Paper Citation Record · LEDGER

Neural Operator: Learning Maps Between Function Spaces

As of 8 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 41 inbound Pith citation observations for arXiv:2108.08481.

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

pith.paper-citation-record.v1
2108.08481 v6

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measured 0 of 0 reference resolution

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measured 41 of 41 standing notices

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

measured 41 of 41 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-08T05:46:28.133504Z

measured 1 of 1 external citation measurements

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

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

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External citation measurements

79
arxiv_reference, observed 2026-08-05T02:28:24.338817Z

Outbound references

No outbound reference observations are available for this paper version.

Pith citing papers

Observation e72c7a0d-9d01-426e-a4f8-c48d40eaea2a · inbound

Generative diffusion learning for parametric partial differential equations cites this paper.

Generative diffusion learning for parametric partial differential equations Neural Operator: Learning Maps Between Function Spaces

Reference 12

Resolution: verified exact; arxiv_id, observed 2026-05-24T09:09:15.695837Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T07:38:14.145609+00:00.

Observation 0ae81296-4958-4e52-ab45-b4575f810be2 · inbound

Kernel Neural Operators (KNOs) for Scalable, Memory-efficient, Geometrically-flexible Operator Learning cites this paper.

Kernel Neural Operators (KNOs) for Scalable, Memory-efficient, Geometrically-flexible Operator Learning Neural Operator: Learning Maps Between Function Spaces

Reference 22

Resolution: verified exact; arxiv_id, observed 2026-05-23T23:13:37.081139Z

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Observation 7cab24c7-16be-49bc-9f95-99cf82168681 · inbound

A Deep Learning approach for parametrized and time dependent Partial Differential Equations using Dimensionality Reduction and Neural ODEs cites this paper.

A Deep Learning approach for parametrized and time dependent Partial Differential Equations using Dimensionality Reduction and Neural ODEs Neural Operator: Learning Maps Between Function Spaces

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-08T05:46:28.133504Z

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Observation dfbca8f4-6bc6-4071-9c2e-12703dbca6e0 · inbound

Phi-FEM-FNO: a new approach to train a Neural Operator as a fast PDE solver for variable geometries cites this paper.

Phi-FEM-FNO: a new approach to train a Neural Operator as a fast PDE solver for variable geometries Neural Operator: Learning Maps Between Function Spaces

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-07T19:43:57.768053Z

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Observation acbca17f-c801-41da-9363-28ec9c5468e0 · inbound

Teaching Artificial Intelligence to Perform Rapid, Resolution-Invariant Grain Growth Modeling via Fourier Neural Operator cites this paper.

Teaching Artificial Intelligence to Perform Rapid, Resolution-Invariant Grain Growth Modeling via Fourier Neural Operator Neural Operator: Learning Maps Between Function Spaces

Reference 66

Resolution: verified exact; arxiv_id, observed 2026-05-22T23:52:16.918861Z

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No event found in the named queried sources as of 2026-08-08T07:38:14.145609+00:00.

Observation 453965a8-81c8-44cf-be95-625fdf05be59 · inbound

A Unified Framework for Simultaneous Parameter and Function Discovery in Differential Equations cites this paper.

A Unified Framework for Simultaneous Parameter and Function Discovery in Differential Equations Neural Operator: Learning Maps Between Function Spaces

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-07T14:58:38.018328Z

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Observation 95b9b567-a5ad-49dd-82f2-e8c218a29413 · inbound

Latent Mamba Operator for Partial Differential Equations cites this paper.

Latent Mamba Operator for Partial Differential Equations Neural Operator: Learning Maps Between Function Spaces

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-07T14:24:44.047914Z

Source-reported events for the cited work

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Observation 54e62085-dc27-4f66-acea-0011bc21ed95 · inbound

Neural Operators for Forward and Inverse Potential-Density Mappings in Classical Density Functional Theory cites this paper.

Neural Operators for Forward and Inverse Potential-Density Mappings in Classical Density Functional Theory Neural Operator: Learning Maps Between Function Spaces

Reference 53

Resolution: unresolved; no resolver link, observed 2026-08-07T06:01:41.912814Z

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Observation e5c31bbc-cb84-4d4c-bd11-e1cc523fddc2 · inbound

Mondrian: Transformer Operators via Domain Decomposition cites this paper.

Mondrian: Transformer Operators via Domain Decomposition Neural Operator: Learning Maps Between Function Spaces

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-07T05:23:49.111356Z

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Observation 73678889-47ce-4b6e-8979-01cbe0406b2d · inbound

Accurate and scalable exchange-correlation with deep learning cites this paper.

Accurate and scalable exchange-correlation with deep learning Neural Operator: Learning Maps Between Function Spaces

Reference 54

Resolution: verified exact; arxiv_id, observed 2026-05-19T09:07:13.947633Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T07:38:14.145609+00:00.

Observation 1b4e4631-634c-431a-842d-0a1d3ee9410c · inbound

Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs cites this paper.

Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs Neural Operator: Learning Maps Between Function Spaces

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-06T21:26:34.338031Z

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Observation ec2973c2-c63c-4f23-9b75-8f9b6b9383ce · inbound

The Fourier Spectral Transformer Networks For Efficient and Generalizable Nonlinear PDEs Prediction cites this paper.

The Fourier Spectral Transformer Networks For Efficient and Generalizable Nonlinear PDEs Prediction Neural Operator: Learning Maps Between Function Spaces

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-06T19:27:46.639151Z

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Observation f8f7839d-69f0-40d9-8b1c-623ea2dbd3a6 · inbound

Time Series Forecasting Through the Lens of Dynamics cites this paper.

Time Series Forecasting Through the Lens of Dynamics Neural Operator: Learning Maps Between Function Spaces

Reference 20

Resolution: metadata mismatch; arxiv_id, observed 2026-05-19T03:32:01.331749Z

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No event found in the named queried sources as of 2026-08-08T07:38:14.145609+00:00.

Observation fb6952aa-d2cb-4603-aeb7-5aadff637db4 · inbound

Bubbleformer: Forecasting Boiling with Transformers cites this paper.

Bubbleformer: Forecasting Boiling with Transformers Neural Operator: Learning Maps Between Function Spaces

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-06T13:02:54.464045Z

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Observation 017054dd-9e09-4ec1-9fee-928057c78a5e · inbound

Toward Intelligent Electronic-Photonic Design Automation for Large-Scale Photonic Integrated Circuits: from Device Inverse Design to Physical Layout Generation cites this paper.

Toward Intelligent Electronic-Photonic Design Automation for Large-Scale Photonic Integrated Circuits: from Device Inverse Design to Physical Layout Generation Neural Operator: Learning Maps Between Function Spaces

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-06T11:54:56.893686Z

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Unavailable: canonical work link unavailable.

Observation d5771126-6644-43fc-86bd-7a27543f2f80 · inbound

Temperature-Aware Recurrent Neural Operator for Temperature-Dependent Anisotropic Plasticity in HCP Materials cites this paper.

Temperature-Aware Recurrent Neural Operator for Temperature-Dependent Anisotropic Plasticity in HCP Materials Neural Operator: Learning Maps Between Function Spaces

Reference 60

Resolution: unresolved; no resolver link, observed 2026-08-05T16:16:13.303354Z

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Unavailable: canonical work link unavailable.

Observation 70de1d89-488e-413b-9b55-ae4160e23cfc · inbound

Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory cites this paper.

Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory Neural Operator: Learning Maps Between Function Spaces

Reference 51

Resolution: unresolved; no resolver link, observed 2026-08-04T17:57:20.298639Z

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Observation d1e7a98a-a8c9-440d-a8da-dc8925ea71c5 · inbound

Flow Straight and Fast in Hilbert Space: Functional Rectified Flow cites this paper.

Flow Straight and Fast in Hilbert Space: Functional Rectified Flow Neural Operator: Learning Maps Between Function Spaces

Reference 41

Resolution: unresolved; no resolver link, observed 2026-08-04T18:00:37.393578Z

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Unavailable: canonical work link unavailable.

Observation 0bc7f050-cf83-4141-83c4-65c0cfcbbfce · inbound

Toward Data-Driven Surrogates of the Solar Wind with Spherical Fourier Neural Operator cites this paper.

Toward Data-Driven Surrogates of the Solar Wind with Spherical Fourier Neural Operator Neural Operator: Learning Maps Between Function Spaces

Reference 22

Resolution: metadata mismatch; arxiv_id, observed 2026-05-17T04:29:01.577905Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T07:38:14.145609+00:00.

Observation 089473c7-acdf-48d8-8017-b2c163fc9a93 · inbound

Diagnosing Failure Modes of Neural Operators Across Diverse PDE Families cites this paper.

Diagnosing Failure Modes of Neural Operators Across Diverse PDE Families Neural Operator: Learning Maps Between Function Spaces

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-03T10:03:08.114701Z

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Unavailable: canonical work link unavailable.

Observation 770e2f02-32e8-47e6-81c6-f30b2ed725a7 · inbound

Physics-Encoded Inverse Modeling for Arctic Snow Depth Estimation cites this paper.

Physics-Encoded Inverse Modeling for Arctic Snow Depth Estimation Neural Operator: Learning Maps Between Function Spaces

Reference 2021

Resolution: unresolved; no resolver link, observed 2026-08-03T08:39:53.658327Z

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Observation 6f14a7d7-4e29-43c5-a9a1-6025b4e9ea56 · inbound

Learning 3D Hypersonic Flow with Physics-Enhanced Neural Fields: A Case Study on the Orion Reentry Capsule cites this paper.

Learning 3D Hypersonic Flow with Physics-Enhanced Neural Fields: A Case Study on the Orion Reentry Capsule Neural Operator: Learning Maps Between Function Spaces

Reference 2017

Resolution: unresolved; no resolver link, observed 2026-08-02T17:47:08.876587Z

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Observation 4bb34af7-2d61-4b35-a07d-30fbc1d9da79 · inbound

Optimal Linear Interpolation under Differential Information: application to the prediction of perfect flows cites this paper.

Optimal Linear Interpolation under Differential Information: application to the prediction of perfect flows Neural Operator: Learning Maps Between Function Spaces

Reference 33

Resolution: metadata mismatch; arxiv_id, observed 2026-05-11T11:51:02.887767Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T07:38:14.145609+00:00.

Observation db4d474d-4d4a-4a05-a4ba-92c2bb20e277 · inbound

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

Learning Neural Operator Surrogates for the Black Hole Accretion Code Neural Operator: Learning Maps Between Function Spaces

Reference 7

Resolution: verified exact; arxiv_id, observed 2026-05-12T00:21:23.706098Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T07:38:14.145609+00:00.

Observation ab798e1b-4da5-49a8-a430-01c00b4238ff · inbound

Large-eddy simulation nets (LESnets) based on physics-informed neural operator for wall-bounded turbulence cites this paper.

Large-eddy simulation nets (LESnets) based on physics-informed neural operator for wall-bounded turbulence Neural Operator: Learning Maps Between Function Spaces

Reference 45

Resolution: metadata mismatch; arxiv_id, observed 2026-05-09T04:00:13.226916Z

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No event found in the named queried sources as of 2026-08-08T07:38:14.145609+00:00.

Observation 9a352f99-0b3f-43c7-a269-373f17867da5 · inbound

Hybrid Fourier Neural Operator-Lattice Boltzmann Method cites this paper.

Hybrid Fourier Neural Operator-Lattice Boltzmann Method Neural Operator: Learning Maps Between Function Spaces

Reference 32

Resolution: verified exact; arxiv_id, observed 2026-05-12T10:01:29.191030Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T07:38:14.145609+00:00.

Observation a7563a6a-68f8-4a24-8e23-9792fd5b8799 · inbound

Physics-Informed Reduced-Order Operator Learning for Hyperelasticity in Continuum Micromechanics cites this paper.

Physics-Informed Reduced-Order Operator Learning for Hyperelasticity in Continuum Micromechanics Neural Operator: Learning Maps Between Function Spaces

Reference 5

Resolution: verified exact; arxiv_id, observed 2026-05-11T03:05:52.639855Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T07:38:14.145609+00:00.

Observation 0577a301-314c-4ce4-a2e2-ed27a03db1d1 · inbound

Quantitative Sobolev Approximation Bounds for Neural Operators with Empirical Validation on Burgers Equation cites this paper.

Quantitative Sobolev Approximation Bounds for Neural Operators with Empirical Validation on Burgers Equation Neural Operator: Learning Maps Between Function Spaces

Reference 20

Resolution: metadata mismatch; arxiv_id, observed 2026-05-12T01:46:14.665992Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T07:38:14.145609+00:00.

Observation b2825f0b-305f-4db1-ae0e-709b9d9f7a9b · inbound

Quantitative Sobolev Approximation Bounds for Neural Operators with Empirical Validation on Burgers Equation cites this paper.

Quantitative Sobolev Approximation Bounds for Neural Operators with Empirical Validation on Burgers Equation Neural Operator: Learning Maps Between Function Spaces

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-04T05:24:02.533981Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8020b2c7-0eff-4682-828a-8711f7e8e7c7 · inbound

Sequential Physics-Constrained Neural Operator Forward Modeling for the $\textit{Norne}$ Reservoir System cites this paper.

Sequential Physics-Constrained Neural Operator Forward Modeling for the $\textit{Norne}$ Reservoir System Neural Operator: Learning Maps Between Function Spaces

Reference 16

Resolution: verified exact; arxiv_id, observed 2026-06-29T14:43:30.814908Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T07:38:14.145609+00:00.

Observation 8a1d67db-173e-42a4-99b6-1a409fb035ed · inbound

Operator learning for the 2D incompressible Navier-Stokes equations: a conformal prediction approach in the data-scarce regime cites this paper.

Operator learning for the 2D incompressible Navier-Stokes equations: a conformal prediction approach in the data-scarce regime Neural Operator: Learning Maps Between Function Spaces

Reference 14

Resolution: verified exact; arxiv_id, observed 2026-07-02T22:47:25.734752Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T07:38:14.145609+00:00.

Observation 7a68dcee-5982-4e44-9b3a-625f89151e7b · inbound

Graph Mamba Operator: A Latent Simulator for Interacting Particle Systems cites this paper.

Graph Mamba Operator: A Latent Simulator for Interacting Particle Systems Neural Operator: Learning Maps Between Function Spaces

Reference 30

Resolution: metadata mismatch; arxiv_id, observed 2026-07-03T00:37:29.962633Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T07:38:14.145609+00:00.

Observation 83867a57-49bb-49a1-9e83-f420380419a3 · inbound

ELADO: Elliptic PDE Assessment Datasets for Operator Learning cites this paper.

ELADO: Elliptic PDE Assessment Datasets for Operator Learning Neural Operator: Learning Maps Between Function Spaces

Reference 4

Resolution: metadata mismatch; arxiv_id, observed 2026-07-04T03:09:30.476831Z

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No event found in the named queried sources as of 2026-08-08T07:38:14.145609+00:00.

Observation 32be2990-fc75-4d23-8324-235d9fbcf085 · inbound

A Neural Surrogate Approach for Simulating Natural Convection Problems cites this paper.

A Neural Surrogate Approach for Simulating Natural Convection Problems Neural Operator: Learning Maps Between Function Spaces

Reference 98

Resolution: metadata mismatch; arxiv_id, observed 2026-06-25T21:18:24.265402Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T07:38:14.145609+00:00.

Observation 31970c1b-1e79-4d27-b105-ec6fecf51f0f · inbound

When is the combined load identifiable from a stress-intensity profile? A coupled forward-inverse study on SIFBench finite-element data cites this paper.

When is the combined load identifiable from a stress-intensity profile? A coupled forward-inverse study on SIFBench finite-element data Neural Operator: Learning Maps Between Function Spaces

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-02T07:10:15.668361Z

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Unavailable: canonical work link unavailable.

Observation 45037c94-c6cc-423f-978c-df46b14d5e62 · inbound

DRIFT: Direct Reduced Fourier Transforms for Distributed Spectral Neural Operators cites this paper.

DRIFT: Direct Reduced Fourier Transforms for Distributed Spectral Neural Operators Neural Operator: Learning Maps Between Function Spaces

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-02T02:17:07.159977Z

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Unavailable: canonical work link unavailable.

Observation eeb4939a-a03e-4a91-aa8c-d7e2a6accdfa · inbound

Energy Manifold Natural Gradient Descent: Riemannian Optimization for Neural PDE Solvers cites this paper.

Energy Manifold Natural Gradient Descent: Riemannian Optimization for Neural PDE Solvers Neural Operator: Learning Maps Between Function Spaces

Reference 2001

Resolution: unresolved; no resolver link, observed 2026-08-01T06:09:01.761928Z

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Unavailable: canonical work link unavailable.

Observation 54143cd1-341d-4100-b70c-ec769592ed0a · inbound

Elliptic Regularity Theory in Barron Spaces and Applications to the Deep Ritz Method cites this paper.

Elliptic Regularity Theory in Barron Spaces and Applications to the Deep Ritz Method Neural Operator: Learning Maps Between Function Spaces

Reference 9

Resolution: unresolved; no resolver link, observed 2026-07-31T01:28:50.733155Z

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Unavailable: canonical work link unavailable.

Observation e069b584-2f4c-412b-9f3b-8ac1dfa9087a · inbound

Cosmo-SPINN: Fuzzy Dark Matter Simulations with Physics-Informed Generative Networks cites this paper.

Cosmo-SPINN: Fuzzy Dark Matter Simulations with Physics-Informed Generative Networks Neural Operator: Learning Maps Between Function Spaces

Reference 98

Resolution: unresolved; no resolver link, observed 2026-07-31T02:27:17.167700Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9718d6a2-f21b-40e5-87f6-3695857158d9 · inbound

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

tFUSOperator: Operator Learning for Transcranial Focused Ultrasound Digital Twins Neural Operator: Learning Maps Between Function Spaces

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-04T19:54:15.550167Z

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Unavailable: canonical work link unavailable.

Observation 1f007116-23d8-4c08-a1a2-75621fd337ac · inbound

Benchmarking Multi-fidelity Neural Operators on Complex PDE Problems with Non-trivial Fidelity Differences cites this paper.

Benchmarking Multi-fidelity Neural Operators on Complex PDE Problems with Non-trivial Fidelity Differences Neural Operator: Learning Maps Between Function Spaces

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-06T18:32:35.100763Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.