Paper Citation Record · LEDGER

Multi-frequency wavefield solutions for variable velocity models using meta-learning enhanced low-rank physics-informed neural network

As of 15 August 2026, this Paper Citation Record lists 36 of 36 outbound references and 1 inbound Pith citation observation for arXiv:2502.00897.

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

pith.paper-citation-record.v1
2502.00897 v1

Coverage vector

measured 36 of 36 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-09T17:22:20.602446Z

measured 37 of 37 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-14T06:32:32.682623+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-07T12:09:04.178190Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-07T12:09:04.922990Z

Reference resolution

36 of 36 outbound references displayed

verified exact0
verified fuzzy22
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 0f6bd364-cbbc-4103-af7e-b8c922e0d8a3 · outbound

This paper cites Seismic modeling.

Multi-frequency wavefield solutions for variable velocity models using meta-learning enhanced low-rank physics-informed neural network Seismic modeling

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-09T17:22:20.493046Z

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Observation 4403b8ae-03e6-4225-989f-da29e958da9c · outbound

This paper cites Full seismic waveform modelling and inversion.

Multi-frequency wavefield solutions for variable velocity models using meta-learning enhanced low-rank physics-informed neural network Full seismic waveform modelling and inversion

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-09T17:22:20.497082Z

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Observation 52a88a22-4702-47d1-a3bd-a7bb06869f54 · outbound

This paper cites Accuracy of finite-difference and finite-element modeling of the scalar and elastic wave equations.

Multi-frequency wavefield solutions for variable velocity models using meta-learning enhanced low-rank physics-informed neural network Accuracy of finite-difference and finite-element modeling of the scalar and elastic wave equations

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T17:22:20.914688Z

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation b14896f2-1112-4e36-9ad7-67c20256bf9d · outbound

This paper cites Seismic waveform inversion in the frequency domain, part 1: Theory and verification in a physical scale model.

Multi-frequency wavefield solutions for variable velocity models using meta-learning enhanced low-rank physics-informed neural network Seismic waveform inversion in the frequency domain, part 1: Theory and verification in a physical scale model

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T17:22:20.905573Z

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Observation 63f4844a-db02-4bae-b0b3-4b240846ac28 · outbound

This paper cites Seismic waveform inversion in the frequency domain, part 2: Fault delineation in sediments using crosshole data.

Multi-frequency wavefield solutions for variable velocity models using meta-learning enhanced low-rank physics-informed neural network Seismic waveform inversion in the frequency domain, part 2: Fault delineation in sediments using crosshole data

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T17:22:20.896134Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 07255a39-56a8-4378-bc2a-e357849d0db9 · outbound

This paper cites Frequency-domain elastic wave modeling by finite differences: A tool for crosshole seismic imaging.

Multi-frequency wavefield solutions for variable velocity models using meta-learning enhanced low-rank physics-informed neural network Frequency-domain elastic wave modeling by finite differences: A tool for crosshole seismic imaging

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T17:22:20.886502Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 8cef25aa-56c5-46f8-a048-2fb1999230c1 · outbound

This paper cites 3d finite-difference frequency-domain modeling of visco-acoustic wave propagation using a massively parallel direct solver: A feasibility study.

Multi-frequency wavefield solutions for variable velocity models using meta-learning enhanced low-rank physics-informed neural network 3d finite-difference frequency-domain modeling of visco-acoustic wave propagation using a massively parallel direct solver: A feasibility study

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T17:22:20.877151Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation edd7157f-1896-43c9-bd36-948a9749419e · outbound

This paper cites A new iterative solver for the time-harmonic wave equation.

Multi-frequency wavefield solutions for variable velocity models using meta-learning enhanced low-rank physics-informed neural network A new iterative solver for the time-harmonic wave equation

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T17:22:20.867569Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 8273ba11-8546-44cd-acea-11ecc6909aa7 · outbound

This paper cites Three-dimensional frequency-domain full-waveform inversion with an iterative solver.

Multi-frequency wavefield solutions for variable velocity models using meta-learning enhanced low-rank physics-informed neural network Three-dimensional frequency-domain full-waveform inversion with an iterative solver

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T17:22:20.857428Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 95b7d55f-15bf-42cb-b62b-908a158ad4be · outbound

This paper cites 3d finite-difference modeling of elastic wave propagation in the laplace-fourier domain.

Multi-frequency wavefield solutions for variable velocity models using meta-learning enhanced low-rank physics-informed neural network 3d finite-difference modeling of elastic wave propagation in the laplace-fourier domain

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T17:22:20.847544Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 3877b938-b860-44d5-acad-fcaabba231be · outbound

This paper cites An efficient helmholtz solver for acoustic transversely isotropic media.

Multi-frequency wavefield solutions for variable velocity models using meta-learning enhanced low-rank physics-informed neural network An efficient helmholtz solver for acoustic transversely isotropic media

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T17:22:20.837283Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation c09986ef-5dbd-4b4e-a178-7cf890a4c824 · outbound

This paper cites An optimal nearly analytic discrete method for 2d acoustic and elastic wave equations.

Multi-frequency wavefield solutions for variable velocity models using meta-learning enhanced low-rank physics-informed neural network An optimal nearly analytic discrete method for 2d acoustic and elastic wave equations

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T17:22:20.828550Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation e2c50b71-129c-4781-9f02-328adedd8229 · outbound

This paper cites A finite-difference iterative solver of the helmholtz equation for frequency-domain seismic wave modeling and full-waveform inversion.

Multi-frequency wavefield solutions for variable velocity models using meta-learning enhanced low-rank physics-informed neural network A finite-difference iterative solver of the helmholtz equation for frequency-domain seismic wave modeling and full-waveform inversion

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T17:22:20.819653Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 6a87ed3b-42dc-4f1e-8bc0-832c00e8fb46 · outbound

This paper cites Accelerating the shifted laplace preconditioner for the helmholtz equation by multilevel deflation.

Multi-frequency wavefield solutions for variable velocity models using meta-learning enhanced low-rank physics-informed neural network Accelerating the shifted laplace preconditioner for the helmholtz equation by multilevel deflation

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T17:22:20.810082Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation cc551f6d-975e-4fb5-94b4-d27cb5a0a863 · outbound

This paper cites An iterative solver for the 3d helmholtz equation.

Multi-frequency wavefield solutions for variable velocity models using meta-learning enhanced low-rank physics-informed neural network An iterative solver for the 3d helmholtz equation

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T17:22:20.800276Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 6c89cbac-bcb5-4951-8f9b-60a8255a0ebc · outbound

This paper cites Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations.

Multi-frequency wavefield solutions for variable velocity models using meta-learning enhanced low-rank physics-informed neural network Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-09T17:22:20.544756Z

Source-reported events for the cited work

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Observation e77976ab-4706-4318-a8d0-0d726bf3c745 · outbound

This paper cites Physics-informed neural networks (pinns) for wave propagation and full waveform inversions.

Multi-frequency wavefield solutions for variable velocity models using meta-learning enhanced low-rank physics-informed neural network Physics-informed neural networks (pinns) for wave propagation and full waveform inversions

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-09T17:22:20.547880Z

Source-reported events for the cited work

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Observation c32e33f5-8201-44f7-ac13-c334c598a970 · outbound

This paper cites Kronecker neural networks overcome spectral bias for pinn-based wavefield computation.

Multi-frequency wavefield solutions for variable velocity models using meta-learning enhanced low-rank physics-informed neural network Kronecker neural networks overcome spectral bias for pinn-based wavefield computation

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T17:22:20.779007Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 5f500048-48c5-4539-8e50-292f77d08756 · outbound

This paper cites Multi-frequency wavefield modeling of acoustic vti wave equation using physics informed neural networks.

Multi-frequency wavefield solutions for variable velocity models using meta-learning enhanced low-rank physics-informed neural network Multi-frequency wavefield modeling of acoustic vti wave equation using physics informed neural networks

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T17:22:20.768713Z

Source-reported events for the cited work

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Observation bc4c1cc9-d26a-4e05-8270-8c511acac4ce · outbound

This paper cites Review of physics-informed machine-learning inversion of geophysical data.

Multi-frequency wavefield solutions for variable velocity models using meta-learning enhanced low-rank physics-informed neural network Review of physics-informed machine-learning inversion of geophysical data

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T17:22:20.758787Z

Source-reported events for the cited work

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Observation 5455eaff-064f-465d-a16a-3a90c0568d7e · outbound

This paper cites Modeling multisource multifrequency acoustic wavefields by a multiscale fourier feature physics-informed neural network with adaptive activation functions.

Multi-frequency wavefield solutions for variable velocity models using meta-learning enhanced low-rank physics-informed neural network Modeling multisource multifrequency acoustic wavefields by a multiscale fourier feature physics-informed neural network with adaptive activation functions

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-09T17:22:20.560390Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0ae4e050-aac9-49dd-bb75-6d3c78f8b55b · outbound

This paper cites Solving the frequency-domain acoustic vti wave equation using physics-informed neural networks.

Multi-frequency wavefield solutions for variable velocity models using meta-learning enhanced low-rank physics-informed neural network Solving the frequency-domain acoustic vti wave equation using physics-informed neural networks

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-09T17:22:20.563331Z

Source-reported events for the cited work

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Observation 54b9f998-c5a4-41c6-92ed-9f60be6d4830 · outbound

This paper cites A versatile framework to solve the helmholtz equation using physics-informed neural networks.

Multi-frequency wavefield solutions for variable velocity models using meta-learning enhanced low-rank physics-informed neural network A versatile framework to solve the helmholtz equation using physics-informed neural networks

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T17:22:20.737327Z

Source-reported events for the cited work

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Observation 8cd9f776-7c6e-4538-9c41-b8051ebf7954 · outbound

This paper cites Pinneik: Eikonal solution using physics-informed neural networks.

Multi-frequency wavefield solutions for variable velocity models using meta-learning enhanced low-rank physics-informed neural network Pinneik: Eikonal solution using physics-informed neural networks

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-09T17:22:20.569565Z

Source-reported events for the cited work

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Observation ad42d4cd-1ef4-43cd-a110-b3c542926a7b · outbound

This paper cites A modified physics-informed neural network with positional encoding.

Multi-frequency wavefield solutions for variable velocity models using meta-learning enhanced low-rank physics-informed neural network A modified physics-informed neural network with positional encoding

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T17:22:20.721222Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 2f68a750-1bd0-4e24-a26d-4fb752b2efff · outbound

This paper cites Helmholtz-equation solution in nonsmooth media by a physics-informed neural network incorporating quadratic terms and a perfectly matching layer condition.

Multi-frequency wavefield solutions for variable velocity models using meta-learning enhanced low-rank physics-informed neural network Helmholtz-equation solution in nonsmooth media by a physics-informed neural network incorporating quadratic terms and a perfectly matching layer condition

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-09T17:22:20.575778Z

Source-reported events for the cited work

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Observation d8b0f305-724c-4805-b11d-4b4ed546fa0d · outbound

This paper cites Physics-informed neural wavefields with gabor basis functions.

Multi-frequency wavefield solutions for variable velocity models using meta-learning enhanced low-rank physics-informed neural network Physics-informed neural wavefields with gabor basis functions

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-09T17:22:20.578799Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 341d3cda-99ad-4d9d-aafd-6e6c90dd321f · outbound

This paper cites Meta-auto-decoder for solving parametric partial differential equations.

Multi-frequency wavefield solutions for variable velocity models using meta-learning enhanced low-rank physics-informed neural network Meta-auto-decoder for solving parametric partial differential equations

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T17:22:20.699415Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 4859a0c0-3316-4a94-8d3d-a2a71bff8909 · outbound

This paper cites Single reference frequency loss for multifrequency wavefield representation using physics-informed neural networks.

Multi-frequency wavefield solutions for variable velocity models using meta-learning enhanced low-rank physics-informed neural network Single reference frequency loss for multifrequency wavefield representation using physics-informed neural networks

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T17:22:20.689764Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation d8059ac1-dbe4-49ca-8e09-6234f2e780ae · outbound

This paper cites Simulating seismic multifrequency wavefields with the fourier feature physics-informed neural network.

Multi-frequency wavefield solutions for variable velocity models using meta-learning enhanced low-rank physics-informed neural network Simulating seismic multifrequency wavefields with the fourier feature physics-informed neural network

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T17:22:20.679539Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 431ce84d-fe7a-4e53-aaf6-9f2c669d2505 · outbound

This paper cites Multiple wavefield solutions in physics-informed neural networks using latent representation.

Multi-frequency wavefield solutions for variable velocity models using meta-learning enhanced low-rank physics-informed neural network Multiple wavefield solutions in physics-informed neural networks using latent representation

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-09T17:22:20.589874Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7af66cd3-dae5-4f07-915f-8004fca935af · outbound

This paper cites Meta learning for improved neural network wavefield solutions.

Multi-frequency wavefield solutions for variable velocity models using meta-learning enhanced low-rank physics-informed neural network Meta learning for improved neural network wavefield solutions

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T17:22:20.663101Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 25d3e96e-13b9-41b8-8153-6df2637c777f · outbound

This paper cites Model-agnostic meta-learning for fast adaptation of deep networks.

Multi-frequency wavefield solutions for variable velocity models using meta-learning enhanced low-rank physics-informed neural network Model-agnostic meta-learning for fast adaptation of deep networks

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-09T17:22:20.594863Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7cd4b8b3-ac21-48b9-b74f-2a4100691242 · outbound

This paper cites Richards.

Multi-frequency wavefield solutions for variable velocity models using meta-learning enhanced low-rank physics-informed neural network Richards

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-09T17:22:20.597434Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8f6d7031-e82b-43ee-9cc4-e951e4a3286e · outbound

This paper cites Wavefield solutions from machine learned functions constrained by the helmholtz equation.

Multi-frequency wavefield solutions for variable velocity models using meta-learning enhanced low-rank physics-informed neural network Wavefield solutions from machine learned functions constrained by the helmholtz equation

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-09T17:22:20.599914Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation adb18256-ef65-473f-8e46-2297768a08bc · outbound

This paper cites Decoupled Weight Decay Regularization.

Multi-frequency wavefield solutions for variable velocity models using meta-learning enhanced low-rank physics-informed neural network Decoupled Weight Decay Regularization

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-09T17:22:20.602446Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation e2c3dce1-abcd-42ae-be27-fb8231029f91 · inbound

DiffPINN: Generative diffusion-initialized physics-informed neural networks for accelerating seismic wavefield representation cites this paper.

DiffPINN: Generative diffusion-initialized physics-informed neural networks for accelerating seismic wavefield representation Multi-frequency wavefield solutions for variable velocity models using meta-learning enhanced low-rank physics-informed neural network

Reference 27

Resolution: verified exact; local_arxiv, observed 2026-08-07T12:09:04.971632Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.