Paper Citation Record · LEDGER

Principal-Part Decomposition for Neural Operator Learning of Dirichlet-to-Neumann Maps

As of 9 August 2026, this Paper Citation Record lists 19 of 19 outbound references and 0 inbound Pith citation observations for arXiv:2606.25952.

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

pith.paper-citation-record.v1
2606.25952 v1

Coverage vector

measured 19 of 19 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-06-25T19:17:06.187973Z

measured 19 of 19 standing notices

One-hop event checks from named stored sources.

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

19 of 19 outbound references displayed

verified exact0
verified fuzzy0
unresolved18
parse uncertain0
malformed identifier0
metadata mismatch1

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 208227c0-b84a-435c-9773-48d5e6cf9673 · outbound

This paper cites Melchers, J.H.M.

Principal-Part Decomposition for Neural Operator Learning of Dirichlet-to-Neumann Maps Melchers, J.H.M

Reference 1

Resolution: unresolved; no resolver link, observed 2026-06-25T19:17:06.187973Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8d0bd411-0aa3-44e3-adc4-9856b99ff1be · outbound

This paper cites On the spectral bias of neural networks.

Principal-Part Decomposition for Neural Operator Learning of Dirichlet-to-Neumann Maps On the spectral bias of neural networks

Reference 2

Resolution: unresolved; no resolver link, observed 2026-06-25T19:17:06.187973Z

Source-reported events for the cited work

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Observation 5bca04eb-836b-4376-bd99-829773e15191 · outbound

This paper cites U-NO: U-shaped Neural Operators.

Principal-Part Decomposition for Neural Operator Learning of Dirichlet-to-Neumann Maps U-NO: U-shaped Neural Operators

Reference 3

Resolution: metadata mismatch; arxiv_id, observed 2026-07-04T21:00:09.180713Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 131cf5b8-21ee-43c7-9479-d0194f400189 · outbound

This paper cites an unresolved cited work.

Principal-Part Decomposition for Neural Operator Learning of Dirichlet-to-Neumann Maps Unresolved cited work

Reference 4

Resolution: unresolved; no resolver link, observed 2026-06-25T19:17:06.187973Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a0ee2334-f1a1-4781-85dd-cbdc2963c33c · outbound

This paper cites Sauter and C.

Principal-Part Decomposition for Neural Operator Learning of Dirichlet-to-Neumann Maps Sauter and C

Reference 5

Resolution: unresolved; no resolver link, observed 2026-06-25T19:17:06.187973Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 07a01c83-b992-4be2-a154-5160737c1919 · outbound

This paper cites an unresolved cited work.

Principal-Part Decomposition for Neural Operator Learning of Dirichlet-to-Neumann Maps Unresolved cited work

Reference 6

Resolution: unresolved; no resolver link, observed 2026-06-25T19:17:06.187973Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 02bd768e-bb25-4a2b-9fac-cb7aabf7824b · outbound

This paper cites Operator learning with neural fields: Tackling PDEs on general geometries.

Principal-Part Decomposition for Neural Operator Learning of Dirichlet-to-Neumann Maps Operator learning with neural fields: Tackling PDEs on general geometries

Reference 7

Resolution: unresolved; no resolver link, observed 2026-06-25T19:17:06.187973Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d82602b6-701b-42da-b78b-84f981f19bcf · outbound

This paper cites Dgm: A deep learning algorithm for solving partial differential equations.Journal of computational physics, 375:1339–1364, 2018.

Principal-Part Decomposition for Neural Operator Learning of Dirichlet-to-Neumann Maps Dgm: A deep learning algorithm for solving partial differential equations.Journal of computational physics, 375:1339–1364, 2018

Reference 8

Resolution: unresolved; no resolver link, observed 2026-06-25T19:17:06.187973Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8c6ac9a2-5504-4bb5-9671-677ff4ac99e1 · outbound

This paper cites A global uniqueness theorem for an inverse boundary value problem.Annals of mathematics, pages 153–169, 1987.

Principal-Part Decomposition for Neural Operator Learning of Dirichlet-to-Neumann Maps A global uniqueness theorem for an inverse boundary value problem.Annals of mathematics, pages 153–169, 1987

Reference 9

Resolution: unresolved; no resolver link, observed 2026-06-25T19:17:06.187973Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a312d132-6034-402d-8f08-2e3e0e23430b · outbound

This paper cites Toselli and O.

Principal-Part Decomposition for Neural Operator Learning of Dirichlet-to-Neumann Maps Toselli and O

Reference 10

Resolution: unresolved; no resolver link, observed 2026-06-25T19:17:06.187973Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a7d476f3-91c6-4597-969d-5ca6c8060aa0 · outbound

This paper cites Factorized fourier neural operators.

Principal-Part Decomposition for Neural Operator Learning of Dirichlet-to-Neumann Maps Factorized fourier neural operators

Reference 11

Resolution: unresolved; no resolver link, observed 2026-06-25T19:17:06.187973Z

Source-reported events for the cited work

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Observation 60430755-46b1-416e-ad86-56f72f5e9718 · outbound

This paper cites BENO: Boundary-embedded neural oper- ators for elliptic PDEs.

Principal-Part Decomposition for Neural Operator Learning of Dirichlet-to-Neumann Maps BENO: Boundary-embedded neural oper- ators for elliptic PDEs

Reference 12

Resolution: unresolved; no resolver link, observed 2026-06-25T19:17:06.187973Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e885a8d8-87ad-45fe-884b-3b49e5d0a60e · outbound

This paper cites Learning the solution operator of parametric partial differential equations with physics-informed deeponets.Science advances, 7(40):eabi8605, 2021.

Principal-Part Decomposition for Neural Operator Learning of Dirichlet-to-Neumann Maps Learning the solution operator of parametric partial differential equations with physics-informed deeponets.Science advances, 7(40):eabi8605, 2021

Reference 13

Resolution: unresolved; no resolver link, observed 2026-06-25T19:17:06.187973Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation eaa7d754-e8a0-4719-9207-d64f791c5aa5 · outbound

This paper cites Iterative training of physics-informed neural networks with fourier-enhanced features.

Principal-Part Decomposition for Neural Operator Learning of Dirichlet-to-Neumann Maps Iterative training of physics-informed neural networks with fourier-enhanced features

Reference 14

Resolution: unresolved; no resolver link, observed 2026-06-25T19:17:06.187973Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a18569c2-5ba3-44e5-b3ce-9e1ce08b2694 · outbound

This paper cites A local deep learning method for solving high order partial differential equations.

Principal-Part Decomposition for Neural Operator Learning of Dirichlet-to-Neumann Maps A local deep learning method for solving high order partial differential equations

Reference 15

Resolution: unresolved; no resolver link, observed 2026-06-25T19:17:06.187973Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5216071a-2a9c-4e15-b6a4-f9dea08046d0 · outbound

This paper cites A scalable frame- work for learning the geometry-dependent solution operators of partial differential equations.Nature computational science, 4(12):928–940, 2024.

Principal-Part Decomposition for Neural Operator Learning of Dirichlet-to-Neumann Maps A scalable frame- work for learning the geometry-dependent solution operators of partial differential equations.Nature computational science, 4(12):928–940, 2024

Reference 16

Resolution: unresolved; no resolver link, observed 2026-06-25T19:17:06.187973Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cbf76087-65b1-4234-be35-a41509607445 · outbound

This paper cites The deep ritz method: a deep learning-based numerical algorithm for solving variational problems.

Principal-Part Decomposition for Neural Operator Learning of Dirichlet-to-Neumann Maps The deep ritz method: a deep learning-based numerical algorithm for solving variational problems

Reference 17

Resolution: unresolved; no resolver link, observed 2026-06-25T19:17:06.187973Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a458deeb-ec9e-4a55-b518-dde007cded6b · outbound

This paper cites All models are trained using theAdamoptimizer.

Principal-Part Decomposition for Neural Operator Learning of Dirichlet-to-Neumann Maps All models are trained using theAdamoptimizer

Reference 18

Resolution: unresolved; no resolver link, observed 2026-06-25T19:17:06.187973Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bbca7fe1-e7be-419e-8c15-743453791e6e · outbound

This paper cites All models are trained using theAdamoptimizer.

Principal-Part Decomposition for Neural Operator Learning of Dirichlet-to-Neumann Maps All models are trained using theAdamoptimizer

Reference 19

Resolution: unresolved; no resolver link, observed 2026-06-25T19:17:06.187973Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.