Paper Citation Record · LEDGER

From Local Interactions to Global Operators: Scalable Gaussian Process Operator for Physical Systems

As of 18 August 2026, this Paper Citation Record lists 40 of 40 outbound references and 0 inbound Pith citation observations for arXiv:2506.15906.

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

pith.paper-citation-record.v1
2506.15906 v1

Coverage vector

measured 40 of 40 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T19:35:43.431603Z

measured 40 of 40 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-18T06:34:40.430872+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

40 of 40 outbound references displayed

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verified fuzzy29
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 0e309b8f-7d79-4b3e-9bdc-6ce893d40f0f · outbound

This paper cites DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators.

From Local Interactions to Global Operators: Scalable Gaussian Process Operator for Physical Systems DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-15T19:35:43.251967Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 35b3af91-5208-42d0-af3e-efcd7df6ae44 · 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.

From Local Interactions to Global Operators: Scalable Gaussian Process Operator for Physical Systems Learning nonlinear operators via deeponet based on the universal approximation theorem of operators.Nature Machine Intelligence, 3(3):218–229, 2021

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-15T19:35:43.257178Z

Source-reported events for the cited work

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Observation 58433629-575d-4b99-bd54-3da240681a33 · outbound

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

From Local Interactions to Global Operators: Scalable Gaussian Process Operator for Physical Systems Fourier Neural Operator for Parametric Partial Differential Equations

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-15T19:35:43.261617Z

Source-reported events for the cited work

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Observation 09032b7c-5993-410e-b0f3-fcbff710368d · outbound

This paper cites an unresolved cited work.

From Local Interactions to Global Operators: Scalable Gaussian Process Operator for Physical Systems Unresolved cited work

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-15T19:35:43.266401Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 962cf9b4-4244-49cb-a747-bf619d8b6c53 · outbound

This paper cites Physics informed WNO.Computer Methods in Applied Mechanics and Engineering, 418:116546, 2024.

From Local Interactions to Global Operators: Scalable Gaussian Process Operator for Physical Systems Physics informed WNO.Computer Methods in Applied Mechanics and Engineering, 418:116546, 2024

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:35:44.022776Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 93ae8172-486e-4fb3-9e86-3238fb7582db · outbound

This paper cites Multi-fidelity wavelet neural operator surrogate model for time-independent and time-dependent reliability analysis.Probabilistic Engineering Mechanics, 77:103672, 2024.

From Local Interactions to Global Operators: Scalable Gaussian Process Operator for Physical Systems Multi-fidelity wavelet neural operator surrogate model for time-independent and time-dependent reliability analysis.Probabilistic Engineering Mechanics, 77:103672, 2024

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:35:44.009093Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 9d954a36-9c86-4560-b972-4e31002cb937 · outbound

This paper cites A foundational neural operator that continuously learns without forgetting, 2023.

From Local Interactions to Global Operators: Scalable Gaussian Process Operator for Physical Systems A foundational neural operator that continuously learns without forgetting, 2023

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:35:43.994122Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation b389a57b-bd22-4457-bd4a-8356c9ddfa6e · outbound

This paper cites LNO: Laplace Neural Operator for Solving Differential Equations, 2023.

From Local Interactions to Global Operators: Scalable Gaussian Process Operator for Physical Systems LNO: Laplace Neural Operator for Solving Differential Equations, 2023

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:35:43.980180Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation e7cb474c-09e8-4725-8b5c-f977f9bafba6 · outbound

This paper cites Variational physics-informed neural operator (vino) for solving partial differential equations.Computer Methods in Applied Mechanics and Engineering, 437:117785, 2025.

From Local Interactions to Global Operators: Scalable Gaussian Process Operator for Physical Systems Variational physics-informed neural operator (vino) for solving partial differential equations.Computer Methods in Applied Mechanics and Engineering, 437:117785, 2025

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:35:43.965067Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 095455ed-4da0-40a0-a04b-233b1b6cb619 · outbound

This paper cites A wavelet neural operator based elastography for localization and quantification of tumors.Computer Methods and Programs in Biomedicine, 232:107436, 2023.

From Local Interactions to Global Operators: Scalable Gaussian Process Operator for Physical Systems A wavelet neural operator based elastography for localization and quantification of tumors.Computer Methods and Programs in Biomedicine, 232:107436, 2023

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:35:43.951048Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation c13ff39d-3cff-41a9-87f3-2832512f8121 · outbound

This paper cites A physics-informed variational deeponet for predicting crack path in quasi-brittle materials.Computer Methods in Applied Mechanics and Engineering, 391:114587, March 2022.

From Local Interactions to Global Operators: Scalable Gaussian Process Operator for Physical Systems A physics-informed variational deeponet for predicting crack path in quasi-brittle materials.Computer Methods in Applied Mechanics and Engineering, 391:114587, March 2022

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:35:43.936896Z

Source-reported events for the cited work

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Observation b88e6f3f-7768-4b44-a0e4-1dac8e09dbe5 · outbound

This paper cites Predicting crack nucleation and propagation in brittle materials using deep operator networks with diverse trunk architectures.

From Local Interactions to Global Operators: Scalable Gaussian Process Operator for Physical Systems Predicting crack nucleation and propagation in brittle materials using deep operator networks with diverse trunk architectures

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:35:43.922463Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 45ec8947-97a4-48c9-8b34-67a4b10d7ccf · outbound

This paper cites Learning bias corrections for climate models using deep neural operators, 2023.

From Local Interactions to Global Operators: Scalable Gaussian Process Operator for Physical Systems Learning bias corrections for climate models using deep neural operators, 2023

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:35:43.908656Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 6d7de41f-677c-4a20-a823-6b711c0f8b32 · outbound

This paper cites Fourcastnet: A global data-driven high-resolution weather model using adaptive fourier neural operators, 2022.

From Local Interactions to Global Operators: Scalable Gaussian Process Operator for Physical Systems Fourcastnet: A global data-driven high-resolution weather model using adaptive fourier neural operators, 2022

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:35:43.893942Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 6b604029-38a8-4b1d-b71d-bd587efcba6a · outbound

This paper cites Spherical neural operator network for global weather prediction.IEEE Transactions on Circuits and Systems for Video Technology, 2023.

From Local Interactions to Global Operators: Scalable Gaussian Process Operator for Physical Systems Spherical neural operator network for global weather prediction.IEEE Transactions on Circuits and Systems for Video Technology, 2023

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:35:43.879436Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 23be43c0-b7c7-4c48-b879-d5a5e2323f71 · outbound

This paper cites Variational Bayes Deep Operator Network: A data-driven Bayesian solver for parametric differential equations, 2022.

From Local Interactions to Global Operators: Scalable Gaussian Process Operator for Physical Systems Variational Bayes Deep Operator Network: A data-driven Bayesian solver for parametric differential equations, 2022

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:35:43.864851Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation bb2451ad-49e9-4e2d-b77f-1653d1d65166 · outbound

This paper cites Randomized prior wavelet neural operator for uncertainty quantification, 2023.

From Local Interactions to Global Operators: Scalable Gaussian Process Operator for Physical Systems Randomized prior wavelet neural operator for uncertainty quantification, 2023

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:35:43.850277Z

Source-reported events for the cited work

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Observation b90d8c0c-63b0-4037-b7f9-1f2458feb60f · outbound

This paper cites Approximate Bayesian Neural Operators: Uncertainty Quantification for Parametric PDEs.

From Local Interactions to Global Operators: Scalable Gaussian Process Operator for Physical Systems Approximate Bayesian Neural Operators: Uncertainty Quantification for Parametric PDEs

Reference 18

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Source-reported events for the cited work

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Observation cf40f9d1-3c9f-4f6a-b1da-359c2abb1310 · outbound

This paper cites Kernel methods are competitive for operator learning, 2023.

From Local Interactions to Global Operators: Scalable Gaussian Process Operator for Physical Systems Kernel methods are competitive for operator learning, 2023

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:35:43.835563Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 2d92e01b-807a-4d9e-a9cb-a46c482ab005 · outbound

This paper cites B-pinns: Bayesian physics-informed neural networks for forward and inverse pde problems with noisy data.Journal of Computational Physics, 425:109913, January 2021.

From Local Interactions to Global Operators: Scalable Gaussian Process Operator for Physical Systems B-pinns: Bayesian physics-informed neural networks for forward and inverse pde problems with noisy data.Journal of Computational Physics, 425:109913, January 2021

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:35:43.820019Z

Source-reported events for the cited work

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Observation b79e34d5-a163-4da6-86fc-37629eb65a28 · outbound

This paper cites an unresolved cited work.

From Local Interactions to Global Operators: Scalable Gaussian Process Operator for Physical Systems Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-08-15T19:35:43.803203Z

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Observation 2ff753ec-ba90-4744-960d-fdeb0c0a3eee · outbound

This paper cites Gaussian Processes for Big Data.

From Local Interactions to Global Operators: Scalable Gaussian Process Operator for Physical Systems Gaussian Processes for Big Data

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-15T19:35:43.348734Z

Source-reported events for the cited work

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Observation fd13f5a9-91ef-490a-8039-ce6b53e8d83c · outbound

This paper cites Hierarchical nearest-neighbor gaussian process models for large geostatistical datasets.Journal of the American Statistical Association, 111(514):800–812, 2016.

From Local Interactions to Global Operators: Scalable Gaussian Process Operator for Physical Systems Hierarchical nearest-neighbor gaussian process models for large geostatistical datasets.Journal of the American Statistical Association, 111(514):800–812, 2016

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:35:43.788890Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation aec1dd4c-d559-4362-8b02-8d8854b5ea8e · outbound

This paper cites Variational nearest neighbor gaussian process.

From Local Interactions to Global Operators: Scalable Gaussian Process Operator for Physical Systems Variational nearest neighbor gaussian process

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:35:43.773493Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 76b5aeca-fe3c-4270-9145-edd588c02643 · outbound

This paper cites Actually sparse variational gaussian processes.

From Local Interactions to Global Operators: Scalable Gaussian Process Operator for Physical Systems Actually sparse variational gaussian processes

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:35:43.757438Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 37db4d11-5bf8-47dc-a51d-5d13712a2d77 · outbound

This paper cites Variational fourier features for gaussian processes.Journal of Machine Learning Research, 18(151):1–52, 2018.

From Local Interactions to Global Operators: Scalable Gaussian Process Operator for Physical Systems Variational fourier features for gaussian processes.Journal of Machine Learning Research, 18(151):1–52, 2018

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:35:43.742540Z

Source-reported events for the cited work

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Observation 65cf984f-53d7-4af1-93e8-5c72181ee642 · outbound

This paper cites Kernel interpolation for scalable structured gaussian processes (kiss-gp).

From Local Interactions to Global Operators: Scalable Gaussian Process Operator for Physical Systems Kernel interpolation for scalable structured gaussian processes (kiss-gp)

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-15T19:35:43.370382Z

Source-reported events for the cited work

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Observation b0cd79e9-9719-47d9-a7fe-2821b507ee90 · outbound

This paper cites Scalable variational Gaussian process classifica- tion.

From Local Interactions to Global Operators: Scalable Gaussian Process Operator for Physical Systems Scalable variational Gaussian process classifica- tion

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:35:43.716712Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 6814886e-3dbe-48bb-b094-7712c54d8a03 · outbound

This paper cites Sparse orthogonal variational inference for gaussian processes.

From Local Interactions to Global Operators: Scalable Gaussian Process Operator for Physical Systems Sparse orthogonal variational inference for gaussian processes

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:35:43.701822Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation fa7b933f-6f4f-4595-9c8c-e0c816f6d2d2 · outbound

This paper cites Stochastic Gradient Descent for Gaussian Processes Done Right.

From Local Interactions to Global Operators: Scalable Gaussian Process Operator for Physical Systems Stochastic Gradient Descent for Gaussian Processes Done Right

Reference 30

Resolution: verified exact; local_arxiv, observed 2026-08-15T19:35:43.490095Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 09502482-59bf-49e2-86f1-873f835b1dc7 · outbound

This paper cites Operator-valued kernels for learning from functional response data.Journal of Machine Learning Research, 17(20):1–54, 2016.

From Local Interactions to Global Operators: Scalable Gaussian Process Operator for Physical Systems Operator-valued kernels for learning from functional response data.Journal of Machine Learning Research, 17(20):1–54, 2016

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:35:43.686349Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 53232971-76d1-4194-9432-b0f2ee18a965 · outbound

This paper cites Operator-Valued Bochner Theorem, Fourier Feature Maps for Operator-Valued Kernels, and Vector-Valued Learning.

From Local Interactions to Global Operators: Scalable Gaussian Process Operator for Physical Systems Operator-Valued Bochner Theorem, Fourier Feature Maps for Operator-Valued Kernels, and Vector-Valued Learning

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-15T19:35:43.392719Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3a3ffe4f-1ad6-43b4-8c88-cd94fc4cba2c · outbound

This paper cites Linearization turns neural operators into function-valued gaussian processes, 2024.

From Local Interactions to Global Operators: Scalable Gaussian Process Operator for Physical Systems Linearization turns neural operators into function-valued gaussian processes, 2024

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:35:43.669617Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 297361f7-ad27-4321-8526-17e59afc8430 · outbound

This paper cites Multi-outputs gaussian process for predicting burkina faso covid-19 spread using correlations from the weather parameters.Infectious Disease Modelling, 2022.

From Local Interactions to Global Operators: Scalable Gaussian Process Operator for Physical Systems Multi-outputs gaussian process for predicting burkina faso covid-19 spread using correlations from the weather parameters.Infectious Disease Modelling, 2022

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:35:43.654787Z

Source-reported events for the cited work

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Observation 752de272-a8fa-4379-9969-c7643507c55d · outbound

This paper cites Derivation of output correlation inferences for multi-output (aka multi-task) gaussian process, 2025.

From Local Interactions to Global Operators: Scalable Gaussian Process Operator for Physical Systems Derivation of output correlation inferences for multi-output (aka multi-task) gaussian process, 2025

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:35:43.638843Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 58e21f4f-a4f4-49ac-94b5-d8f4c3065fbf · outbound

This paper cites Alvarez, Lorenzo Rosasco, and Neil D.

From Local Interactions to Global Operators: Scalable Gaussian Process Operator for Physical Systems Alvarez, Lorenzo Rosasco, and Neil D

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:35:43.622901Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation fca54456-65ad-4d61-80a6-10c711db3dd0 · outbound

This paper cites Geostatistical space-time models, stationarity, separability, and full symmetry.Monographs On Statistics and Applied Probability, 107:151, 2006.

From Local Interactions to Global Operators: Scalable Gaussian Process Operator for Physical Systems Geostatistical space-time models, stationarity, separability, and full symmetry.Monographs On Statistics and Applied Probability, 107:151, 2006

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:35:43.606537Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 2df904ce-cf98-4e79-998f-fec9b2bdd70c · outbound

This paper cites Springer Berlin Heidelberg, Berlin, Heidelberg, 2004.

From Local Interactions to Global Operators: Scalable Gaussian Process Operator for Physical Systems Springer Berlin Heidelberg, Berlin, Heidelberg, 2004

Reference 38

Resolution: unresolved; no resolver link, observed 2026-08-15T19:35:43.422526Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1eb9867d-ec1f-4121-bf7d-70790f3620bb · outbound

This paper cites Neural operator induced Gaussian process framework for probabilistic solution of parametric partial differential equations, 2024.

From Local Interactions to Global Operators: Scalable Gaussian Process Operator for Physical Systems Neural operator induced Gaussian process framework for probabilistic solution of parametric partial differential equations, 2024

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:35:43.581865Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 4f3d1c52-db85-46d4-a3c4-71307210993d · outbound

This paper cites Springer, 2015.

From Local Interactions to Global Operators: Scalable Gaussian Process Operator for Physical Systems Springer, 2015

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:35:43.566796Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Pith citing papers

No inbound Pith citation observations are available.