Paper Citation Record · LEDGER

Neural Preconditioning Operator for Efficient PDE Solves

As of 9 August 2026, this Paper Citation Record lists 29 of 29 outbound references and 5 inbound Pith citation observations for arXiv:2502.01337.

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

pith.paper-citation-record.v1
2502.01337 v2

Coverage vector

measured 29 of 29 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-09T15:42:31.788171Z

measured 34 of 34 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-09T06:31:02.800959+00:00

measured 5 of 5 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-03T02:19:22.490570Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-02T20:17:21.228475Z

Reference resolution

29 of 29 outbound references displayed

verified exact4
verified fuzzy12
unresolved11
parse uncertain0
malformed identifier1
metadata mismatch1

External citation measurements

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Outbound references

Observation 4df73987-d9b2-437c-a0db-6c2d496c47e4 · outbound

This paper cites Düben, Tim N.

Neural Preconditioning Operator for Efficient PDE Solves Düben, Tim N

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-09T15:42:31.714461Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 167c8177-7222-4509-b6c3-9dbc84766669 · outbound

This paper cites Briggs, V .E.

Neural Preconditioning Operator for Efficient PDE Solves Briggs, V .E

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T15:42:32.721686Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 956a022b-56e9-490a-b54b-fa60fd00ec3a · outbound

This paper cites Neural-network preconditioners for solving the Dirac equation in lattice gauge theory.

Neural Preconditioning Operator for Efficient PDE Solves Neural-network preconditioners for solving the Dirac equation in lattice gauge theory

Reference 3

Resolution: metadata mismatch; local_arxiv, observed 2026-08-09T15:42:32.331678Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation f3c7939e-f6d2-4762-80cc-2319914cd1ba · outbound

This paper cites Choose a transformer: Fourier or galerkin.

Neural Preconditioning Operator for Efficient PDE Solves Choose a transformer: Fourier or galerkin

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T15:42:32.714049Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 46c92ea3-7f9e-4a14-93df-7f1cb62140c4 · outbound

This paper cites Finite volume methods.

Neural Preconditioning Operator for Efficient PDE Solves Finite volume methods

Reference 5

Resolution: malformed identifier; raw_fallback, observed 2026-08-09T15:42:32.707140Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 33e3d2a8-4b19-4bd7-aa59-2bafd429590f · outbound

This paper cites an unresolved cited work.

Neural Preconditioning Operator for Efficient PDE Solves Unresolved cited work

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-09T15:42:31.730031Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0013fc9f-5a38-4a5b-b17f-cf1919acbc84 · outbound

This paper cites an unresolved cited work.

Neural Preconditioning Operator for Efficient PDE Solves Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-09T15:42:32.700013Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 958dd6c8-8ce6-4324-86fd-60084e8f1451 · outbound

This paper cites Learn- ing neural PDE solvers with convergence guarantees.

Neural Preconditioning Operator for Efficient PDE Solves Learn- ing neural PDE solvers with convergence guarantees

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T15:42:32.693280Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation bc73e9e8-c9d1-450d-93ba-b9448612a939 · outbound

This paper cites Numerical Solution of Partial Differential Equations by the Finite Element Method.

Neural Preconditioning Operator for Efficient PDE Solves Numerical Solution of Partial Differential Equations by the Finite Element Method

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T15:42:32.686146Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation e65bb694-1ed3-48ca-91df-cd7036228e9d · outbound

This paper cites DeepOnet Based Preconditioning Strategies For Solving Parametric Linear Systems of Equations.

Neural Preconditioning Operator for Efficient PDE Solves DeepOnet Based Preconditioning Strategies For Solving Parametric Linear Systems of Equations

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-09T15:42:31.740407Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e881e542-c479-4fd5-b2b6-677fd053f99d · outbound

This paper cites Kovachki, Zongyi Li, Burigede Liu, Kamyar Azizzadenesheli, Kaushik Bhattacharya, Andrew M.

Neural Preconditioning Operator for Efficient PDE Solves Kovachki, Zongyi Li, Burigede Liu, Kamyar Azizzadenesheli, Kaushik Bhattacharya, Andrew M

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T15:42:32.679130Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation d8835a60-8628-400d-9763-6c237712abe0 · outbound

This paper cites Multigrid-augmented deep learning preconditioners for the helmholtz equation using compact implicit layers.

Neural Preconditioning Operator for Efficient PDE Solves Multigrid-augmented deep learning preconditioners for the helmholtz equation using compact implicit layers

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T15:42:32.670575Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 4898d238-4c20-420c-85a7-560a00f7e378 · outbound

This paper cites an unresolved cited work.

Neural Preconditioning Operator for Efficient PDE Solves Unresolved cited work

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-09T15:42:31.747936Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7b69c518-07b5-4c8d-b3d6-a5997dc4bce9 · outbound

This paper cites Machine learning for preconditioning elliptic equations in porous microstructures: A path to error control.

Neural Preconditioning Operator for Efficient PDE Solves Machine learning for preconditioning elliptic equations in porous microstructures: A path to error control

Reference 14

Resolution: verified exact; arxiv_id_nonexistent, observed 2026-08-09T15:42:32.314625Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation ee4b7b08-3a94-4a25-8af8-5177ed12d3c9 · outbound

This paper cites Learning preconditioners for conjugate gradient PDE solvers.

Neural Preconditioning Operator for Efficient PDE Solves Learning preconditioners for conjugate gradient PDE solvers

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T15:42:32.601898Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 4db2ac53-e390-48f9-bca1-86ace8f1e47c · outbound

This paper cites M2NO: multiresolution operator learning with multiwavelet-based algebraic multigrid method.

Neural Preconditioning Operator for Efficient PDE Solves M2NO: multiresolution operator learning with multiwavelet-based algebraic multigrid method

Reference 16

Resolution: verified exact; arxiv_id, observed 2026-08-09T15:42:32.070161Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 5472448d-dd21-4962-9c47-5550ae9b0003 · outbound

This paper cites Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries.

Neural Preconditioning Operator for Efficient PDE Solves Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-09T15:42:31.757357Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 24a5156b-3abb-4eac-80d2-0e7e98948f0a · outbound

This paper cites Stuart, and Anima Anandkumar.

Neural Preconditioning Operator for Efficient PDE Solves Stuart, and Anima Anandkumar

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T15:42:32.490721Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 1300071c-32be-4fcb-ae8c-66a11126d056 · outbound

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

Neural Preconditioning Operator for Efficient PDE Solves Learning nonlinear operators via deeponet based on the universal approximation theorem of operators

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T15:42:32.395355Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 17d05316-66ac-4db3-ba96-1a11c29d12da · outbound

This paper cites Brenner, and Shmuel M.

Neural Preconditioning Operator for Efficient PDE Solves Brenner, and Shmuel M

Reference 20

Resolution: verified exact; doi, observed 2026-08-09T15:42:31.826920Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 417f1034-6038-4a52-9150-14769a71fb1c · outbound

This paper cites an unresolved cited work.

Neural Preconditioning Operator for Efficient PDE Solves Unresolved cited work

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-09T15:42:31.767995Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d8019d0d-a2b8-49fa-a27e-6de94545539f · outbound

This paper cites U-net: Convolutional networks for biomedical image segmentation.

Neural Preconditioning Operator for Efficient PDE Solves U-net: Convolutional networks for biomedical image segmentation

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T15:42:32.388175Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation f8a04604-8d41-4566-9252-1891d184506c · outbound

This paper cites Muravleva, Yuri M.

Neural Preconditioning Operator for Efficient PDE Solves Muravleva, Yuri M

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T15:42:32.381036Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation b3c6fe27-e8fb-4bf5-a00a-91e67c78b412 · outbound

This paper cites Rumelhart, Geoffrey E.

Neural Preconditioning Operator for Efficient PDE Solves Rumelhart, Geoffrey E

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-09T15:42:31.775078Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fc9c6a09-f761-448b-be81-72dcddc87600 · outbound

This paper cites an unresolved cited work.

Neural Preconditioning Operator for Efficient PDE Solves Unresolved cited work

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-09T15:42:31.777671Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5eca5b7f-1e51-4cb5-9508-683efd62c8c7 · outbound

This paper cites Computational Science and Engineering.

Neural Preconditioning Operator for Efficient PDE Solves Computational Science and Engineering

Reference 26

Resolution: verified exact; doi, observed 2026-08-09T15:42:31.810211Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation e1a54ff9-5c36-423a-a845-df3f780d4551 · outbound

This paper cites Partial Differential Equations: Methods and Applications.

Neural Preconditioning Operator for Efficient PDE Solves Partial Differential Equations: Methods and Applications

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T15:42:32.363143Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation b764f2eb-b39f-41ba-b035-1b77dce65675 · outbound

This paper cites Transolver: A Fast Transformer Solver for PDEs on General Geometries.

Neural Preconditioning Operator for Efficient PDE Solves Transolver: A Fast Transformer Solver for PDEs on General Geometries

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-09T15:42:31.785182Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 18b4f342-edc8-4801-80bf-18d5c47c74a3 · outbound

This paper cites Blending Neural Operators and Relaxation Methods in PDE Numerical Solvers.

Neural Preconditioning Operator for Efficient PDE Solves Blending Neural Operators and Relaxation Methods in PDE Numerical Solvers

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-09T15:42:31.788171Z

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Unavailable: canonical work link unavailable.

Pith citing papers

Observation 691a40e0-a3e5-4693-b392-6d796d9423ce · inbound

When can a neural operator replace a coarse solve? Architectural principles for two-level preconditioning cites this paper.

When can a neural operator replace a coarse solve? Architectural principles for two-level preconditioning Neural Preconditioning Operator for Efficient PDE Solves

Reference 36

Resolution: verified exact; arxiv_id, observed 2026-05-20T02:02:58.430561Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation e07f7a4b-ed54-471e-9405-a0515158139c · inbound

RAPNet: Accelerating Algebraic Multigrid with Learned Sparse Corrections cites this paper.

RAPNet: Accelerating Algebraic Multigrid with Learned Sparse Corrections Neural Preconditioning Operator for Efficient PDE Solves

Reference 2023

Resolution: unresolved; no resolver link, observed 2026-08-03T02:19:22.490570Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2e83bf8f-9377-4a1e-8696-bac512839bd9 · inbound

Interface-Aware Neural Newton Preconditioning for Robust Cohesive Zone Model Simulations cites this paper.

Interface-Aware Neural Newton Preconditioning for Robust Cohesive Zone Model Simulations Neural Preconditioning Operator for Efficient PDE Solves

Reference 32

Resolution: verified exact; arxiv_id, observed 2026-07-01T09:25:41.623887Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 00cba073-653a-47fc-b3f9-ba67a99c844b · inbound

Interface-Aware Neural Newton Preconditioning for Robust Cohesive Zone Model Simulations cites this paper.

Interface-Aware Neural Newton Preconditioning for Robust Cohesive Zone Model Simulations Neural Preconditioning Operator for Efficient PDE Solves

Reference 32

Resolution: verified exact; arxiv_id, observed 2026-07-02T20:17:21.230127Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 330cc934-ce6e-4710-9294-e1b9aa7ef50f · inbound

Neural operator preconditioning from mixed dataset for the Helmholtz equations: Application to transcranial ultrasound cites this paper.

Neural operator preconditioning from mixed dataset for the Helmholtz equations: Application to transcranial ultrasound Neural Preconditioning Operator for Efficient PDE Solves

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-01T19:41:32.474250Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.