Paper Citation Record · LEDGER

Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory

As of 9 August 2026, this Paper Citation Record lists 63 of 63 outbound references and 1 inbound Pith citation observation for arXiv:2509.10378.

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pith.paper-citation-record.v1
2509.10378 v1

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measured 63 of 63 reference resolution

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Source: paper_references, paper_reference_links, observed 2026-08-04T17:57:21.013316Z

measured 64 of 64 standing notices

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

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-05-15T19:01:40.879901Z

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

Outbound references

Observation b7ac2844-0d9a-4bc4-8e1a-093041974c6c · outbound

This paper cites Hadrons and nuclei.The European Physical Journal A, 55:1–27, 2019.

Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory Hadrons and nuclei.The European Physical Journal A, 55:1–27, 2019

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-04T17:57:17.393828Z

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Observation 8f7ce356-f6c0-4b76-ba8f-37b58adf9874 · outbound

This paper cites Review of particle physics.Progress of Theoretical and Experimental Physics, 2020(8):083C01, 2020.

Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory Review of particle physics.Progress of Theoretical and Experimental Physics, 2020(8):083C01, 2020

Reference 2

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Observation 61370699-7351-4ecd-b67f-5bfc1ddcef64 · outbound

This paper cites Hot-dense lattice qcd.The European Physical Journal A, 55:1–11, 2019.

Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory Hot-dense lattice qcd.The European Physical Journal A, 55:1–11, 2019

Reference 3

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Observation 9b9ceee5-0ebd-42b1-998f-6ab671b73631 · outbound

This paper cites Status and future perspectives for lattice gauge theory calculations to the exascale and beyond.The European Physical Journal A, 55:1–26, 2019.

Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory Status and future perspectives for lattice gauge theory calculations to the exascale and beyond.The European Physical Journal A, 55:1–26, 2019

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-04T17:57:17.552383Z

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Observation cd3eaa0a-d681-4569-99b7-a3db6f57743c · outbound

This paper cites SIAM, 2003.

Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory SIAM, 2003

Reference 5

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Observation d49d99bb-fd72-4454-8c21-6f0424a6cc44 · outbound

This paper cites Hackett, Yin Lin, Phiala E.

Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory Hackett, Yin Lin, Phiala E

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-04T17:57:17.653210Z

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Observation 03a2fad4-7dcf-4909-a4ea-da6ea6d36b92 · outbound

This paper cites Brannick and K.

Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory Brannick and K

Reference 7

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Observation 9985c440-5392-4f31-b5ea-402423677851 · outbound

This paper cites Adaptive multigrid algorithm for lattice qcd.Physical review letters, 100(4):041601, 2008.

Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory Adaptive multigrid algorithm for lattice qcd.Physical review letters, 100(4):041601, 2008

Reference 8

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Observation ff58cc9a-9cbd-4b1c-bf4d-46c37d9e5af7 · outbound

This paper cites Adaptive multigrid algorithm for the lattice wilson-dirac operator.Physical review letters, 105(20):201602, 2010.

Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory Adaptive multigrid algorithm for the lattice wilson-dirac operator.Physical review letters, 105(20):201602, 2010

Reference 9

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Observation 0cf95e60-e331-41f6-9396-43c5b3c122b0 · outbound

This paper cites Brower, M.

Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory Brower, M

Reference 10

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Observation c37547e7-31f7-4403-bfcb-532f99968fb3 · outbound

This paper cites Brower, M.

Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory Brower, M

Reference 11

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Observation 6ad4b193-7bb3-4c25-8f0c-b43167640208 · outbound

This paper cites Babich, M.

Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory Babich, M

Reference 12

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Observation fc01b4bc-2947-4c6a-982c-6ed4ef7be95f · outbound

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Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory Unresolved cited work

Reference 13

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Observation 8f5660a9-e595-43cf-8921-36aa6435b610 · outbound

This paper cites Adaptive Aggregation-Based Domain Decomposition Multigrid for the Lattice Wilson–Dirac Operator.SIAM J.

Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory Adaptive Aggregation-Based Domain Decomposition Multigrid for the Lattice Wilson–Dirac Operator.SIAM J

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-04T17:57:18.212767Z

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Observation 45725ede-54d0-4ac6-b26d-7806749e2455 · outbound

This paper cites Comparison of Domain Wall Fermion Multigrid Methods.

Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory Comparison of Domain Wall Fermion Multigrid Methods

Reference 15

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Observation 4c1f2e02-909a-4558-a795-8398a5e0cdd6 · outbound

This paper cites Adaptive Aggregation-based Domain Decomposition Multigrid for Twisted Mass Fermions.Phys.

Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory Adaptive Aggregation-based Domain Decomposition Multigrid for Twisted Mass Fermions.Phys

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-04T17:57:18.285929Z

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Observation 9f8e128c-6d11-4448-9c3a-307346cbd2da · outbound

This paper cites Multigrid Preconditioning for the Overlap Operator in Lattice QCD.Numer.

Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory Multigrid Preconditioning for the Overlap Operator in Lattice QCD.Numer

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-04T17:57:18.329759Z

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Observation cce5dae0-8cc8-4503-9776-0cfbc3578f30 · outbound

This paper cites Brower, Robert G.

Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory Brower, Robert G

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-04T17:57:18.374377Z

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Observation 4b0b3d20-9dad-4e83-a139-4916478709b6 · outbound

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Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory Unresolved cited work

Reference 19

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Observation f439b463-449e-439b-908f-6dc1cb82132d · outbound

This paper cites Accelerating multigrid with streaming chiral SVD for Wilson fermions in lattice QCD.

Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory Accelerating multigrid with streaming chiral SVD for Wilson fermions in lattice QCD

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-04T17:57:18.566319Z

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Observation e973157c-d0c6-43ad-99b8-eb5e5c341400 · outbound

This paper cites Multigrid low-mode averaging.Phys.

Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory Multigrid low-mode averaging.Phys

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-04T17:57:18.669204Z

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Observation 72c45520-8d4a-45d3-95dc-b92998b50ca4 · outbound

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Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory Unresolved cited work

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-04T17:57:18.744104Z

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Observation e1ff44e6-9ba4-4276-90c8-bb457a554586 · outbound

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Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory Unresolved cited work

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-04T17:57:18.764610Z

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Observation de8a5503-e15a-4f7f-bf46-d1b869b6e1d9 · outbound

This paper cites Deflated Multigrid Multilevel Monte Carlo.PoS, LAT- TICE2022:030, 2023.

Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory Deflated Multigrid Multilevel Monte Carlo.PoS, LAT- TICE2022:030, 2023

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-04T17:57:18.803646Z

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Observation b6ab81d9-79fa-4850-bc04-e2bee18c44eb · outbound

This paper cites MRHS multigrid solver for Wilson-clover fermions.PoS, LATTICE2022:285, 2023.

Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory MRHS multigrid solver for Wilson-clover fermions.PoS, LATTICE2022:285, 2023

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-04T17:57:18.907402Z

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Observation fd623212-087d-42b0-a1df-cbf327c61bad · outbound

This paper cites Boyle, and Tilo Wettig.

Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory Boyle, and Tilo Wettig

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-04T17:57:18.981377Z

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Observation 2904fd62-ab54-4cb6-b3aa-ce64886151e7 · outbound

This paper cites Coarsest-level improvements in multigrid for lattice QCD on large-scale computers.Comput.

Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory Coarsest-level improvements in multigrid for lattice QCD on large-scale computers.Comput

Reference 27

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Observation 2ea98213-b69c-45fd-a1bc-edea50e83f32 · outbound

This paper cites SIAM, 1994.

Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory SIAM, 1994

Reference 28

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Observation 98e6596f-6f8b-4333-b0a2-b47dde1ddc3f · outbound

This paper cites Neural incomplete factorization: learning preconditioners for the conjugate gradient method.

Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory Neural incomplete factorization: learning preconditioners for the conjugate gradient method

Reference 29

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Observation 738b8ca1-b875-4b96-8bb7-a7d8930efd9e · outbound

This paper cites Hicken, and Shaowu Pan.

Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory Hicken, and Shaowu Pan

Reference 30

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Observation 82a86da8-34e4-42ea-b777-758ed8a8e767 · outbound

This paper cites NeuralPCG: Learning Preconditioner for Solving Partial Differential Equations with Graph Neural Network.

Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory NeuralPCG: Learning Preconditioner for Solving Partial Differential Equations with Graph Neural Network

Reference 31

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Observation ea6f0652-2164-40a3-b535-77e3e207cdbb · outbound

This paper cites Multigrid-augmented deep learning preconditioners for the Helmholtz equation.

Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory Multigrid-augmented deep learning preconditioners for the Helmholtz equation

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Observation ba4500fb-f824-49a1-bab1-1825041e712a · outbound

This paper cites Deep Learning of Preconditioners for Conjugate Gradient Solvers in Urban Water Related Problems.

Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory Deep Learning of Preconditioners for Conjugate Gradient Solvers in Urban Water Related Problems

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Observation 4fc7f783-9950-4b2d-8f6a-56dd357c4ab5 · outbound

This paper cites Graph Neural Networks for Selection of Preconditioners and Krylov Solvers.

Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory Graph Neural Networks for Selection of Preconditioners and Krylov Solvers

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Observation fea59815-d952-4dc7-9790-c46108e595ea · outbound

This paper cites Preconditioning.Acta Numerica, 24:329–376, 2015.

Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory Preconditioning.Acta Numerica, 24:329–376, 2015

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Observation c9d8b8ef-d203-4812-b3e7-fbefdc7ac930 · outbound

This paper cites SIAM, 1997.

Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory SIAM, 1997

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Observation fd1082a1-0472-4794-b376-ac4993f59bb6 · outbound

This paper cites Number 13.

Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory Number 13

Reference 37

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Observation 18a5e21c-9c34-4ba9-bb26-e85b3e812924 · outbound

This paper cites SIAM, 2014.

Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory SIAM, 2014

Reference 38

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Observation a045c1a9-0a7c-4f40-b2da-db2d49b1d85d · outbound

This paper cites Preconditioning discretizations of systems of partial differential equations.

Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory Preconditioning discretizations of systems of partial differential equations

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Observation 6de0469a-bec1-4020-b5f7-26c3bd47da8a · outbound

This paper cites A note on preconditioners and scalar products in krylov subspace methods for self-adjoint problems in hilbert space.Electron.

Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory A note on preconditioners and scalar products in krylov subspace methods for self-adjoint problems in hilbert space.Electron

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Resolution: unresolved; no resolver link, observed 2026-08-04T17:57:19.722967Z

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Observation 7eda7a7c-500a-49d8-bdae-77a5d1c1a6f5 · outbound

This paper cites SIAM, 2014.

Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory SIAM, 2014

Reference 41

Resolution: unresolved; no resolver link, observed 2026-08-04T17:57:19.777599Z

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Observation 74ceed8a-26f9-4f45-9433-39cd3527d83c · outbound

This paper cites Preconditioning techniques for large linear systems: a survey.Journal of computational Physics, 182(2):418–477, 2002.

Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory Preconditioning techniques for large linear systems: a survey.Journal of computational Physics, 182(2):418–477, 2002

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Observation d8b8b388-b667-4348-a79b-ac332af27236 · outbound

This paper cites Graph Networks as a Universal Machine Learning Framework for Molecules and Crystals.Chemistry of Materials, 31(9):3564–3572, May 2019.

Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory Graph Networks as a Universal Machine Learning Framework for Molecules and Crystals.Chemistry of Materials, 31(9):3564–3572, May 2019

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Observation 475334d4-4f1b-402d-a590-ddd048d9af36 · outbound

This paper cites Düben, Tim N.

Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory Düben, Tim N

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Observation c8b5fc91-8e28-4e11-a338-2d61dc3d78ee · outbound

This paper cites Graph neural preconditioners for iterative solutions of sparse linear systems, 2025.

Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory Graph neural preconditioners for iterative solutions of sparse linear systems, 2025

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Resolution: unresolved; no resolver link, observed 2026-08-04T17:57:19.945878Z

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Observation b2aff152-1347-4db1-8d0a-6a6406c83925 · outbound

This paper cites Gauge-equivariant neural networks as preconditioners in lattice QCD, February.

Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory Gauge-equivariant neural networks as preconditioners in lattice QCD, February

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Observation e7cd1070-643f-418f-92dd-2419c4796271 · outbound

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Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory Unresolved cited work

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Observation f6c47d63-abc5-496a-96fc-36ba4a0cd871 · outbound

This paper cites Multilayer feedforward networks are universal approxi- mators.Neural Networks, 2(5):359–366, January 1989.

Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory Multilayer feedforward networks are universal approxi- mators.Neural Networks, 2(5):359–366, January 1989

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Observation 40d557cf-7f1f-46b6-8767-31800bc71187 · outbound

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

Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory Fourier Neural Operator for Parametric Partial Differential Equations

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Resolution: unresolved; no resolver link, observed 2026-08-04T17:57:20.158538Z

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Observation bf460760-d032-4861-be29-319c63d24ae5 · outbound

This paper cites Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators.Nature Machine Intelligence, 3(3):218–229, March 2021.

Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators.Nature Machine Intelligence, 3(3):218–229, March 2021

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Resolution: unresolved; no resolver link, observed 2026-08-04T17:57:20.242978Z

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

This paper cites Neural Operator: Learning Maps Between Function Spaces.

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

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

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Observation 899cac90-a1f2-4dcf-8f3c-7109cb27c280 · outbound

This paper cites A physics-informed operator regression framework for extracting data-driven continuum models.

Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory A physics-informed operator regression framework for extracting data-driven continuum models

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Resolution: unresolved; no resolver link, observed 2026-08-04T17:57:20.352204Z

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Observation 96ac513b-eac1-46a8-9595-8050a48b01ee · outbound

This paper cites A physics-informed variational DeepONet for predicting the crack path in brittle materials.

Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory A physics-informed variational DeepONet for predicting the crack path in brittle materials

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Resolution: unresolved; no resolver link, observed 2026-08-04T17:57:20.412216Z

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Observation d02475b3-f7f5-47c6-aaf3-94a8d2b8e3c3 · outbound

This paper cites DeepGraphONet: A Deep Graph Operator Network to Learn and Zero-Shot Transfer the Dynamic Response of Networked Systems.IEEE Systems Journal, 17(3):4360– 4370, September 2023.

Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory DeepGraphONet: A Deep Graph Operator Network to Learn and Zero-Shot Transfer the Dynamic Response of Networked Systems.IEEE Systems Journal, 17(3):4360– 4370, September 2023

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Resolution: unresolved; no resolver link, observed 2026-08-04T17:57:20.466461Z

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Observation 570f73eb-9b3e-4883-b6c7-bb59819b0fbe · outbound

This paper cites A Mathematical Guide to Operator Learning.

Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory A Mathematical Guide to Operator Learning

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Observation 1b701174-d1ea-4074-bba2-9f5577032701 · outbound

This paper cites Fully Convolutional Networks for Semantic Segmentation.

Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory Fully Convolutional Networks for Semantic Segmentation

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Observation 37af0b93-d2af-4f23-8510-6b223051f9aa · outbound

This paper cites Confinement of quarks.Physical review D, 10(8):2445, 1974.

Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory Confinement of quarks.Physical review D, 10(8):2445, 1974

Reference 57

Resolution: unresolved; no resolver link, observed 2026-08-04T17:57:20.689632Z

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Observation 928862ae-9b82-4e11-9caf-38e03977ee42 · outbound

This paper cites CASK: A Gauge Covariant Transformer for Lattice Gauge Theory.

Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory CASK: A Gauge Covariant Transformer for Lattice Gauge Theory

Reference 58

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Observation e9c813a4-887b-438d-b496-fa05abf8af1c · outbound

This paper cites Differentiating Through Linear Solvers.

Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory Differentiating Through Linear Solvers

Reference 59

Resolution: unresolved; no resolver link, observed 2026-08-04T17:57:20.822268Z

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Observation e4ea6fc1-76a1-4323-a1cd-416684f89605 · outbound

This paper cites A taxonomy of automatic differentiation pitfalls.Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery, 14(6):e1555, 2024.

Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory A taxonomy of automatic differentiation pitfalls.Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery, 14(6):e1555, 2024

Reference 60

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Observation 8563001a-673a-454f-a342-0b815417db9d · outbound

This paper cites Scaling test of fermion actions in the schwinger model.

Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory Scaling test of fermion actions in the schwinger model

Reference 61

Resolution: unresolved; no resolver link, observed 2026-08-04T17:57:20.955592Z

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Observation 2cbc072f-8b33-4edf-b82c-5b0d38bd46b7 · outbound

This paper cites Cambridge University Press, 2003.

Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory Cambridge University Press, 2003

Reference 62

Resolution: unresolved; no resolver link, observed 2026-08-04T17:57:21.013316Z

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Observation c4a89151-39b2-4cc8-b7b8-5be5c8c47114 · outbound

This paper cites Gauge-equivariant neural networks as preconditioners in lattice QCD.

Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory Gauge-equivariant neural networks as preconditioners in lattice QCD

Reference 2023

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Pith citing papers

Observation 6e61cee8-5daa-4925-ade1-b0a6b244fdb9 · inbound

A novel gauge-equivariant neural-network architecture for preconditioners in lattice QCD cites this paper.

A novel gauge-equivariant neural-network architecture for preconditioners in lattice QCD Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory

Reference 9

Resolution: verified exact; arxiv_id, observed 2026-05-15T19:06:30.469466Z

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