Paper Citation Record · LEDGER

Neural operator preconditioning from mixed dataset for the Helmholtz equations: Application to transcranial ultrasound

As of 9 August 2026, this Paper Citation Record lists 30 of 30 outbound references and 0 inbound Pith citation observations for arXiv:2607.16906.

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pith.paper-citation-record.v1
2607.16906 v1

Coverage vector

measured 30 of 30 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-01T19:41:34.480983Z

measured 30 of 30 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

30 of 30 outbound references displayed

verified exact5
verified fuzzy0
unresolved23
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External citation measurements

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Outbound references

Observation 7e50e854-3247-41fc-9852-953b72826ed6 · outbound

This paper cites Conditional Denoising Diffusion Model-BasedRobustMRImageReconstructionfromHighlyUndersampledData.

Neural operator preconditioning from mixed dataset for the Helmholtz equations: Application to transcranial ultrasound Conditional Denoising Diffusion Model-BasedRobustMRImageReconstructionfromHighlyUndersampledData

Reference 1

Resolution: verified exact; arxiv_id, observed 2026-08-01T19:43:20.051234Z

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 fca280e4-db9b-41cb-a419-b66eae5165e8 · outbound

This paper cites Multigrid-Augmented Deep Learning Preconditioners for the Helmholtz Equation.

Neural operator preconditioning from mixed dataset for the Helmholtz equations: Application to transcranial ultrasound Multigrid-Augmented Deep Learning Preconditioners for the Helmholtz Equation

Reference 2

Resolution: verified exact; doi, observed 2026-08-01T19:43:19.853198Z

Source-reported events for the cited work

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Observation 1dfb1f0c-fe69-4de4-b5e0-5aba3cb213bc · outbound

This paper cites A Perfectly Matched Layer for the Absorption of Electromagnetic Waves.

Neural operator preconditioning from mixed dataset for the Helmholtz equations: Application to transcranial ultrasound A Perfectly Matched Layer for the Absorption of Electromagnetic Waves

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-01T19:41:31.379182Z

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Observation b3d57c4f-593d-4850-8e23-f87bfaf59ab5 · outbound

This paper cites Autoencoders.

Neural operator preconditioning from mixed dataset for the Helmholtz equations: Application to transcranial ultrasound Autoencoders

Reference 4

Resolution: malformed identifier; no resolver link, observed 2026-08-01T19:41:31.485852Z

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Observation 15183857-9b46-4cb7-9ca7-4903a93748c6 · outbound

This paper cites Message Passing Neural PDE Solvers.

Neural operator preconditioning from mixed dataset for the Helmholtz equations: Application to transcranial ultrasound Message Passing Neural PDE Solvers

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-01T19:41:31.598943Z

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Observation 40ef1861-d5eb-4c2b-8644-64f09ad72bf7 · outbound

This paper cites OpenFWI: Large-scale Multi-structural Benchmark Datasets for Full Waveform Inversion.

Neural operator preconditioning from mixed dataset for the Helmholtz equations: Application to transcranial ultrasound OpenFWI: Large-scale Multi-structural Benchmark Datasets for Full Waveform Inversion

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-01T19:41:31.715653Z

Source-reported events for the cited work

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Observation 43a3f5c6-e2b1-4be9-9e3f-4875957fbaf9 · outbound

This paper cites Numerical Solution of Mixed-Dimensional PDEs Using a Neural Preconditioner.

Neural operator preconditioning from mixed dataset for the Helmholtz equations: Application to transcranial ultrasound Numerical Solution of Mixed-Dimensional PDEs Using a Neural Preconditioner

Reference 7

Resolution: verified exact; local_arxiv, observed 2026-08-01T19:43:19.665544Z

Source-reported events for the cited work

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Observation 176a76ca-35a1-418d-b990-a28437cd57d0 · outbound

This paper cites Scientific machine learning.

Neural operator preconditioning from mixed dataset for the Helmholtz equations: Application to transcranial ultrasound Scientific machine learning

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-01T19:41:32.009780Z

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Observation ee855b39-6156-4398-9ec8-d0dadc8211d0 · outbound

This paper cites Giraud, C.

Neural operator preconditioning from mixed dataset for the Helmholtz equations: Application to transcranial ultrasound Giraud, C

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-01T19:41:32.120697Z

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Observation 20574852-ae10-439e-b19d-2835bb58bad7 · outbound

This paper cites an unresolved cited work.

Neural operator preconditioning from mixed dataset for the Helmholtz equations: Application to transcranial ultrasound Unresolved cited work

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-01T19:41:32.134124Z

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Observation 7bae6d14-a8c0-4cb7-ab15-27ae31f8109a · outbound

This paper cites DeepONet Based Preconditioning Strategies for Solving Para- metric Linear Systems of Equations.

Neural operator preconditioning from mixed dataset for the Helmholtz equations: Application to transcranial ultrasound DeepONet Based Preconditioning Strategies for Solving Para- metric Linear Systems of Equations

Reference 11

Resolution: verified exact; doi, observed 2026-08-01T19:43:19.526459Z

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 459c6247-3e71-4573-ad16-d821196ea418 · outbound

This paper cites Neural Operator: Learning Maps Between Function Spaces with Applications to PDEs.

Neural operator preconditioning from mixed dataset for the Helmholtz equations: Application to transcranial ultrasound Neural Operator: Learning Maps Between Function Spaces with Applications to PDEs

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-01T19:41:32.355989Z

Source-reported events for the cited work

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

This paper cites Neural Preconditioning Operator for Efficient PDE Solves.

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

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Observation 9b2f7829-c4ac-46dc-8418-bd5ba6ab4f4f · outbound

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

Neural operator preconditioning from mixed dataset for the Helmholtz equations: Application to transcranial ultrasound Fourier Neural Operator for Parametric Partial Differential Equations

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-01T19:41:32.594570Z

Source-reported events for the cited work

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Observation 4a181fc1-f812-411c-98e7-131a4eaa8a5b · outbound

This paper cites AI-Augmented Adaptive Digital Twin Modeling for Brain Tumor Evolution Prediction and Treatment Scheduling.

Neural operator preconditioning from mixed dataset for the Helmholtz equations: Application to transcranial ultrasound AI-Augmented Adaptive Digital Twin Modeling for Brain Tumor Evolution Prediction and Treatment Scheduling

Reference 15

Resolution: verified exact; local_arxiv, observed 2026-08-01T19:43:19.361823Z

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 bec2a1d3-4e8c-4710-8095-e91a6f5ca7c8 · outbound

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

Neural operator preconditioning from mixed dataset for the Helmholtz equations: Application to transcranial ultrasound Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-01T19:41:32.935941Z

Source-reported events for the cited work

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Observation 9ea6816d-5792-4139-8145-38a0afe65061 · outbound

This paper cites Neural Operator: Learning Maps Between Function Spaces With Applications to PDEs.

Neural operator preconditioning from mixed dataset for the Helmholtz equations: Application to transcranial ultrasound Neural Operator: Learning Maps Between Function Spaces With Applications to PDEs

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-01T19:41:33.071060Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d7e0ff50-d911-444d-be34-4bfe10625638 · outbound

This paper cites FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators.

Neural operator preconditioning from mixed dataset for the Helmholtz equations: Application to transcranial ultrasound FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-01T19:41:33.182622Z

Source-reported events for the cited work

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Observation 693e6d32-4c0f-42ee-a4a5-c188fee3875a · outbound

This paper cites Meta-learning PINN loss functions.

Neural operator preconditioning from mixed dataset for the Helmholtz equations: Application to transcranial ultrasound Meta-learning PINN loss functions

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-01T19:41:33.329749Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 03195582-ca9f-49da-93bf-4f069b7fffd4 · outbound

This paper cites On the Compatibility of a Given Solution With the Data of a Linear System.

Neural operator preconditioning from mixed dataset for the Helmholtz equations: Application to transcranial ultrasound On the Compatibility of a Given Solution With the Data of a Linear System

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-01T19:41:33.458305Z

Source-reported events for the cited work

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Observation 3b66bd0f-1c56-435c-91f4-d4b76eefd9fc · outbound

This paper cites U-Net: Convolutional Networks for Biomedical Image Segmentation.

Neural operator preconditioning from mixed dataset for the Helmholtz equations: Application to transcranial ultrasound U-Net: Convolutional Networks for Biomedical Image Segmentation

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-01T19:41:33.520612Z

Source-reported events for the cited work

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Observation 5cd0ed05-ab96-4fa6-a330-0ffaf0f8b0d7 · outbound

This paper cites Development and Validation of Deep Learning Algorithms for Detection of Critical Findings in Head CT Scans.

Neural operator preconditioning from mixed dataset for the Helmholtz equations: Application to transcranial ultrasound Development and Validation of Deep Learning Algorithms for Detection of Critical Findings in Head CT Scans

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-01T19:41:33.596291Z

Source-reported events for the cited work

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Observation 19135099-4aca-4802-8430-a84c98988937 · outbound

This paper cites A flexible inner-outer preconditioned GMRES algorithm.

Neural operator preconditioning from mixed dataset for the Helmholtz equations: Application to transcranial ultrasound A flexible inner-outer preconditioned GMRES algorithm

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-01T19:41:33.699783Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 16a4fbd5-3d3e-45b6-a38c-9ea82ddeda1b · outbound

This paper cites GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems.

Neural operator preconditioning from mixed dataset for the Helmholtz equations: Application to transcranial ultrasound GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-01T19:41:33.757691Z

Source-reported events for the cited work

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Observation ddb0d6e1-991a-479f-8c06-db5488063de8 · outbound

This paper cites Shpakovych.Neural Network Preconditioning of Large Linear Systems.

Neural operator preconditioning from mixed dataset for the Helmholtz equations: Application to transcranial ultrasound Shpakovych.Neural Network Preconditioning of Large Linear Systems

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-01T19:41:33.836231Z

Source-reported events for the cited work

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Observation fdaf1604-17e2-409e-901c-d098a87c291f · outbound

This paper cites A Helmholtz Equation Solver Using Un- supervised Learning: Application to Transcranial Ultrasound.

Neural operator preconditioning from mixed dataset for the Helmholtz equations: Application to transcranial ultrasound A Helmholtz Equation Solver Using Un- supervised Learning: Application to Transcranial Ultrasound

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-01T19:41:33.951195Z

Source-reported events for the cited work

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Observation 0659caae-ec4a-4597-92f5-0b840202a397 · outbound

This paper cites Efficient preconditioning for iterative methods with graph neural networks.

Neural operator preconditioning from mixed dataset for the Helmholtz equations: Application to transcranial ultrasound Efficient preconditioning for iterative methods with graph neural networks

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-01T19:41:34.076565Z

Source-reported events for the cited work

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Observation d7e71fb8-4806-4fa6-871c-996d6991cd66 · outbound

This paper cites an unresolved cited work.

Neural operator preconditioning from mixed dataset for the Helmholtz equations: Application to transcranial ultrasound Unresolved cited work

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-01T19:41:34.223387Z

Source-reported events for the cited work

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Observation 79eda56d-82ae-42cd-9227-68ded6369dd1 · outbound

This paper cites Solution of Large Linear Systems with a Massive Number of Right-Hand Sides and Ma- chine Learning.

Neural operator preconditioning from mixed dataset for the Helmholtz equations: Application to transcranial ultrasound Solution of Large Linear Systems with a Massive Number of Right-Hand Sides and Ma- chine Learning

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-01T19:41:34.345573Z

Source-reported events for the cited work

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Observation 498453cc-1a37-426a-b9a5-19034b09ba03 · outbound

This paper cites Xiang.Unsupervised convolution neural operator preconditioning for the solution of some hetero- geneous fluid PDEs.

Neural operator preconditioning from mixed dataset for the Helmholtz equations: Application to transcranial ultrasound Xiang.Unsupervised convolution neural operator preconditioning for the solution of some hetero- geneous fluid PDEs

Reference 30

Resolution: malformed identifier; no resolver link, observed 2026-08-01T19:41:34.480983Z

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Unavailable: canonical work link unavailable.

Pith citing papers

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