:35.188675Z

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Observation c0a3c2c4-887b-4b17-9072-a34171d3e748 · inbound

Flow marching for a generative PDE foundation model cites this paper.

Flow marching for a generative PDE foundation model Transformer for Partial Differential Equations' Operator Learning

Reference 35

Resolution: verified exact; arxiv_id, observed 2026-05-18T13:51:25.535307Z

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Observation 8d28bb80-ed6f-47b6-9f13-ddab7199f406 · inbound

Differentiable Autoencoding Neural Operator for Interpretable and Integrable Latent Space Modeling cites this paper.

Differentiable Autoencoding Neural Operator for Interpretable and Integrable Latent Space Modeling Transformer for Partial Differential Equations' Operator Learning

Reference 30

Resolution: verified exact; arxiv_id, observed 2026-05-18T11:26:18.386249Z

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Observation 8da20306-1e5b-47b8-a83f-9258329e4db6 · inbound

Deep Gaussian Processes for Functional Maps cites this paper.

Deep Gaussian Processes for Functional Maps Transformer for Partial Differential Equations' Operator Learning

Reference 5

Resolution: verified exact; arxiv_id, observed 2026-05-18T04:05:50.868336Z

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Observation ec5258e7-c08d-49e6-aff9-01ddd39e10a8 · inbound

Integrating Fourier Neural Operator with Diffusion Model for Autoregressive Predictions of Three-dimensional Turbulence cites this paper.

Integrating Fourier Neural Operator with Diffusion Model for Autoregressive Predictions of Three-dimensional Turbulence Transformer for Partial Differential Equations' Operator Learning

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-03T16:37:34.453554Z

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Observation 5b8975ac-d7af-402a-87e1-23a6d7016971 · inbound

Latent Generative Solvers for Generalizable Long-Term Physics Simulation cites this paper.

Latent Generative Solvers for Generalizable Long-Term Physics Simulation Transformer for Partial Differential Equations' Operator Learning

Reference 23

Resolution: metadata mismatch; arxiv_id, observed 2026-05-16T05:22:22.692307Z

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Observation ed9b8de7-5101-42a7-8b63-ff2ccdfca209 · inbound

ArGEnT: Arbitrary Geometry-encoded Transformer for Operator Learning cites this paper.

ArGEnT: Arbitrary Geometry-encoded Transformer for Operator Learning Transformer for Partial Differential Equations' Operator Learning

Reference 27

Resolution: verified exact; arxiv_id, observed 2026-05-16T02:32:08.996619Z

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Observation 5f0be9f3-5c10-4ac3-80dd-c3f2335824d5 · inbound

Pretrained Video Models as Differentiable Physics Simulators for Urban Wind Flows cites this paper.

Pretrained Video Models as Differentiable Physics Simulators for Urban Wind Flows Transformer for Partial Differential Equations' Operator Learning

Reference 24

Resolution: verified exact; arxiv_id, observed 2026-05-15T07:05:11.489689Z

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Observation f624c738-f362-4def-8c9b-e8a939800dd8 · inbound

One Scale at a Time: Scale-Autoregressive Modeling for Fluid Flow Distributions cites this paper.

One Scale at a Time: Scale-Autoregressive Modeling for Fluid Flow Distributions Transformer for Partial Differential Equations' Operator Learning

Reference 11

Resolution: metadata mismatch; arxiv_id, observed 2026-05-11T09:16:03.657068Z

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Observation b49e0df6-2c11-4be2-ab07-3ab83e1229ff · inbound

Learning Neural Operator Surrogates for the Black Hole Accretion Code cites this paper.

Learning Neural Operator Surrogates for the Black Hole Accretion Code Transformer for Partial Differential Equations' Operator Learning

Reference 47

Resolution: verified exact; arxiv_id, observed 2026-05-12T00:21:23.567778Z

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Observation 0c2131dd-cdd6-442e-bc38-8e73141d164a · inbound

RETO: A Rotary-Enhanced Transformer Operator for High-Fidelity Prediction of Automotive Aerodynamics cites this paper.

RETO: A Rotary-Enhanced Transformer Operator for High-Fidelity Prediction of Automotive Aerodynamics Transformer for Partial Differential Equations' Operator Learning

Reference 4

Resolution: verified exact; arxiv_id, observed 2026-05-11T15:11:04.360686Z

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Observation 65bca672-71e7-4495-877a-7ea55112f2e8 · inbound

QuadNorm: Resolution-Robust Normalization for Neural Operators cites this paper.

QuadNorm: Resolution-Robust Normalization for Neural Operators Transformer for Partial Differential Equations' Operator Learning

Reference 22

Resolution: verified exact; arxiv_id, observed 2026-05-11T04:05:55.909992Z

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Observation c762e66d-e6c3-42d8-9e78-a2d52733daae · inbound

CATO: Charted Attention for Neural PDE Operators cites this paper.

CATO: Charted Attention for Neural PDE Operators Transformer for Partial Differential Equations' Operator Learning

Reference 14

Resolution: verified exact; arxiv_id, observed 2026-05-12T01:56:15.054540Z

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Observation 7bec3190-34c4-4248-adef-0d0dda5df05d · inbound

HS-FNO: History-Space Fourier Neural Operator for Non-Markovian Partial Differential Equations cites this paper.

HS-FNO: History-Space Fourier Neural Operator for Non-Markovian Partial Differential Equations Transformer for Partial Differential Equations' Operator Learning

Reference 34

Resolution: verified exact; arxiv_id, observed 2026-05-12T07:16:30.489258Z

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Observation 06a8931b-7209-43b7-92d4-f35f7add8511 · inbound

HS-FNO: History-Space Fourier Neural Operator for Non-Markovian Partial Differential Equations cites this paper.

HS-FNO: History-Space Fourier Neural Operator for Non-Markovian Partial Differential Equations Transformer for Partial Differential Equations' Operator Learning

Reference 38

Resolution: verified exact; arxiv_id, observed 2026-05-13T07:12:28.217260Z

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Observation f96d5de5-80e4-4e31-bc07-450e143e1fb1 · inbound

AOT-POT: Adaptive Operator Transformation for Large-Scale PDE Pre-training cites this paper.

AOT-POT: Adaptive Operator Transformation for Large-Scale PDE Pre-training Transformer for Partial Differential Equations' Operator Learning

Reference 25

Resolution: verified exact; arxiv_id, observed 2026-05-20T21:03:46.685000Z

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Observation dca58a15-de1d-49d8-8099-d2848277a916 · inbound

IV-Net: A neural network for elliptic PDEs with random and highly varying coefficients cites this paper.

IV-Net: A neural network for elliptic PDEs with random and highly varying coefficients Transformer for Partial Differential Equations' Operator Learning

Reference 23

Resolution: verified exact; arxiv_id, observed 2026-06-29T23:54:03.206617Z

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Observation c90ae161-8948-4551-9be9-8583919284b6 · inbound

High-Fidelity Industrial Crash Dynamics Prediction via Geometry-Aware Operator Learning with Memory-Efficient Low-Rank Attention cites this paper.

High-Fidelity Industrial Crash Dynamics Prediction via Geometry-Aware Operator Learning with Memory-Efficient Low-Rank Attention Transformer for Partial Differential Equations' Operator Learning

Reference 35

Resolution: verified exact; arxiv_id, observed 2026-06-29T18:13:48.942540Z

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Observation 5f963be9-2498-407c-afc8-72a45c7d2a74 · inbound

EqGINO: Equivariant Geometry-Informed Fourier Neural Operators for 3D PDEs cites this paper.

EqGINO: Equivariant Geometry-Informed Fourier Neural Operators for 3D PDEs Transformer for Partial Differential Equations' Operator Learning

Reference 21

Resolution: metadata mismatch; arxiv_id, observed 2026-07-02T02:16:26.930936Z

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Observation 86c5ad62-e606-444a-a570-c8b626671739 · inbound

MeshTok: Efficient Multi-Scale Tokenization for Scalable PDE Transformers cites this paper.

MeshTok: Efficient Multi-Scale Tokenization for Scalable PDE Transformers Transformer for Partial Differential Equations' Operator Learning

Reference 7

Resolution: metadata mismatch; arxiv_id, observed 2026-07-02T07:06:44.820531Z

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Observation c27c55ed-a5de-4632-b353-82811b085e47 · inbound

On the training of physics-informed neural operators for solving parametric partial differential equations cites this paper.

On the training of physics-informed neural operators for solving parametric partial differential equations Transformer for Partial Differential Equations' Operator Learning

Reference 21

Resolution: verified exact; arxiv_id, observed 2026-07-02T11:36:55.266857Z

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Observation 1db88eb8-dc93-4f79-9dc7-23085ad50567 · inbound

HAMNO: A Hierarchical Adaptive Multi-scale Neural Operator with Physics-Informed Learning for Dynamical Systems cites this paper.

HAMNO: A Hierarchical Adaptive Multi-scale Neural Operator with Physics-Informed Learning for Dynamical Systems Transformer for Partial Differential Equations' Operator Learning

Reference 13

Resolution: verified exact; arxiv_id, observed 2026-07-03T10:17:57.358703Z

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Observation e074ee1f-c1c3-4d2a-a8a1-ba257426235e · inbound

PI-DOSnet: A Physics-Informed Deep Operator-Splitting Network for Evolution Partial Differential Equations cites this paper.

PI-DOSnet: A Physics-Informed Deep Operator-Splitting Network for Evolution Partial Differential Equations Transformer for Partial Differential Equations' Operator Learning

Reference 24

Resolution: verified exact; arxiv_id, observed 2026-07-04T09:29:43.198844Z

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Observation 4c232a09-8ad9-468d-92d0-eacb851d703e · inbound

Attention mechanism for scalable mesh-based neural surrogates of free-surface fluids cites this paper.

Attention mechanism for scalable mesh-based neural surrogates of free-surface fluids Transformer for Partial Differential Equations' Operator Learning

Reference 29

Resolution: verified exact; arxiv_id, observed 2026-06-26T06:19:03.896171Z

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Observation ad37c22e-1224-440f-a885-aab4d47e99b4 · inbound

Temperature Field Reconstruction of Tungsten Monoblock Divertor on EAST using Physics-aware Neural Operator Transformer cites this paper.

Temperature Field Reconstruction of Tungsten Monoblock Divertor on EAST using Physics-aware Neural Operator Transformer Transformer for Partial Differential Equations' Operator Learning

Reference 16

Resolution: metadata mismatch; arxiv_id, observed 2026-07-01T10:15:44.189466Z

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Observation ee0bab9e-7264-4118-a74b-cbaf8c640f44 · inbound

GAIA: Geometry-Adaptive Operator Learning for Forward and Inverse Problems cites this paper.

GAIA: Geometry-Adaptive Operator Learning for Forward and Inverse Problems Transformer for Partial Differential Equations' Operator Learning

Reference 41

Resolution: verified exact; arxiv_id, observed 2026-07-02T15:37:05.892350Z

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Observation 6e7470a3-36ac-484d-b972-40b1c103425a · inbound

Evaluation of State-of-the-Art Deep Learning Architectures for Aerodynamical Predictions cites this paper.

Evaluation of State-of-the-Art Deep Learning Architectures for Aerodynamical Predictions Transformer for Partial Differential Equations' Operator Learning

Reference 12

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Observation 55d8346f-82cc-403d-8027-78030ed16ea0 · inbound

Adaptive Mamba Neural Operators cites this paper.

Adaptive Mamba Neural Operators Transformer for Partial Differential Equations' Operator Learning

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-01T16:25:00.099140Z

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Observation 454b2ceb-aa2b-4b13-87e5-d7d81a70ca8c · inbound

Physics Transformer: Tailoring Transformer for General PDE Prediction cites this paper.

Physics Transformer: Tailoring Transformer for General PDE Prediction Transformer for Partial Differential Equations' Operator Learning

Reference 8

Resolution: unresolved; no resolver link, observed 2026-07-31T12:51:44.759288Z

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Observation 0c7f40a0-1333-4dba-86b4-e42db52700c7 · inbound

tFUSOperator: Operator Learning for Transcranial Focused Ultrasound Digital Twins cites this paper.

tFUSOperator: Operator Learning for Transcranial Focused Ultrasound Digital Twins Transformer for Partial Differential Equations' Operator Learning

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-04T19:54:15.563278Z

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