Paper Citation Record · LEDGER

Kernel-based Operator Learning: Error Analysis, Budget Allocation, and a Physics-Informed Extension

As of 17 August 2026, this Paper Citation Record lists 37 of 37 outbound references and 0 inbound Pith citation observations for arXiv:2607.06287.

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

pith.paper-citation-record.v1
2607.06287 v1

Coverage vector

measured 37 of 37 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-07-08T11:15:22.032661Z

measured 37 of 37 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-17T06:30:58.91139+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

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measured 0 of 1 external citation measurements

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Source: cited_works

Reference resolution

37 of 37 outbound references displayed

verified exact24
verified fuzzy8
unresolved0
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External citation measurements

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Outbound references

Observation ca8fccb5-1687-4c02-b583-3c6e207d5f3f · outbound

This paper cites Arcangeli, M.

Kernel-based Operator Learning: Error Analysis, Budget Allocation, and a Physics-Informed Extension Arcangeli, M

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T11:24:55.684868Z

Source-reported events for the cited work

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Observation 40184fa9-af70-4cb9-81cc-558fde91c427 · outbound

This paper cites Kernel methods are competitive for operator learning.

Kernel-based Operator Learning: Error Analysis, Budget Allocation, and a Physics-Informed Extension Kernel methods are competitive for operator learning

Reference 2

Resolution: verified exact; arxiv_id, observed 2026-07-08T11:24:54.679147Z

Source-reported events for the cited work

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Observation eb53e4fc-16b4-4c67-924a-cb6ad9eb41a6 · outbound

This paper cites Brenner and L.

Kernel-based Operator Learning: Error Analysis, Budget Allocation, and a Physics-Informed Extension Brenner and L

Reference 3

Resolution: verified exact; doi, observed 2026-07-08T11:24:54.714505Z

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Observation c0529381-c201-4d93-81e5-1114fe8cd1a6 · outbound

This paper cites an unresolved cited work.

Kernel-based Operator Learning: Error Analysis, Budget Allocation, and a Physics-Informed Extension Unresolved cited work

Reference 4

Resolution: verified exact; arxiv_id, observed 2026-07-08T11:24:54.760738Z

Source-reported events for the cited work

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Observation 77be2495-9b07-4fa5-8e56-0b03f0c05423 · outbound

This paper cites Sur l erreur d interpolation des fonctions de plusieurs variables par les d^m -splines.

Kernel-based Operator Learning: Error Analysis, Budget Allocation, and a Physics-Informed Extension Sur l erreur d interpolation des fonctions de plusieurs variables par les d^m -splines

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T11:24:55.699841Z

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Observation 15dc9072-511e-4247-8305-d66bb872682c · outbound

This paper cites Partial Differential Equations.

Kernel-based Operator Learning: Error Analysis, Budget Allocation, and a Physics-Informed Extension Partial Differential Equations

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T11:24:55.682292Z

Source-reported events for the cited work

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Observation 9b196e78-5418-4447-8de0-3145e5b140c2 · outbound

This paper cites Kernel-based Approximation Meth ods using MATLAB.

Kernel-based Operator Learning: Error Analysis, Budget Allocation, and a Physics-Informed Extension Kernel-based Approximation Meth ods using MATLAB

Reference 7

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Observation d672403f-ff75-4444-9e59-7e5503c44030 · outbound

This paper cites Fuselier.

Kernel-based Operator Learning: Error Analysis, Budget Allocation, and a Physics-Informed Extension Fuselier

Reference 8

Resolution: verified exact; arxiv_id, observed 2026-07-08T11:24:54.949921Z

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Observation b5ba55d5-dc9c-47dc-9873-462a99df7cc6 · outbound

This paper cites Vector-valued gaussian processes for approximating divergence- or rotation-free vector fields, 2025.

Kernel-based Operator Learning: Error Analysis, Budget Allocation, and a Physics-Informed Extension Vector-valued gaussian processes for approximating divergence- or rotation-free vector fields, 2025

Reference 9

Resolution: verified exact; arxiv_id, observed 2026-07-08T11:24:54.944452Z

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Observation 3ac00fe4-4503-4fb3-aae5-a3e0f24602e9 · outbound

This paper cites Operator-valued kernels for learning from functional response data.

Kernel-based Operator Learning: Error Analysis, Budget Allocation, and a Physics-Informed Extension Operator-valued kernels for learning from functional response data

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T11:24:55.702829Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation a8fe1299-b6b0-41e6-9232-348db954bb69 · outbound

This paper cites an unresolved cited work.

Kernel-based Operator Learning: Error Analysis, Budget Allocation, and a Physics-Informed Extension Unresolved cited work

Reference 11

Resolution: verified exact; doi, observed 2026-07-08T11:24:54.689107Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation a2af14f5-1743-47a3-809e-46eeb3f3e41a · outbound

This paper cites Stuart, and Anima Anandkumar.

Kernel-based Operator Learning: Error Analysis, Budget Allocation, and a Physics-Informed Extension Stuart, and Anima Anandkumar

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T11:24:55.696834Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 81d0d11b-d4ce-4cfd-9b62-18341b31d0af · outbound

This paper cites A kernel framework for learning differential equations and their solution operators.

Kernel-based Operator Learning: Error Analysis, Budget Allocation, and a Physics-Informed Extension A kernel framework for learning differential equations and their solution operators

Reference 13

Resolution: verified exact; arxiv_id, observed 2026-07-08T11:24:54.779713Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation be2136ae-f8d3-47da-8171-89c5f4fdab0a · outbound

This paper cites Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators.

Kernel-based Operator Learning: Error Analysis, Budget Allocation, and a Physics-Informed Extension Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators

Reference 14

Resolution: verified exact; doi, observed 2026-07-08T11:24:54.789072Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation f1b634e8-0cf2-4708-905f-10b9ee996960 · outbound

This paper cites A comprehensive and fair comparison of two neural operators (with practical extensions) based on FAIR data.

Kernel-based Operator Learning: Error Analysis, Budget Allocation, and a Physics-Informed Extension A comprehensive and fair comparison of two neural operators (with practical extensions) based on FAIR data

Reference 15

Resolution: verified exact; arxiv_id, observed 2026-07-08T11:24:54.750962Z

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Observation 2f001e9f-0084-4437-a642-bec60b889f4d · outbound

This paper cites Mat \'e rn.

Kernel-based Operator Learning: Error Analysis, Budget Allocation, and a Physics-Informed Extension Mat \'e rn

Reference 16

Resolution: verified exact; doi, observed 2026-07-08T11:24:54.773014Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 6c90879c-3ff0-4ed1-bf37-927cc4250f6e · outbound

This paper cites Neural Computation , author =.

Kernel-based Operator Learning: Error Analysis, Budget Allocation, and a Physics-Informed Extension Neural Computation , author =

Reference 17

Resolution: metadata mismatch; doi, observed 2026-07-08T11:24:54.768795Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 877a3e4e-cf06-4149-a4e2-f98e95fd89e4 · outbound

This paper cites Operator learning with gaussian processes.

Kernel-based Operator Learning: Error Analysis, Budget Allocation, and a Physics-Informed Extension Operator learning with gaussian processes

Reference 18

Resolution: verified exact; arxiv_id, observed 2026-07-08T11:24:54.705432Z

Source-reported events for the cited work

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Observation 1eae863b-1636-4031-b315-594c9b3d359b · outbound

This paper cites Narcowich and Joseph D.

Kernel-based Operator Learning: Error Analysis, Budget Allocation, and a Physics-Informed Extension Narcowich and Joseph D

Reference 19

Resolution: verified exact; doi, observed 2026-07-08T11:24:54.764537Z

Source-reported events for the cited work

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Observation 1d2639ff-4ed6-48f5-8863-25103932cc11 · outbound

This paper cites Narcowich, Joseph D.

Kernel-based Operator Learning: Error Analysis, Budget Allocation, and a Physics-Informed Extension Narcowich, Joseph D

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T11:24:55.694123Z

Source-reported events for the cited work

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Observation a8a739c0-8552-4286-97ed-ec4fa730301f · outbound

This paper cites Sobolev error estimates and a bernstein inequality for scattered data interpolation via radial basis functions.

Kernel-based Operator Learning: Error Analysis, Budget Allocation, and a Physics-Informed Extension Sobolev error estimates and a bernstein inequality for scattered data interpolation via radial basis functions

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T11:24:55.691425Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 0b33359f-081b-469b-a343-49b3dc7cd1cc · outbound

This paper cites Narcowich, Joseph D.

Kernel-based Operator Learning: Error Analysis, Budget Allocation, and a Physics-Informed Extension Narcowich, Joseph D

Reference 22

Resolution: verified exact; doi, observed 2026-07-08T11:24:54.699373Z

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Observation 54c8e0cd-99b5-47e1-bbce-702bb0616bdc · outbound

This paper cites Nelsen and Andrew M.

Kernel-based Operator Learning: Error Analysis, Budget Allocation, and a Physics-Informed Extension Nelsen and Andrew M

Reference 23

Resolution: verified exact; doi, observed 2026-07-08T11:24:54.742807Z

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Observation 0f45995f-aa30-4f43-a191-5e13247f64c4 · outbound

This paper cites Do ideas have shape? idea registration as the continuous limit of artificial neural networks.

Kernel-based Operator Learning: Error Analysis, Budget Allocation, and a Physics-Informed Extension Do ideas have shape? idea registration as the continuous limit of artificial neural networks

Reference 24

Resolution: verified exact; arxiv_id, observed 2026-07-08T11:24:54.734656Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation fb5b3071-f924-47e6-a905-7ba94ecdba29 · outbound

This paper cites Operator-Adapted Wavelets, Fast Solvers, and Numerical Homogenization: From a Game Theoretic Approach to Numerical Approximation and Algorithm Design.

Kernel-based Operator Learning: Error Analysis, Budget Allocation, and a Physics-Informed Extension Operator-Adapted Wavelets, Fast Solvers, and Numerical Homogenization: From a Game Theoretic Approach to Numerical Approximation and Algorithm Design

Reference 25

Resolution: verified exact; doi, observed 2026-07-08T11:24:54.784335Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 2b109e20-f08c-4367-81ce-d7a9d55081ca · outbound

This paper cites U ber die Zerlegung einer empirischen Funktion in Sinuswellen . Schl \.

Kernel-based Operator Learning: Error Analysis, Budget Allocation, and a Physics-Informed Extension U ber die Zerlegung einer empirischen Funktion in Sinuswellen . Schl \

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T11:24:55.688104Z

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Observation e5abed9c-c87d-4150-afa2-37b578a3f030 · outbound

This paper cites Unsymmetric meshless methods for operator equations.

Kernel-based Operator Learning: Error Analysis, Budget Allocation, and a Physics-Informed Extension Unsymmetric meshless methods for operator equations

Reference 27

Resolution: verified exact; doi, observed 2026-07-08T11:24:54.718414Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation c985b67c-5f42-457f-b9e9-af89ed0e1426 · outbound

This paper cites Kernel techniques: From machine learning to meshless methods.

Kernel-based Operator Learning: Error Analysis, Budget Allocation, and a Physics-Informed Extension Kernel techniques: From machine learning to meshless methods

Reference 28

Resolution: verified exact; doi, observed 2026-07-08T11:24:54.793022Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation ab3a6859-a43d-4d5e-837c-4bc9382f10b4 · outbound

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Kernel-based Operator Learning: Error Analysis, Budget Allocation, and a Physics-Informed Extension 2018 , Bdsk-Url-1 =

Reference 29

Resolution: verified exact; doi, observed 2026-07-08T11:24:54.722847Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation d59624b9-586a-4137-9800-497cb0a20007 · outbound

This paper cites Fluids You Can Trust: Property-Preserving Operator Learning for Incompressible Flows.

Kernel-based Operator Learning: Error Analysis, Budget Allocation, and a Physics-Informed Extension Fluids You Can Trust: Property-Preserving Operator Learning for Incompressible Flows

Reference 30

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Observation 7e45427c-a655-415d-8081-8016b721ff56 · outbound

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Kernel-based Operator Learning: Error Analysis, Budget Allocation, and a Physics-Informed Extension Support vector machines

Reference 31

Resolution: verified exact; doi, observed 2026-07-08T11:24:54.726097Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 892b7ad6-f65d-4ed1-94cb-2010ce8542fc · outbound

This paper cites Optimizing shape parameters in rbf methods: A systematic review of techniques, applications, and computational challenges.

Kernel-based Operator Learning: Error Analysis, Budget Allocation, and a Physics-Informed Extension Optimizing shape parameters in rbf methods: A systematic review of techniques, applications, and computational challenges

Reference 32

Resolution: verified exact; arxiv_id, observed 2026-07-08T11:24:54.710463Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation cbf3d6e2-0fbd-4992-8c47-fe3d9146c14c · outbound

This paper cites Learning the solution operator of parametric partial differential equations with physics-informed DeepONets.

Kernel-based Operator Learning: Error Analysis, Budget Allocation, and a Physics-Informed Extension Learning the solution operator of parametric partial differential equations with physics-informed DeepONets

Reference 33

Resolution: verified exact; doi, observed 2026-07-08T11:24:54.684626Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 8741b756-8ac8-4e76-a55f-f49f66bb3553 · outbound

This paper cites Improved architectures and training algorithms for deep operator networks.

Kernel-based Operator Learning: Error Analysis, Budget Allocation, and a Physics-Informed Extension Improved architectures and training algorithms for deep operator networks

Reference 34

Resolution: verified exact; doi, observed 2026-07-08T11:24:54.694499Z

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Observation cd643087-b182-4302-9d7d-9a1fa11b86ae · outbound

This paper cites Advances in Computational Mathematics , author =.

Kernel-based Operator Learning: Error Analysis, Budget Allocation, and a Physics-Informed Extension Advances in Computational Mathematics , author =

Reference 35

Resolution: metadata mismatch; doi, observed 2026-07-08T11:24:54.673349Z

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Observation 43df3f2f-96dc-4277-9127-727c26097b23 · outbound

This paper cites Wendland, Scattered Data Approximation, Cambridge Monographs on Applied and Computational Mathematics, Cambridge University Press, Cambridge.

Kernel-based Operator Learning: Error Analysis, Budget Allocation, and a Physics-Informed Extension Wendland, Scattered Data Approximation, Cambridge Monographs on Applied and Computational Mathematics, Cambridge University Press, Cambridge

Reference 36

Resolution: metadata mismatch; doi, observed 2026-07-08T11:24:54.669810Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation c6538fd0-31cf-437e-ab07-9040255f56b4 · outbound

This paper cites Wendland and C.

Kernel-based Operator Learning: Error Analysis, Budget Allocation, and a Physics-Informed Extension Wendland and C

Reference 37

Resolution: metadata mismatch; doi, observed 2026-07-08T11:24:54.737966Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Pith citing papers

No inbound Pith citation observations are available.