Paper Citation Record · LEDGER

A Morphology-Adaptive Random Feature Method for Inverse Source Problem of the Helmholtz Equation

As of 10 August 2026, this Paper Citation Record lists 41 of 41 outbound references and 2 inbound Pith citation observations for arXiv:2510.09213.

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pith.paper-citation-record.v1
2510.09213 v2

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measured 41 of 41 reference resolution

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Source: paper_references, paper_reference_links, observed 2026-08-04T10:45:11.693335Z

measured 43 of 43 standing notices

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

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-06-27T09:29:37.336541Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-07-03T11:38:04.764093Z

Reference resolution

41 of 41 outbound references displayed

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Outbound references

Observation 7add7dad-b8ef-4416-bc82-9f302aa29b14 · outbound

This paper cites The inverse source problem for Maxwell’s equations.

A Morphology-Adaptive Random Feature Method for Inverse Source Problem of the Helmholtz Equation The inverse source problem for Maxwell’s equations

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-04T10:45:07.125149Z

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Observation a82ca784-915c-4f2f-9e5e-4487edff8952 · outbound

This paper cites Optical tomography in medical imaging.Inverse Problems, 15(2):R41, 1999.

A Morphology-Adaptive Random Feature Method for Inverse Source Problem of the Helmholtz Equation Optical tomography in medical imaging.Inverse Problems, 15(2):R41, 1999

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-04T10:45:07.277809Z

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Observation 0c0168c5-2a59-4452-8a6f-433c7d02e36d · outbound

This paper cites The unique determination of neuronal currents in the brain via magnetoencephalography.Inverse Problems, 20(4):1067, 2004.

A Morphology-Adaptive Random Feature Method for Inverse Source Problem of the Helmholtz Equation The unique determination of neuronal currents in the brain via magnetoencephalography.Inverse Problems, 20(4):1067, 2004

Reference 3

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Observation 1bc22970-e938-41f1-bf27-623aacb99686 · outbound

This paper cites Application of inverse source concepts to photoacoustic tomography.Inverse Problems, 23(6):S21, 2007.

A Morphology-Adaptive Random Feature Method for Inverse Source Problem of the Helmholtz Equation Application of inverse source concepts to photoacoustic tomography.Inverse Problems, 23(6):S21, 2007

Reference 4

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Observation 628e62e6-d80f-46b8-a684-d12dd64874fb · outbound

This paper cites Inverse source problem in nonhomoge- neous background media.SIAM Journal on Applied Mathematics, 67(5):1353–1378, 2007.

A Morphology-Adaptive Random Feature Method for Inverse Source Problem of the Helmholtz Equation Inverse source problem in nonhomoge- neous background media.SIAM Journal on Applied Mathematics, 67(5):1353–1378, 2007

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-04T10:45:07.675983Z

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Observation ce7f8428-abcf-4874-8dad-27ec6cd09bdd · outbound

This paper cites Multidimensional inverse scattering problems.

A Morphology-Adaptive Random Feature Method for Inverse Source Problem of the Helmholtz Equation Multidimensional inverse scattering problems

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-04T10:45:07.829025Z

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Observation 241401b5-c55e-4da7-8da9-42ecce32e85e · outbound

This paper cites Thermoacoustic tomography with variable sound speed.Inverse Problems, 25(7):075011, 2009.

A Morphology-Adaptive Random Feature Method for Inverse Source Problem of the Helmholtz Equation Thermoacoustic tomography with variable sound speed.Inverse Problems, 25(7):075011, 2009

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-04T10:45:07.974858Z

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Observation 80d7c8fd-44f0-47bd-9f9e-0f38772f3a22 · outbound

This paper cites Inverse scattering.Sect.

A Morphology-Adaptive Random Feature Method for Inverse Source Problem of the Helmholtz Equation Inverse scattering.Sect

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-04T10:45:08.111681Z

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Observation 9f6adc44-9270-4fc0-b1f2-3e189933a026 · outbound

This paper cites Helmholtz surface wave tomography for isotropic and azimuthally anisotropic structure.Geophysical Journal International, 186(3):1104–1120, 2011.

A Morphology-Adaptive Random Feature Method for Inverse Source Problem of the Helmholtz Equation Helmholtz surface wave tomography for isotropic and azimuthally anisotropic structure.Geophysical Journal International, 186(3):1104–1120, 2011

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-04T10:45:08.193136Z

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Observation d5f8905b-418a-420a-ae9c-fc40150b7036 · outbound

This paper cites Image formation with arbitrary holographic type surfaces.Physics Letters A, 29(4):193–194, 1969.

A Morphology-Adaptive Random Feature Method for Inverse Source Problem of the Helmholtz Equation Image formation with arbitrary holographic type surfaces.Physics Letters A, 29(4):193–194, 1969

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-04T10:45:08.249869Z

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Observation 831e6df9-6fc5-4093-8301-c71854335463 · outbound

This paper cites Diffraction-limited, scalar image formation with holograms of arbitrary shape.Journal of the Optical Society of America, 60(8):1051–1059, 1970.

A Morphology-Adaptive Random Feature Method for Inverse Source Problem of the Helmholtz Equation Diffraction-limited, scalar image formation with holograms of arbitrary shape.Journal of the Optical Society of America, 60(8):1051–1059, 1970

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-04T10:45:08.338726Z

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Observation 1d1357ce-cac4-490a-bea8-598b98ab52b8 · outbound

This paper cites Nonuniqueness in the inverse source problem in acoustics and electromagnetics.Journal of Mathematical Physics, 18(2):194–201, 1977.

A Morphology-Adaptive Random Feature Method for Inverse Source Problem of the Helmholtz Equation Nonuniqueness in the inverse source problem in acoustics and electromagnetics.Journal of Mathematical Physics, 18(2):194–201, 1977

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-04T10:45:08.392558Z

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Observation 7d2bd30a-39a2-48ce-b16e-fed5d8371b1d · outbound

This paper cites Number 34 in CBMS-NSF Regional Conference Series in Applied Mathematics.

A Morphology-Adaptive Random Feature Method for Inverse Source Problem of the Helmholtz Equation Number 34 in CBMS-NSF Regional Conference Series in Applied Mathematics

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-04T10:45:08.469496Z

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Observation 7b9bf4c9-0953-4bb4-bf03-98211993059c · outbound

This paper cites A multi-frequency inverse source problem.Journal of Differential Equations, 249(12):3443–3465, 2010.

A Morphology-Adaptive Random Feature Method for Inverse Source Problem of the Helmholtz Equation A multi-frequency inverse source problem.Journal of Differential Equations, 249(12):3443–3465, 2010

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-04T10:45:08.579770Z

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Observation 43d3807d-0e0c-4475-891f-1c055c9de97a · outbound

This paper cites Numerical solution of the inverse source problem for the Helmholtz equation with multiple frequency data.Contemp.

A Morphology-Adaptive Random Feature Method for Inverse Source Problem of the Helmholtz Equation Numerical solution of the inverse source problem for the Helmholtz equation with multiple frequency data.Contemp

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-04T10:45:08.685574Z

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Observation 48cc83af-54b4-4241-b473-d55b2d065b20 · outbound

This paper cites Acoustic source identification using multiple frequency information.Inverse Problems, 25(11):115005, 2009.

A Morphology-Adaptive Random Feature Method for Inverse Source Problem of the Helmholtz Equation Acoustic source identification using multiple frequency information.Inverse Problems, 25(11):115005, 2009

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-04T10:45:08.869410Z

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Observation 19aa2106-4574-459f-9ae1-dc03f898784f · outbound

This paper cites Fourier method for solving the multi-frequency inverse source problem for the Helmholtz equation.Inverse Problems, 31(3):035007, 2015.

A Morphology-Adaptive Random Feature Method for Inverse Source Problem of the Helmholtz Equation Fourier method for solving the multi-frequency inverse source problem for the Helmholtz equation.Inverse Problems, 31(3):035007, 2015

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-04T10:45:08.975527Z

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Observation d97b7c8b-3079-4b2b-b8f6-b0e3d937c38e · outbound

This paper cites an unresolved cited work.

A Morphology-Adaptive Random Feature Method for Inverse Source Problem of the Helmholtz Equation Unresolved cited work

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-04T10:45:09.049674Z

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Observation 8cd26f5c-1140-4656-a875-b8d27f36fd51 · outbound

This paper cites DGM: A deep learning algorithm for solving partial differential equations.Journal of Computational Physics, 375:1339–1364, 2018.

A Morphology-Adaptive Random Feature Method for Inverse Source Problem of the Helmholtz Equation DGM: A deep learning algorithm for solving partial differential equations.Journal of Computational Physics, 375:1339–1364, 2018

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-04T10:45:09.129712Z

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Observation f013bc91-e3a1-41c1-a1d7-2cb9c7f18e14 · outbound

This paper cites The deep Ritz method: A deep learning-based numerical algorithm for solving variational problems.Communications in Mathematics and Statistics, 6(1):1–12, 2018.

A Morphology-Adaptive Random Feature Method for Inverse Source Problem of the Helmholtz Equation The deep Ritz method: A deep learning-based numerical algorithm for solving variational problems.Communications in Mathematics and Statistics, 6(1):1–12, 2018

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-04T10:45:09.225695Z

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Observation 53377cae-1916-42a4-acc5-496af374e64c · outbound

This paper cites an unresolved cited work.

A Morphology-Adaptive Random Feature Method for Inverse Source Problem of the Helmholtz Equation Unresolved cited work

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-04T10:45:09.299145Z

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Observation 7209ac7a-41f1-4464-9c34-bc6d62e2848f · outbound

This paper cites hp-VPINNs: Variational physics-informed neural networks with domain decomposition.Computer Methods in Applied Mechanics and Engineering, 374:113547, 2021.

A Morphology-Adaptive Random Feature Method for Inverse Source Problem of the Helmholtz Equation hp-VPINNs: Variational physics-informed neural networks with domain decomposition.Computer Methods in Applied Mechanics and Engineering, 374:113547, 2021

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-04T10:45:09.365341Z

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Observation a4d0e722-a6f5-490f-a17e-4887f2cc6870 · outbound

This paper cites Solving the inverse source problem of the fractional Poisson equation by MC-fPINNs.

A Morphology-Adaptive Random Feature Method for Inverse Source Problem of the Helmholtz Equation Solving the inverse source problem of the fractional Poisson equation by MC-fPINNs

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-04T10:45:09.458253Z

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Observation 90a41dc3-b491-4817-8d5a-d84904e611ab · outbound

This paper cites Ham- precht, Yoshua Bengio, and Aaron Courville.

A Morphology-Adaptive Random Feature Method for Inverse Source Problem of the Helmholtz Equation Ham- precht, Yoshua Bengio, and Aaron Courville

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-04T10:45:09.573346Z

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Observation c184ae86-1a03-45da-8983-c054f58bce1d · outbound

This paper cites Frequency principle: Fourier analysis sheds light on deep neural networks.Commun.

A Morphology-Adaptive Random Feature Method for Inverse Source Problem of the Helmholtz Equation Frequency principle: Fourier analysis sheds light on deep neural networks.Commun

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-04T10:45:09.689181Z

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Observation 0395d5e4-fc75-456c-9c2d-142e8439571d · outbound

This paper cites Bi-GreenNet: learning Green’s functions by boundary integral network.Communications in Mathematics and Statistics, 11(1):103–129, 2023.

A Morphology-Adaptive Random Feature Method for Inverse Source Problem of the Helmholtz Equation Bi-GreenNet: learning Green’s functions by boundary integral network.Communications in Mathematics and Statistics, 11(1):103–129, 2023

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-04T10:45:09.862682Z

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Observation c00e070e-c6e5-4429-81af-c7a55403232a · outbound

This paper cites an unresolved cited work.

A Morphology-Adaptive Random Feature Method for Inverse Source Problem of the Helmholtz Equation Unresolved cited work

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-04T10:45:09.964073Z

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Observation 2b71a362-d4eb-4fd5-af59-3ce0e50fbba5 · outbound

This paper cites An extreme learning machine-based method for computa- tional PDEs in higher dimensions.Computer Methods in Applied Mechanics and Engineering, 418:116578, 2024.

A Morphology-Adaptive Random Feature Method for Inverse Source Problem of the Helmholtz Equation An extreme learning machine-based method for computa- tional PDEs in higher dimensions.Computer Methods in Applied Mechanics and Engineering, 418:116578, 2024

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-04T10:45:10.103652Z

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Observation a6d0cce7-f4e0-4f47-a601-ad729fe430aa · outbound

This paper cites Bridging traditional and machine learning- based algorithms for solving PDEs: the random feature method.J Mach Learn, 1(3):268–298, 2022.

A Morphology-Adaptive Random Feature Method for Inverse Source Problem of the Helmholtz Equation Bridging traditional and machine learning- based algorithms for solving PDEs: the random feature method.J Mach Learn, 1(3):268–298, 2022

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-04T10:45:10.229159Z

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Observation a9118eb2-3c9b-4097-9054-b320bdbaf662 · outbound

This paper cites Physics-informed extreme learning machine (PIELM)–a rapid method for the numerical solution of partial differential equations.Neurocomputing, 391:96–118, 2020.

A Morphology-Adaptive Random Feature Method for Inverse Source Problem of the Helmholtz Equation Physics-informed extreme learning machine (PIELM)–a rapid method for the numerical solution of partial differential equations.Neurocomputing, 391:96–118, 2020

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-04T10:45:10.377726Z

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Observation bea94510-7f75-40c4-b789-1a2d6122e691 · outbound

This paper cites The random feature method for solving interface problems.Computer Methods in Applied Mechanics and Engineering, 420:116719, 2024.

A Morphology-Adaptive Random Feature Method for Inverse Source Problem of the Helmholtz Equation The random feature method for solving interface problems.Computer Methods in Applied Mechanics and Engineering, 420:116719, 2024

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-04T10:45:10.504932Z

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Observation e3347a32-3ee4-49a8-946f-0060dda0a692 · outbound

This paper cites Adaptive feature capture method for solving partial differential equations with near singular solutions.

A Morphology-Adaptive Random Feature Method for Inverse Source Problem of the Helmholtz Equation Adaptive feature capture method for solving partial differential equations with near singular solutions

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-04T10:45:10.678037Z

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Observation 08baf47b-1f9f-4590-aa2e-9591b44c9610 · outbound

This paper cites Theh,pandhpversions of the finite element method in 1 dimension: Part I.

A Morphology-Adaptive Random Feature Method for Inverse Source Problem of the Helmholtz Equation Theh,pandhpversions of the finite element method in 1 dimension: Part I

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-04T10:45:10.781350Z

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Observation 3422c1fd-da87-4de9-936e-e66589126e06 · outbound

This paper cites Theh,pandhpversions of the finite element method in 1 dimension: Part II.

A Morphology-Adaptive Random Feature Method for Inverse Source Problem of the Helmholtz Equation Theh,pandhpversions of the finite element method in 1 dimension: Part II

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-04T10:45:10.882504Z

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Observation c62ee23e-1420-4635-b2dd-96161f1a1155 · outbound

This paper cites The p-version of the finite element method.

A Morphology-Adaptive Random Feature Method for Inverse Source Problem of the Helmholtz Equation The p-version of the finite element method

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-04T10:45:11.019205Z

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Observation 88d33c04-4461-47b1-85c3-f17e96340911 · outbound

This paper cites Thep-andhpversions of the finite element method, an overview.

A Morphology-Adaptive Random Feature Method for Inverse Source Problem of the Helmholtz Equation Thep-andhpversions of the finite element method, an overview

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-04T10:45:11.143375Z

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Observation 4963f864-cca9-4e74-8fa6-c9c149102670 · outbound

This paper cites Cambridge University Press, 2000.

A Morphology-Adaptive Random Feature Method for Inverse Source Problem of the Helmholtz Equation Cambridge University Press, 2000

Reference 37

Resolution: unresolved; no resolver link, observed 2026-08-04T10:45:11.233349Z

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Observation f05c5af9-165a-43a6-b820-5628b05b5bca · outbound

This paper cites Applied Numerical Mathematics, 26(1-2):97–104, 1998.

A Morphology-Adaptive Random Feature Method for Inverse Source Problem of the Helmholtz Equation Applied Numerical Mathematics, 26(1-2):97–104, 1998

Reference 38

Resolution: unresolved; no resolver link, observed 2026-08-04T10:45:11.352838Z

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Observation 8d2a7614-2a24-4608-92aa-4d602bc892d2 · outbound

This paper cites Analysis of a spectral-Galerkin approximation to the Helmholtz equation in exterior domains.SIAM J.

A Morphology-Adaptive Random Feature Method for Inverse Source Problem of the Helmholtz Equation Analysis of a spectral-Galerkin approximation to the Helmholtz equation in exterior domains.SIAM J

Reference 39

Resolution: unresolved; no resolver link, observed 2026-08-04T10:45:11.476565Z

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Observation c16a59ef-dafb-4646-bc0a-1e62b07698f1 · outbound

This paper cites Analysis of discrete ill-posed problems by means of the L-curve.SIAM Review, 34(4):561–580, 1992.

A Morphology-Adaptive Random Feature Method for Inverse Source Problem of the Helmholtz Equation Analysis of discrete ill-posed problems by means of the L-curve.SIAM Review, 34(4):561–580, 1992

Reference 40

Resolution: unresolved; no resolver link, observed 2026-08-04T10:45:11.585718Z

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Observation cfd8482d-3215-45f2-bc22-36148fd59f74 · outbound

This paper cites On the uniqueness theorem of Holmgren.Mathematische Zeitschrift, 281(1):357–378, 2015.

A Morphology-Adaptive Random Feature Method for Inverse Source Problem of the Helmholtz Equation On the uniqueness theorem of Holmgren.Mathematische Zeitschrift, 281(1):357–378, 2015

Reference 41

Resolution: unresolved; no resolver link, observed 2026-08-04T10:45:11.693335Z

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Pith citing papers

Observation 8da78406-d9cd-448b-b5ae-7f8769b0bfe9 · inbound

Solving and learning advective multiscale Darcian dynamics with the Neural Basis Method cites this paper.

Solving and learning advective multiscale Darcian dynamics with the Neural Basis Method A Morphology-Adaptive Random Feature Method for Inverse Source Problem of the Helmholtz Equation

Reference 33

Resolution: verified exact; arxiv_id, observed 2026-06-02T03:04:01.521540Z

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Observation 9e563190-e1c7-4ad7-9654-396d85b7d646 · inbound

Recovering the initial condition and physical coefficients in a nonlinear PDE model of cell invasion cites this paper.

Recovering the initial condition and physical coefficients in a nonlinear PDE model of cell invasion A Morphology-Adaptive Random Feature Method for Inverse Source Problem of the Helmholtz Equation

Reference 131

Resolution: metadata mismatch; local_arxiv, observed 2026-07-03T11:38:04.765435Z

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