Paper Citation Record · LEDGER

Solving engineering eigenvalue problems with neural networks using the Rayleigh quotient

As of 9 August 2026, this Paper Citation Record lists 52 of 52 outbound references and 1 inbound Pith citation observation for arXiv:2506.04375.

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

pith.paper-citation-record.v1
2506.04375 v1

Coverage vector

measured 52 of 52 reference resolution

Typed states for the displayed outbound observations.

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One-hop event checks from named stored sources.

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measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-02T23:34:48.705247Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

52 of 52 outbound references displayed

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verified fuzzy28
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External citation measurements

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Outbound references

Observation 8ce2eb44-95b7-4b3d-bdcc-b917f09d8d8e · outbound

This paper cites A deep learning energy method for hyperelasticity and viscoelasticity.

Solving engineering eigenvalue problems with neural networks using the Rayleigh quotient A deep learning energy method for hyperelasticity and viscoelasticity

Reference 1

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Observation ac8784bf-eb9d-4904-b3d6-e7be35e89c2a · outbound

This paper cites Neural Operators for Accelerating Scientific Simulations and Design.

Solving engineering eigenvalue problems with neural networks using the Rayleigh quotient Neural Operators for Accelerating Scientific Simulations and Design

Reference 2

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Observation 87c6ac11-861d-46da-af46-3724b0ba0ef5 · outbound

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Solving engineering eigenvalue problems with neural networks using the Rayleigh quotient Unresolved cited work

Reference 3

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Solving engineering eigenvalue problems with neural networks using the Rayleigh quotient Unresolved cited work

Reference 4

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Observation 27749589-c805-4627-9869-582d9f4012f0 · outbound

This paper cites Deep Learning Solution of the Eigenvalue Problem for Differential Operators.

Solving engineering eigenvalue problems with neural networks using the Rayleigh quotient Deep Learning Solution of the Eigenvalue Problem for Differential Operators

Reference 5

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Observation 585bc0e1-e83c-4714-abbd-e24a94b3a341 · outbound

This paper cites Stress ﬁeld prediction in ﬁber-reinforced composite materials using a deep learning approach.

Solving engineering eigenvalue problems with neural networks using the Rayleigh quotient Stress ﬁeld prediction in ﬁber-reinforced composite materials using a deep learning approach

Reference 6

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Observation e7b7f8b0-f711-452d-a904-89f649aef8bd · outbound

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Solving engineering eigenvalue problems with neural networks using the Rayleigh quotient Unresolved cited work

Reference 7

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This paper cites De ep least-squares methods: an unsupervised learning- based numerical method for solving elliptic PDEs.

Solving engineering eigenvalue problems with neural networks using the Rayleigh quotient De ep least-squares methods: an unsupervised learning- based numerical method for solving elliptic PDEs

Reference 8

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Observation 01dc6655-a7ad-4537-9dee-875c7d5b0af0 · outbound

This paper cites The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems.

Solving engineering eigenvalue problems with neural networks using the Rayleigh quotient The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems

Reference 9

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Observation 0beded49-cd45-4e34-bede-9247c3f2b953 · outbound

This paper cites Karhunen–Loéve Ex pansion of Temporal and Spatio-Temporal Processes.

Solving engineering eigenvalue problems with neural networks using the Rayleigh quotient Karhunen–Loéve Ex pansion of Temporal and Spatio-Temporal Processes

Reference 10

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Observation 6a47e7d3-5372-423d-95bb-aba10062f6b7 · outbound

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Solving engineering eigenvalue problems with neural networks using the Rayleigh quotient Unresolved cited work

Reference 11

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Observation 847fb4f3-c71f-4441-b841-57c1bfeadcc2 · outbound

This paper cites Numerical integr ation using sparse grids.

Solving engineering eigenvalue problems with neural networks using the Rayleigh quotient Numerical integr ation using sparse grids

Reference 12

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Observation 367de7a7-8d17-41af-b7fa-d4c91dd256f3 · outbound

This paper cites Jimack, and René de Bo rst.

Solving engineering eigenvalue problems with neural networks using the Rayleigh quotient Jimack, and René de Bo rst

Reference 13

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Observation a7875e71-9953-4f0a-9892-af98abf027df · outbound

This paper cites Laplacian Eigenfunction- Based Neural Operator for Learning Nonlinear Partial Differential Equations, February 2025.

Solving engineering eigenvalue problems with neural networks using the Rayleigh quotient Laplacian Eigenfunction- Based Neural Operator for Learning Nonlinear Partial Differential Equations, February 2025

Reference 14

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Observation ae60d349-bf55-4ccf-9a59-859932a6ac8d · outbound

This paper cites Deep autoen coders for physics-constrained data-driven nonlinear materials modeling.

Solving engineering eigenvalue problems with neural networks using the Rayleigh quotient Deep autoen coders for physics-constrained data-driven nonlinear materials modeling

Reference 15

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Observation 58a53bcb-a483-46f3-ae1e-bee50f58a61c · outbound

This paper cites Latent Diffusion Models for Structural Component Design.

Solving engineering eigenvalue problems with neural networks using the Rayleigh quotient Latent Diffusion Models for Structural Component Design

Reference 16

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Observation 8195cfcd-4331-44ab-ad17-ff16320f19c7 · outbound

This paper cites Solving two-dimensional quantum eigenvalue problems using physics-informed machine learning.

Solving engineering eigenvalue problems with neural networks using the Rayleigh quotient Solving two-dimensional quantum eigenvalue problems using physics-informed machine learning

Reference 17

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Observation fbb2deef-eab3-439b-ab2e-144ba8c786d0 · outbound

This paper cites Densely connected neural networks for nonlinear regression.

Solving engineering eigenvalue problems with neural networks using the Rayleigh quotient Densely connected neural networks for nonlinear regression

Reference 18

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Observation f3839c13-7390-4d73-bada-c53b48c87389 · outbound

This paper cites Physics-Informed Neural Networks for Quantum Eigenvalue Problems.

Solving engineering eigenvalue problems with neural networks using the Rayleigh quotient Physics-Informed Neural Networks for Quantum Eigenvalue Problems

Reference 19

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This paper cites NSFnets (Navier-Stokes Flow nets): Physics- informed neural networks for the incompressible Navier-St okes equations.

Solving engineering eigenvalue problems with neural networks using the Rayleigh quotient NSFnets (Navier-Stokes Flow nets): Physics- informed neural networks for the incompressible Navier-St okes equations

Reference 20

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Observation 18842c82-8a06-4073-a48e-1ecaffc69959 · outbound

This paper cites Physics-informed ne ural network for modeling dynamic linear elasticity, January 2024.

Solving engineering eigenvalue problems with neural networks using the Rayleigh quotient Physics-informed ne ural network for modeling dynamic linear elasticity, January 2024

Reference 21

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Observation 1e7798f3-ec86-4ee4-8cf9-ae093236aec1 · outbound

This paper cites Kharazmi, Z.

Solving engineering eigenvalue problems with neural networks using the Rayleigh quotient Kharazmi, Z

Reference 22

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Observation 9ae60f10-8595-429a-8534-98be9d654e96 · outbound

This paper cites hp-VPINNs: V ariational Physics-Informed Neural Networks With Domain Decomposition.

Solving engineering eigenvalue problems with neural networks using the Rayleigh quotient hp-VPINNs: V ariational Physics-Informed Neural Networks With Domain Decomposition

Reference 23

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Solving engineering eigenvalue problems with neural networks using the Rayleigh quotient VarNet: Variational Neural Networks for the Solution of Partial Differential Equations

Reference 24

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Solving engineering eigenvalue problems with neural networks using the Rayleigh quotient Conditional physics informed neural networks

Reference 25

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Observation f2668645-a86e-4a30-ae25-6322b43c406e · outbound

This paper cites Lagaris, A.

Solving engineering eigenvalue problems with neural networks using the Rayleigh quotient Lagaris, A

Reference 26

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Observation ae474517-a55a-4034-bbd3-20ca1d28319f · outbound

This paper cites Ap- plication of neural networks to modelling nonlinear relati onships in ecology.

Solving engineering eigenvalue problems with neural networks using the Rayleigh quotient Ap- plication of neural networks to modelling nonlinear relati onships in ecology

Reference 27

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Observation 47fe7cbf-f2da-4f27-b9fa-9761ae60a6b0 · outbound

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

Solving engineering eigenvalue problems with neural networks using the Rayleigh quotient Fourier Neural Operator for Parametric Partial Differential Equations

Reference 28

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This paper cites Deep Ritz met hod with adaptive quadrature for linear elasticity.

Solving engineering eigenvalue problems with neural networks using the Rayleigh quotient Deep Ritz met hod with adaptive quadrature for linear elasticity

Reference 29

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Observation aa967edb-dc48-4469-94f4-73d38d089265 · outbound

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Solving engineering eigenvalue problems with neural networks using the Rayleigh quotient Image Classification with Classic and Deep Learning Techniques

Reference 30

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Solving engineering eigenvalue problems with neural networks using the Rayleigh quotient DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators

Reference 31

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Solving engineering eigenvalue problems with neural networks using the Rayleigh quotient Physics Informed Neural Networks for heat conduction with phase change

Reference 32

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This paper cites PRINC IP AL COMPONENTS ANALYSIS (PCA).Comput- ers and geosciences, 1992.

Solving engineering eigenvalue problems with neural networks using the Rayleigh quotient PRINC IP AL COMPONENTS ANALYSIS (PCA).Comput- ers and geosciences, 1992

Reference 33

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Observation da5cf3a9-e64a-4384-8c0d-7b2132d72732 · outbound

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Solving engineering eigenvalue problems with neural networks using the Rayleigh quotient Manav, R

Reference 34

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Observation 2554ad1e-3f4c-4ff3-b096-e1c56bf85cba · outbound

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Solving engineering eigenvalue problems with neural networks using the Rayleigh quotient Implementation of CALFEM for Python

Reference 35

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Solving engineering eigenvalue problems with neural networks using the Rayleigh quotient On the Spectral Bias of Neural Networks

Reference 36

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Solving engineering eigenvalue problems with neural networks using the Rayleigh quotient Raissi, P

Reference 37

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This paper cites Deep Generative Models in Engineering Design: A Review.

Solving engineering eigenvalue problems with neural networks using the Rayleigh quotient Deep Generative Models in Engineering Design: A Review

Reference 38

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Observation 90debebb-9259-4e4e-b983-af1d11486820 · outbound

This paper cites Numerical Methods for Large Eigenvalue Problems: Revised E dition.

Solving engineering eigenvalue problems with neural networks using the Rayleigh quotient Numerical Methods for Large Eigenvalue Problems: Revised E dition

Reference 39

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Observation edaf372d-b6ee-4050-a5eb-cbef1f233f2d · outbound

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Solving engineering eigenvalue problems with neural networks using the Rayleigh quotient Sahin, M

Reference 40

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Solving engineering eigenvalue problems with neural networks using the Rayleigh quotient Unresolved cited work

Reference 41

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Observation 556dc597-56b6-465d-aefe-5343834a5c99 · outbound

This paper cites Deep Petrov-Galerkin Method for Solving Partial Differential Equations.

Solving engineering eigenvalue problems with neural networks using the Rayleigh quotient Deep Petrov-Galerkin Method for Solving Partial Differential Equations

Reference 42

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Solving engineering eigenvalue problems with neural networks using the Rayleigh quotient DGM: A deep learning algorithm for solving partial differential equations

Reference 43

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Solving engineering eigenvalue problems with neural networks using the Rayleigh quotient Sukumar and Ankit Srivastava

Reference 44

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Observation 626848de-67b2-4390-9e7b-b6e54afe1220 · outbound

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Solving engineering eigenvalue problems with neural networks using the Rayleigh quotient Unresolved cited work

Reference 45

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Observation 5f6d0f19-2cf3-4f43-83ab-dbef3870b637 · outbound

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Solving engineering eigenvalue problems with neural networks using the Rayleigh quotient V allet and B

Reference 46

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:48:11.357782Z

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Observation fecc607f-d61f-4d8a-91c7-a4d0c7d40c9a · outbound

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Solving engineering eigenvalue problems with neural networks using the Rayleigh quotient Dee p Sturm–Liouville: Learnable orthogonal basis func- tions parameterized by neural networks

Reference 47

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:48:11.323782Z

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Observation 4ecdb8ba-3a8f-41d1-babd-b641b27c2950 · outbound

This paper cites Mo, Bassam Izzuddin, and Chul-Woo Kim.

Solving engineering eigenvalue problems with neural networks using the Rayleigh quotient Mo, Bassam Izzuddin, and Chul-Woo Kim

Reference 48

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:48:11.306157Z

Source-reported events for the cited work

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Observation c0080a54-ee32-420e-8436-aa2407c17ac9 · outbound

This paper cites Neural networks based on power method and inverse power method for solving linear eigenvalue prob lems.

Solving engineering eigenvalue problems with neural networks using the Rayleigh quotient Neural networks based on power method and inverse power method for solving linear eigenvalue prob lems

Reference 49

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:48:11.289175Z

Source-reported events for the cited work

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Observation 5eacb48b-49f7-4cae-a043-4abe32c76fbb · outbound

This paper cites A Physics-Informed Neural Network Approach for Solving the Engineering Eigenvalue Problem.

Solving engineering eigenvalue problems with neural networks using the Rayleigh quotient A Physics-Informed Neural Network Approach for Solving the Engineering Eigenvalue Problem

Reference 50

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:48:11.268412Z

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Observation 75ef4ec6-6291-43d1-98bc-4a71a0e1f210 · outbound

This paper cites A review of convo- lutional neural networks in computer vision.

Solving engineering eigenvalue problems with neural networks using the Rayleigh quotient A review of convo- lutional neural networks in computer vision

Reference 51

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:48:11.243025Z

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Observation 1ef429ad-0f5a-4f91-beee-8df8601770e5 · outbound

This paper cites Solving Forward and Inverse Problems of Contact Mechanics using Physics-Informed Neural Networks.

Solving engineering eigenvalue problems with neural networks using the Rayleigh quotient Solving Forward and Inverse Problems of Contact Mechanics using Physics-Informed Neural Networks

Reference 2024

Resolution: verified exact; local_arxiv, observed 2026-08-07T10:48:10.712601Z

Source-reported events for the cited work

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Pith citing papers

Observation c569eec7-37df-413c-a651-ad11b9ab1b66 · inbound

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization cites this paper.

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization Solving engineering eigenvalue problems with neural networks using the Rayleigh quotient

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