Paper Citation Record · LEDGER

fTNN: a tensor neural network for fractional PDEs

As of 16 August 2026, this Paper Citation Record lists 36 of 36 outbound references and 0 inbound Pith citation observations for arXiv:2606.27140.

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pith.paper-citation-record.v1
2606.27140 v1

Coverage vector

measured 36 of 36 reference resolution

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Source: paper_references, paper_reference_links, observed 2026-06-26T05:09:15.152114Z

measured 36 of 36 standing notices

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Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+00:00

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measured 0 of 1 external citation measurements

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Reference resolution

36 of 36 outbound references displayed

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Outbound references

Observation afc97a98-fa92-4b28-b7e5-ec7ba67dfbe9 · outbound

This paper cites A short FE imple- mentation for a 2d homogeneous Dirichlet problem of a fractional Laplacian.Computers & Mathematics with Applications, 74(4):784–816, 2017.

fTNN: a tensor neural network for fractional PDEs A short FE imple- mentation for a 2d homogeneous Dirichlet problem of a fractional Laplacian.Computers & Mathematics with Applications, 74(4):784–816, 2017

Reference 1

Resolution: unresolved; no resolver link, observed 2026-06-26T05:09:15.152114Z

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Observation ac43e78d-cf55-40b6-a317-28ae74f692fc · outbound

This paper cites Towards an efficient finite element method for the integral fractional Laplacian on polygonal domains.

fTNN: a tensor neural network for fractional PDEs Towards an efficient finite element method for the integral fractional Laplacian on polygonal domains

Reference 2

Resolution: unresolved; no resolver link, observed 2026-06-26T05:09:15.152114Z

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Observation cb273699-d341-4833-b28a-4e6aa84dc28d · outbound

This paper cites Numerical methods for fractional diffusion.Computing and Visualization in Science, 19(5):19–46, 2018.

fTNN: a tensor neural network for fractional PDEs Numerical methods for fractional diffusion.Computing and Visualization in Science, 19(5):19–46, 2018

Reference 3

Resolution: unresolved; no resolver link, observed 2026-06-26T05:09:15.152114Z

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Observation 676f8359-a0ae-4fb2-8e08-b27ec3a077bd · outbound

This paper cites QMC designs: optimal order quasi Monte Carlo integration schemes on the sphere.Mathematics of Computation, 83(290):2821–2851, 2014.

fTNN: a tensor neural network for fractional PDEs QMC designs: optimal order quasi Monte Carlo integration schemes on the sphere.Mathematics of Computation, 83(290):2821–2851, 2014

Reference 4

Resolution: unresolved; no resolver link, observed 2026-06-26T05:09:15.152114Z

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Observation fddd7e6a-0ac1-4d15-a2d7-b2aa5deb35fe · outbound

This paper cites Computation of Gauss-Jacobi quadrature nodes and weights with arbitrary precision.

fTNN: a tensor neural network for fractional PDEs Computation of Gauss-Jacobi quadrature nodes and weights with arbitrary precision

Reference 5

Resolution: unresolved; no resolver link, observed 2026-06-26T05:09:15.152114Z

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Observation 1ee48e9d-ba36-4a02-bf1d-4fdd5e338b1b · outbound

This paper cites An extension problem related to the fractional Laplacian.

fTNN: a tensor neural network for fractional PDEs An extension problem related to the fractional Laplacian

Reference 6

Resolution: unresolved; no resolver link, observed 2026-06-26T05:09:15.152114Z

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Observation 1d08a4ad-d928-42e1-95f8-b5c81bb8a796 · outbound

This paper cites Numerical methods for nonlocal and fractional models.Acta Numerica, 29:1–124, 2020.

fTNN: a tensor neural network for fractional PDEs Numerical methods for nonlocal and fractional models.Acta Numerica, 29:1–124, 2020

Reference 7

Resolution: unresolved; no resolver link, observed 2026-06-26T05:09:15.152114Z

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Observation 9fa8a415-bae9-4492-b7af-81bbdac16532 · outbound

This paper cites an unresolved cited work.

fTNN: a tensor neural network for fractional PDEs Unresolved cited work

Reference 8

Resolution: unresolved; no resolver link, observed 2026-06-26T05:09:15.152114Z

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Observation bbd66299-7b2b-47df-b220-552a8a00dc5a · outbound

This paper cites Upper and lower estimates for numerical integration errors on spheres of arbitrary dimension.Journal of Complexity, 53:113–132, 2019.

fTNN: a tensor neural network for fractional PDEs Upper and lower estimates for numerical integration errors on spheres of arbitrary dimension.Journal of Complexity, 53:113–132, 2019

Reference 9

Resolution: unresolved; no resolver link, observed 2026-06-26T05:09:15.152114Z

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Observation 67d8a2e9-e605-4ed2-b771-80d8dcd50fc9 · outbound

This paper cites Fractional Laplacians on domains, a development of H¨ ormander’s theory of µ-transmission pseudodifferential operators.Advances in Mathematics, 268:478–528, 2015.

fTNN: a tensor neural network for fractional PDEs Fractional Laplacians on domains, a development of H¨ ormander’s theory of µ-transmission pseudodifferential operators.Advances in Mathematics, 268:478–528, 2015

Reference 10

Resolution: unresolved; no resolver link, observed 2026-06-26T05:09:15.152114Z

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Observation 2e8f3dec-2248-442d-9117-cb834872c00e · outbound

This paper cites an unresolved cited work.

fTNN: a tensor neural network for fractional PDEs Unresolved cited work

Reference 11

Resolution: unresolved; no resolver link, observed 2026-06-26T05:09:15.152114Z

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Observation 1c2a691f-74f4-4bed-8f2b-18aa288c65bf · outbound

This paper cites A deep learning method for computing eigenvalues of the fractional Schr¨ odinger operator.Journal of Systems Science and Complexity, 37(2):391– 412, 2024.

fTNN: a tensor neural network for fractional PDEs A deep learning method for computing eigenvalues of the fractional Schr¨ odinger operator.Journal of Systems Science and Complexity, 37(2):391– 412, 2024

Reference 12

Resolution: unresolved; no resolver link, observed 2026-06-26T05:09:15.152114Z

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Observation 0e89970b-bae6-4745-8109-2db96c853249 · outbound

This paper cites an unresolved cited work.

fTNN: a tensor neural network for fractional PDEs Unresolved cited work

Reference 13

Resolution: unresolved; no resolver link, observed 2026-06-26T05:09:15.152114Z

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Observation 3348f345-2c35-402d-8297-31c066044e14 · outbound

This paper cites A grid-overlay finite difference method for the frac- tional Laplacian on arbitrary bounded domains.SIAM Journal on Scientific Computing, 46(2):A744–A769, 2024.

fTNN: a tensor neural network for fractional PDEs A grid-overlay finite difference method for the frac- tional Laplacian on arbitrary bounded domains.SIAM Journal on Scientific Computing, 46(2):A744–A769, 2024

Reference 14

Resolution: unresolved; no resolver link, observed 2026-06-26T05:09:15.152114Z

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Observation 2ad65843-61d1-44f4-926f-4e15e5a134ad · outbound

This paper cites Artificial neural networks for solving ordinary and partial differential equations.IEEE Transactions on Neural Networks, 9(5):987–1000, 1998.

fTNN: a tensor neural network for fractional PDEs Artificial neural networks for solving ordinary and partial differential equations.IEEE Transactions on Neural Networks, 9(5):987–1000, 1998

Reference 15

Resolution: unresolved; no resolver link, observed 2026-06-26T05:09:15.152114Z

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Observation 52abc9fc-ffaa-4063-acc7-1e1ca1b62e44 · outbound

This paper cites Tensor Neural Network Interpolation and Its Applications.

fTNN: a tensor neural network for fractional PDEs Tensor Neural Network Interpolation and Its Applications

Reference 16

Resolution: verified exact; arxiv_id, observed 2026-07-04T13:29:51.899598Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 60fca27f-c476-4a43-89a2-4378cadb66f5 · outbound

This paper cites Solving Schr\"{o}dinger Equation Using Tensor Neural Network.

fTNN: a tensor neural network for fractional PDEs Solving Schr\"{o}dinger Equation Using Tensor Neural Network

Reference 17

Resolution: verified exact; arxiv_id, observed 2026-07-04T13:29:51.902268Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 563f8e52-c876-4887-a260-da0fe3b20ef8 · outbound

This paper cites Solving time-fractional partial integro-differential equations using tensor neural network.SIAM Journal on Scientific Computing, 48(1):C164–C189, 2026.

fTNN: a tensor neural network for fractional PDEs Solving time-fractional partial integro-differential equations using tensor neural network.SIAM Journal on Scientific Computing, 48(1):C164–C189, 2026

Reference 18

Resolution: unresolved; no resolver link, observed 2026-06-26T05:09:15.152114Z

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Observation 28edd391-ea83-4a1d-965a-df25b061b336 · outbound

This paper cites What is the fractional Laplacian? A comparative review with new results.Journal of Computational Physics, 404:109009, 2020.

fTNN: a tensor neural network for fractional PDEs What is the fractional Laplacian? A comparative review with new results.Journal of Computational Physics, 404:109009, 2020

Reference 19

Resolution: unresolved; no resolver link, observed 2026-06-26T05:09:15.152114Z

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Observation 4d803081-afbf-449d-ba47-8199ccce7af4 · outbound

This paper cites DeepXDE: a deep learning library for solving differential equations.SIAM Review, 63(1):208–228, 2021.

fTNN: a tensor neural network for fractional PDEs DeepXDE: a deep learning library for solving differential equations.SIAM Review, 63(1):208–228, 2021

Reference 20

Resolution: unresolved; no resolver link, observed 2026-06-26T05:09:15.152114Z

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Observation 7c2a928c-2770-4c86-b6ce-8da56e1045d3 · outbound

This paper cites Bi-Orthogonal fPINN: a physics-informed neural network method for solving time-dependent stochastic fractional PDEs.Communications in Computational Physics, 34(4):1133–1176, 2023.

fTNN: a tensor neural network for fractional PDEs Bi-Orthogonal fPINN: a physics-informed neural network method for solving time-dependent stochastic fractional PDEs.Communications in Computational Physics, 34(4):1133–1176, 2023

Reference 21

Resolution: unresolved; no resolver link, observed 2026-06-26T05:09:15.152114Z

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Observation b639dd10-cb9b-45c4-9d4e-31f791256c08 · outbound

This paper cites Quadrature-Enhanced Monte Carlo fPINN Method for High-Dimensional Fractional PDEs.

fTNN: a tensor neural network for fractional PDEs Quadrature-Enhanced Monte Carlo fPINN Method for High-Dimensional Fractional PDEs

Reference 22

Resolution: verified exact; local_arxiv, observed 2026-07-04T13:29:51.897119Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 2574b59c-be0c-4e57-8105-44fadc0f2089 · outbound

This paper cites Finite difference meth- ods for two-dimensional fractional dispersion equation.Journal of Computational Physics, 211(1):249–261, 2006.

fTNN: a tensor neural network for fractional PDEs Finite difference meth- ods for two-dimensional fractional dispersion equation.Journal of Computational Physics, 211(1):249–261, 2006

Reference 23

Resolution: unresolved; no resolver link, observed 2026-06-26T05:09:15.152114Z

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Observation bb0aacf6-892c-4e50-8ad1-836d999a9539 · outbound

This paper cites Space-fractional advection–dispersion equations by the Kansa method.Journal of Computational Physics, 293:280–296, 2015.

fTNN: a tensor neural network for fractional PDEs Space-fractional advection–dispersion equations by the Kansa method.Journal of Computational Physics, 293:280–296, 2015

Reference 24

Resolution: unresolved; no resolver link, observed 2026-06-26T05:09:15.152114Z

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Observation be37027f-3b33-42a7-a795-413b76ffb535 · outbound

This paper cites fPINNs: fractional physics-informed neural networks.SIAM Journal on Scientific Computing, 41(4):A2603–A2626, 2019.

fTNN: a tensor neural network for fractional PDEs fPINNs: fractional physics-informed neural networks.SIAM Journal on Scientific Computing, 41(4):A2603–A2626, 2019

Reference 25

Resolution: unresolved; no resolver link, observed 2026-06-26T05:09:15.152114Z

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Observation 37b52b7f-3cef-4c02-b815-f44ac1719f74 · outbound

This paper cites an unresolved cited work.

fTNN: a tensor neural network for fractional PDEs Unresolved cited work

Reference 26

Resolution: unresolved; no resolver link, observed 2026-06-26T05:09:15.152114Z

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Observation 0108d2f1-adc5-4eb6-b227-83dd53b1f9ed · outbound

This paper cites Boundary regularity for fully nonlinear integro- differential equations.Duke Mathematical Journal, 165(11):2079–2154, 2016.

fTNN: a tensor neural network for fractional PDEs Boundary regularity for fully nonlinear integro- differential equations.Duke Mathematical Journal, 165(11):2079–2154, 2016

Reference 27

Resolution: unresolved; no resolver link, observed 2026-06-26T05:09:15.152114Z

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Observation ee75c160-afce-42ba-a109-6c6ee9f5d9df · outbound

This paper cites Springer Science & Business Media, 2011.

fTNN: a tensor neural network for fractional PDEs Springer Science & Business Media, 2011

Reference 28

Resolution: unresolved; no resolver link, observed 2026-06-26T05:09:15.152114Z

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Observation 0b270980-c645-48e7-aada-7d86c90698f9 · outbound

This paper cites Efficient Monte Carlo method for inte- gral fractional Laplacian in multiple dimensions.SIAM Journal on Numerical Analysis, 61(5):2035–2061, 2023.

fTNN: a tensor neural network for fractional PDEs Efficient Monte Carlo method for inte- gral fractional Laplacian in multiple dimensions.SIAM Journal on Numerical Analysis, 61(5):2035–2061, 2023

Reference 29

Resolution: unresolved; no resolver link, observed 2026-06-26T05:09:15.152114Z

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Observation e935eeaa-f4fe-47ae-bb99-6605b6b3d25f · outbound

This paper cites Fast implementation of FEM for integral fractional Laplacian on rectangular meshes.Communications in Compu- tational Physics, 36(3):673–710, 2024.

fTNN: a tensor neural network for fractional PDEs Fast implementation of FEM for integral fractional Laplacian on rectangular meshes.Communications in Compu- tational Physics, 36(3):673–710, 2024

Reference 30

Resolution: unresolved; no resolver link, observed 2026-06-26T05:09:15.152114Z

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Observation f0961e4a-70de-42fb-a512-387d7251053a · outbound

This paper cites A second-order accurate numerical method for the two-dimensional fractional diffusion equation.Journal of Computational Physics, 220(2):813–823, 2007.

fTNN: a tensor neural network for fractional PDEs A second-order accurate numerical method for the two-dimensional fractional diffusion equation.Journal of Computational Physics, 220(2):813–823, 2007

Reference 31

Resolution: unresolved; no resolver link, observed 2026-06-26T05:09:15.152114Z

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Observation 59adbb40-9b7e-440f-a06e-90ad477420e3 · outbound

This paper cites GMC-PINNs: a new general Monte Carlo PINNs method for solving fractional partial differential equations on irregular domains.

fTNN: a tensor neural network for fractional PDEs GMC-PINNs: a new general Monte Carlo PINNs method for solving fractional partial differential equations on irregular domains

Reference 32

Resolution: unresolved; no resolver link, observed 2026-06-26T05:09:15.152114Z

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Observation 0dc435cc-11c9-4595-8852-d6e7640c6be4 · outbound

This paper cites Tensor neural network and its numerical inte- gration.Journal of Computational Mathematics, 42(6):1714–1742, 2024.

fTNN: a tensor neural network for fractional PDEs Tensor neural network and its numerical inte- gration.Journal of Computational Mathematics, 42(6):1714–1742, 2024

Reference 33

Resolution: unresolved; no resolver link, observed 2026-06-26T05:09:15.152114Z

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Observation 990374df-f123-40b5-80aa-5f469efff134 · outbound

This paper cites Solving high- dimensional partial differential equations using tensor neural network and a posteriori error estimators.Journal of Scientific Computing, 101(3):67, 2024.

fTNN: a tensor neural network for fractional PDEs Solving high- dimensional partial differential equations using tensor neural network and a posteriori error estimators.Journal of Scientific Computing, 101(3):67, 2024

Reference 34

Resolution: unresolved; no resolver link, observed 2026-06-26T05:09:15.152114Z

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Observation 0201e69c-50ef-49e6-9f39-ef8bc58041e4 · outbound

This paper cites Computing multi-eigenpairs of high-dimensional eigenvalue problems using tensor neural networks.Journal of Computational Physics, 506:112928, 2024.

fTNN: a tensor neural network for fractional PDEs Computing multi-eigenpairs of high-dimensional eigenvalue problems using tensor neural networks.Journal of Computational Physics, 506:112928, 2024

Reference 35

Resolution: unresolved; no resolver link, observed 2026-06-26T05:09:15.152114Z

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Observation 9f4060c6-7ace-4b9b-971f-6d9ffd160c6d · outbound

This paper cites Spectral-fPINNs: spectral method based fractional physics-informed neural networks for solving fractional partial differential equations.Nonlinear Dynamics, 113(11):12565, 2025.

fTNN: a tensor neural network for fractional PDEs Spectral-fPINNs: spectral method based fractional physics-informed neural networks for solving fractional partial differential equations.Nonlinear Dynamics, 113(11):12565, 2025

Reference 36

Resolution: unresolved; no resolver link, observed 2026-06-26T05:09:15.152114Z

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