Paper Citation Record · LEDGER

Operator Learning for Reconstructing Flow Fields from Sparse Measurements: an Energy Transformer Approach

As of 11 August 2026, this Paper Citation Record lists 42 of 42 outbound references and 3 inbound Pith citation observations for arXiv:2501.08339.

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

pith.paper-citation-record.v1
2501.08339 v1

Coverage vector

measured 42 of 42 reference resolution

Typed states for the displayed outbound observations.

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One-hop event checks from named stored sources.

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measured 3 of 3 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-05-25T02:24:29.814889Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-25T02:25:14.806375Z

Reference resolution

42 of 42 outbound references displayed

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External citation measurements

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Outbound references

Observation b1fbdfff-8675-4a4b-8c92-46d9c3b93933 · outbound

This paper cites Andersson, Andrew El-Kadi, Dominic Masters, Timo Ewalds, Jacklynn Stott, Shakir Mohamed, Peter Battaglia, Remi Lam, and Matthew Willson.

Operator Learning for Reconstructing Flow Fields from Sparse Measurements: an Energy Transformer Approach Andersson, Andrew El-Kadi, Dominic Masters, Timo Ewalds, Jacklynn Stott, Shakir Mohamed, Peter Battaglia, Remi Lam, and Matthew Willson

Reference 1

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Observation 846d7be9-445c-4164-bc93-a326fd2be581 · outbound

This paper cites an unresolved cited work.

Operator Learning for Reconstructing Flow Fields from Sparse Measurements: an Energy Transformer Approach Unresolved cited work

Reference 2

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Observation 723e51ed-a990-44e3-9ac2-c79671958ecc · outbound

This paper cites Observation of a new particle in the search for the standard model higgs boson with the atlas detector at the lhc.

Operator Learning for Reconstructing Flow Fields from Sparse Measurements: an Energy Transformer Approach Observation of a new particle in the search for the standard model higgs boson with the atlas detector at the lhc

Reference 3

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Observation 96732d84-836b-4806-b8d0-896cd3d6d67f · outbound

This paper cites Physics-informed neural networks (pinns) for fluid mechanics: A review.

Operator Learning for Reconstructing Flow Fields from Sparse Measurements: an Energy Transformer Approach Physics-informed neural networks (pinns) for fluid mechanics: A review

Reference 4

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Observation d4dcc8ad-d495-4f66-a4f0-f01b13505a24 · outbound

This paper cites Solving the quantum many-body problem with artificial neural networks.

Operator Learning for Reconstructing Flow Fields from Sparse Measurements: an Energy Transformer Approach Solving the quantum many-body problem with artificial neural networks

Reference 5

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Observation 1c50b480-e179-4939-9e3a-133ef6ca85b6 · outbound

This paper cites Sympnets: Intrinsic structure-preserving symplectic networks for identifying hamiltonian systems.

Operator Learning for Reconstructing Flow Fields from Sparse Measurements: an Energy Transformer Approach Sympnets: Intrinsic structure-preserving symplectic networks for identifying hamiltonian systems

Reference 6

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Observation b71c2bcf-0f1a-465f-94b8-7155819292db · outbound

This paper cites Sms: Spiking marching scheme for efficient long time integration of differential equations.

Operator Learning for Reconstructing Flow Fields from Sparse Measurements: an Energy Transformer Approach Sms: Spiking marching scheme for efficient long time integration of differential equations

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:31:42.340291Z

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Observation 441f27f2-ddec-411e-81c7-fb4ca4638073 · outbound

This paper cites Artificial to Spiking Neural Networks Conversion for Scientific Machine Learning.

Operator Learning for Reconstructing Flow Fields from Sparse Measurements: an Energy Transformer Approach Artificial to Spiking Neural Networks Conversion for Scientific Machine Learning

Reference 8

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Observation 9a6b5638-0df1-455b-9b55-9b9ec56c7a9c · outbound

This paper cites Theilman, Qian Zhang, Adar Kahana, Eric C.

Operator Learning for Reconstructing Flow Fields from Sparse Measurements: an Energy Transformer Approach Theilman, Qian Zhang, Adar Kahana, Eric C

Reference 9

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Observation 0d6dede2-29cd-45cb-9bb9-d28f08a46e8c · outbound

This paper cites A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks.

Operator Learning for Reconstructing Flow Fields from Sparse Measurements: an Energy Transformer Approach A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks

Reference 10

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Observation 750daeed-92eb-4398-88dd-dd29c50c874e · outbound

This paper cites Randomized Forward Mode Gradient for Spiking Neural Networks in Scientific Machine Learning.

Operator Learning for Reconstructing Flow Fields from Sparse Measurements: an Energy Transformer Approach Randomized Forward Mode Gradient for Spiking Neural Networks in Scientific Machine Learning

Reference 11

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Observation cfd00874-b390-48dd-b42c-ffffc4959981 · outbound

This paper cites Highly accurate protein structure prediction with alphafold.

Operator Learning for Reconstructing Flow Fields from Sparse Measurements: an Energy Transformer Approach Highly accurate protein structure prediction with alphafold

Reference 12

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This paper cites Scaling deep learning for materials discovery.

Operator Learning for Reconstructing Flow Fields from Sparse Measurements: an Energy Transformer Approach Scaling deep learning for materials discovery

Reference 13

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This paper cites LNO: Laplace Neural Operator for Solving Differential Equations.

Operator Learning for Reconstructing Flow Fields from Sparse Measurements: an Energy Transformer Approach LNO: Laplace Neural Operator for Solving Differential Equations

Reference 14

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Observation 6ad10d21-1820-4b64-9992-c2fc69be2625 · outbound

This paper cites Systems Biology: Identifiability analysis and parameter identification via systems-biology informed neural networks.

Operator Learning for Reconstructing Flow Fields from Sparse Measurements: an Energy Transformer Approach Systems Biology: Identifiability analysis and parameter identification via systems-biology informed neural networks

Reference 15

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Observation c14efe78-6743-4fb6-b701-4c8815b6a170 · outbound

This paper cites Sun, and George Em Karniadakis.

Operator Learning for Reconstructing Flow Fields from Sparse Measurements: an Energy Transformer Approach Sun, and George Em Karniadakis

Reference 16

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Observation 31f52e50-a826-4415-9de5-8c205e08b530 · outbound

This paper cites An integrated framework for building trustworthy data-driven epidemiological models: Application to the covid-19 outbreak in new york city.

Operator Learning for Reconstructing Flow Fields from Sparse Measurements: an Energy Transformer Approach An integrated framework for building trustworthy data-driven epidemiological models: Application to the covid-19 outbreak in new york city

Reference 17

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Observation 3e99da4b-7807-4a15-ba26-0e1cffa378fe · outbound

This paper cites Iden- tifiability and predictability of integer- and fractional-order epidemiological models using physics-informed neural networks.

Operator Learning for Reconstructing Flow Fields from Sparse Measurements: an Energy Transformer Approach Iden- tifiability and predictability of integer- and fractional-order epidemiological models using physics-informed neural networks

Reference 18

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Observation 2706c67e-1f94-4467-a0dc-0c123b76d40f · outbound

This paper cites Learning nonlin- ear operators via deeponet based on the universal approximation theorem of operators.

Operator Learning for Reconstructing Flow Fields from Sparse Measurements: an Energy Transformer Approach Learning nonlin- ear operators via deeponet based on the universal approximation theorem of operators

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:31:42.241945Z

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Observation b55b1572-da2b-48a2-9e4b-8bed134d4e2f · outbound

This paper cites A physics-informed variational deeponet for predicting crack path in quasi-brittle materials.

Operator Learning for Reconstructing Flow Fields from Sparse Measurements: an Energy Transformer Approach A physics-informed variational deeponet for predicting crack path in quasi-brittle materials

Reference 20

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Observation 8e0bed9e-d51d-4450-8065-ecda47a153ef · outbound

This paper cites Spiking Neural Operators for Scientific Machine Learning.

Operator Learning for Reconstructing Flow Fields from Sparse Measurements: an Energy Transformer Approach Spiking Neural Operators for Scientific Machine Learning

Reference 21

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Operator Learning for Reconstructing Flow Fields from Sparse Measurements: an Energy Transformer Approach Blending Neural Operators and Relaxation Methods in PDE Numerical Solvers

Reference 22

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Observation 55ea6992-df7e-4c6e-a61f-0b8ddbab6042 · outbound

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

Operator Learning for Reconstructing Flow Fields from Sparse Measurements: an Energy Transformer Approach Fourier Neural Operator for Parametric Partial Differential Equations

Reference 23

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This paper cites Vito: Vision transformer-operator.

Operator Learning for Reconstructing Flow Fields from Sparse Measurements: an Energy Transformer Approach Vito: Vision transformer-operator

Reference 24

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Observation d32e64a0-2781-4551-8f34-01f9eae15da2 · outbound

This paper cites A physics-informed diffusion model for high-fidelity flow field reconstruction.

Operator Learning for Reconstructing Flow Fields from Sparse Measurements: an Energy Transformer Approach A physics-informed diffusion model for high-fidelity flow field reconstruction

Reference 25

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This paper cites Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations.

Operator Learning for Reconstructing Flow Fields from Sparse Measurements: an Energy Transformer Approach Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

Reference 26

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This paper cites Nsfnets (navier-stokes flow nets): Physics- informed neural networks for the incompressible navier-stokes equations.

Operator Learning for Reconstructing Flow Fields from Sparse Measurements: an Energy Transformer Approach Nsfnets (navier-stokes flow nets): Physics- informed neural networks for the incompressible navier-stokes equations

Reference 27

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Observation 71edcdcb-d8f2-4c26-b8ce-1ec5868d74a8 · outbound

This paper cites Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations.

Operator Learning for Reconstructing Flow Fields from Sparse Measurements: an Energy Transformer Approach Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations

Reference 28

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This paper cites Artificial intelligence velocimetry and microaneurysm-on-a-chip for three-dimensional analysis of blood flow in physiology and disease.

Operator Learning for Reconstructing Flow Fields from Sparse Measurements: an Energy Transformer Approach Artificial intelligence velocimetry and microaneurysm-on-a-chip for three-dimensional analysis of blood flow in physiology and disease

Reference 29

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This paper cites Physics-informed neural networks enhanced par- ticle tracking velocimetry: An example for turbulent jet flow.

Operator Learning for Reconstructing Flow Fields from Sparse Measurements: an Energy Transformer Approach Physics-informed neural networks enhanced par- ticle tracking velocimetry: An example for turbulent jet flow

Reference 30

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Observation 1c64eb8b-7dd5-4d7f-b335-11c4bbdeb1e0 · outbound

This paper cites Artificial intelligence velocimetry reveals in vivo flow rates, pressure gradients, and shear stresses in murine perivascular flows.

Operator Learning for Reconstructing Flow Fields from Sparse Measurements: an Energy Transformer Approach Artificial intelligence velocimetry reveals in vivo flow rates, pressure gradients, and shear stresses in murine perivascular flows

Reference 31

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Observation c48621b0-0fe6-480b-a33c-11b87db932bd · outbound

This paper cites Inferring turbulent velocity and temperature fields and their statistics from Lagrangian velocity measurements using physics-informed Kolmogorov-Arnold Networks.

Operator Learning for Reconstructing Flow Fields from Sparse Measurements: an Energy Transformer Approach Inferring turbulent velocity and temperature fields and their statistics from Lagrangian velocity measurements using physics-informed Kolmogorov-Arnold Networks

Reference 32

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Operator Learning for Reconstructing Flow Fields from Sparse Measurements: an Energy Transformer Approach Energy transformer

Reference 33

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Operator Learning for Reconstructing Flow Fields from Sparse Measurements: an Energy Transformer Approach Dense associative memory for pattern recognition

Reference 34

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Operator Learning for Reconstructing Flow Fields from Sparse Measurements: an Energy Transformer Approach A new frontier for hopfield networks

Reference 35

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Operator Learning for Reconstructing Flow Fields from Sparse Measurements: an Energy Transformer Approach Neural networks and physical systems with emergent collective computational abilities

Reference 36

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Operator Learning for Reconstructing Flow Fields from Sparse Measurements: an Energy Transformer Approach Large associative memory problem in neurobiology and machine learning

Reference 37

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Operator Learning for Reconstructing Flow Fields from Sparse Measurements: an Energy Transformer Approach Hierarchical Associative Memory

Reference 38

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Operator Learning for Reconstructing Flow Fields from Sparse Measurements: an Energy Transformer Approach Deep learning of vortex-induced vibrations

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:31:42.071800Z

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Observation 0317bf9d-d701-4d4a-90c7-8c56d8065487 · outbound

This paper cites A review of recent developments in schlieren and shadowgraph techniques.

Operator Learning for Reconstructing Flow Fields from Sparse Measurements: an Energy Transformer Approach A review of recent developments in schlieren and shadowgraph techniques

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:31:42.054833Z

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Observation c5930b57-3f13-4690-bd3b-2bc50ed98299 · outbound

This paper cites Deep-learning- based super-resolution reconstruction of high-speed imaging in fluids.

Operator Learning for Reconstructing Flow Fields from Sparse Measurements: an Energy Transformer Approach Deep-learning- based super-resolution reconstruction of high-speed imaging in fluids

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:31:42.040140Z

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Observation 61df51f9-5ee9-4d32-9924-21a653e00d0e · outbound

This paper cites Physics-informed neural networks enhanced par- ticle tracking velocimetry: An example for turbulent jet flow.

Reference 42

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Pith citing papers

Observation 94d54e26-691f-4753-a145-37da9eec2ef3 · inbound

Energy-Based Dynamical Models for Neurocomputation, Learning, and Optimization cites this paper.

Energy-Based Dynamical Models for Neurocomputation, Learning, and Optimization Operator Learning for Reconstructing Flow Fields from Sparse Measurements: an Energy Transformer Approach

Reference 85

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Observation 23a5a5d0-1f16-4b7b-9c8f-1e4ad0c08a9a · inbound

Flow Field Reconstruction with Sensor Placement Policy Learning cites this paper.

Flow Field Reconstruction with Sensor Placement Policy Learning Operator Learning for Reconstructing Flow Fields from Sparse Measurements: an Energy Transformer Approach

Reference 21

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Observation fad254c6-c569-4c06-9ab4-c271fe26281e · inbound

Operator Learning for Reconstructing Flow Fields from Sparse Measurements: a Language Model Approach cites this paper.

Operator Learning for Reconstructing Flow Fields from Sparse Measurements: a Language Model Approach Operator Learning for Reconstructing Flow Fields from Sparse Measurements: an Energy Transformer Approach

Reference 31

Resolution: verified exact; arxiv_id, observed 2026-05-25T02:25:14.810160Z

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