Paper Citation Record · LEDGER

Adaptive Neural Network Subspace Method for Solving Partial Differential Equations with High Accuracy

As of 14 August 2026, this Paper Citation Record lists 38 of 38 outbound references and 3 inbound Pith citation observations for arXiv:2412.02586.

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

pith.paper-citation-record.v1
2412.02586 v1

Coverage vector

measured 38 of 38 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-11T23:24:51.316229Z

measured 41 of 41 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 3 of 3 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-07T13:52:37.368569Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-23T06:02:38.169353Z

Reference resolution

38 of 38 outbound references displayed

verified exact3
verified fuzzy8
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation d9d98e49-f627-40c9-9985-c4ea0807a675 · outbound

This paper cites an unresolved cited work.

Adaptive Neural Network Subspace Method for Solving Partial Differential Equations with High Accuracy Unresolved cited work

Reference 1

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Observation ab67b152-9735-450c-9c40-d6f5779472b8 · outbound

This paper cites an unresolved cited work.

Adaptive Neural Network Subspace Method for Solving Partial Differential Equations with High Accuracy Unresolved cited work

Reference 2

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Observation 5dc477a6-3724-4dac-82ac-69977db05e57 · outbound

This paper cites Chen and Y.

Adaptive Neural Network Subspace Method for Solving Partial Differential Equations with High Accuracy Chen and Y

Reference 3

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Observation 671a3bc2-9bc7-4943-8aef-d99ddb4605b0 · outbound

This paper cites Chen and Y.

Adaptive Neural Network Subspace Method for Solving Partial Differential Equations with High Accuracy Chen and Y

Reference 4

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Observation 580d730b-6123-448d-a9c6-a1d4001c94cf · outbound

This paper cites Chen and J.

Adaptive Neural Network Subspace Method for Solving Partial Differential Equations with High Accuracy Chen and J

Reference 5

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This paper cites an unresolved cited work.

Adaptive Neural Network Subspace Method for Solving Partial Differential Equations with High Accuracy Unresolved cited work

Reference 7

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This paper cites an unresolved cited work.

Adaptive Neural Network Subspace Method for Solving Partial Differential Equations with High Accuracy Unresolved cited work

Reference 8

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This paper cites an unresolved cited work.

Adaptive Neural Network Subspace Method for Solving Partial Differential Equations with High Accuracy Unresolved cited work

Reference 9

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Adaptive Neural Network Subspace Method for Solving Partial Differential Equations with High Accuracy Unresolved cited work

Reference 10

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This paper cites an unresolved cited work.

Adaptive Neural Network Subspace Method for Solving Partial Differential Equations with High Accuracy Unresolved cited work

Reference 11

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Observation c819458f-def3-4a74-9bc8-cbe021dee873 · outbound

This paper cites Huang and R.

Adaptive Neural Network Subspace Method for Solving Partial Differential Equations with High Accuracy Huang and R

Reference 12

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Observation bd37cd8a-cff5-4a0e-9694-41ccb6aca829 · outbound

This paper cites Tackling the Curse of Dimensionality with Physics-Informed Neural Networks.

Adaptive Neural Network Subspace Method for Solving Partial Differential Equations with High Accuracy Tackling the Curse of Dimensionality with Physics-Informed Neural Networks

Reference 13

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Adaptive Neural Network Subspace Method for Solving Partial Differential Equations with High Accuracy Unresolved cited work

Reference 14

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Observation adf908c8-b579-4ecd-96c0-a0fa22a4e611 · outbound

This paper cites Huang, Q.

Adaptive Neural Network Subspace Method for Solving Partial Differential Equations with High Accuracy Huang, Q

Reference 15

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This paper cites an unresolved cited work.

Adaptive Neural Network Subspace Method for Solving Partial Differential Equations with High Accuracy Unresolved cited work

Reference 16

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Observation fb624591-2c92-4c72-96c2-8b7296ead62c · outbound

This paper cites Adam: A Method for Stochastic Optimization.

Adaptive Neural Network Subspace Method for Solving Partial Differential Equations with High Accuracy Adam: A Method for Stochastic Optimization

Reference 17

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This paper cites an unresolved cited work.

Adaptive Neural Network Subspace Method for Solving Partial Differential Equations with High Accuracy Unresolved cited work

Reference 18

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Observation 13534c5b-746e-4777-bafd-f5ccd4f34e2d · outbound

This paper cites an unresolved cited work.

Adaptive Neural Network Subspace Method for Solving Partial Differential Equations with High Accuracy Unresolved cited work

Reference 19

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Observation b27e9cef-a1f8-4b4b-b548-369d89d68701 · outbound

This paper cites Local Randomized Neural Networks Methods for Interface Problems.

Adaptive Neural Network Subspace Method for Solving Partial Differential Equations with High Accuracy Local Randomized Neural Networks Methods for Interface Problems

Reference 20

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Observation 252db9b4-68eb-43e5-9e4b-199c70011d01 · outbound

This paper cites Subspace method based on neural networks for solving the partial differential equation in weak form.

Adaptive Neural Network Subspace Method for Solving Partial Differential Equations with High Accuracy Subspace method based on neural networks for solving the partial differential equation in weak form

Reference 21

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This paper cites an unresolved cited work.

Adaptive Neural Network Subspace Method for Solving Partial Differential Equations with High Accuracy Unresolved cited work

Reference 22

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Observation 9c760f72-0ffd-4816-8664-72706dad14a2 · outbound

This paper cites Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations.

Adaptive Neural Network Subspace Method for Solving Partial Differential Equations with High Accuracy Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-11T23:24:51.247511Z

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Observation f44e296b-afe1-40c1-aedd-3926f2f2aad4 · outbound

This paper cites Shang, F.

Adaptive Neural Network Subspace Method for Solving Partial Differential Equations with High Accuracy Shang, F

Reference 24

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Observation 4ba47e2f-cd8c-4540-ab4b-801c7ec5b720 · outbound

This paper cites an unresolved cited work.

Adaptive Neural Network Subspace Method for Solving Partial Differential Equations with High Accuracy Unresolved cited work

Reference 25

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Observation 9046490e-a96c-43b5-90f0-79f277cc683a · outbound

This paper cites Sirignano and K.

Adaptive Neural Network Subspace Method for Solving Partial Differential Equations with High Accuracy Sirignano and K

Reference 26

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Observation 05439be4-4f56-4fa8-95aa-30d3e7fa905b · outbound

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Adaptive Neural Network Subspace Method for Solving Partial Differential Equations with High Accuracy Unresolved cited work

Reference 27

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Observation 1af2014b-f99b-4491-9550-161da01d7ff4 · outbound

This paper cites Vejchodsk` y, Complementarity based a posteriori error estimates and their properties, Math.

Adaptive Neural Network Subspace Method for Solving Partial Differential Equations with High Accuracy Vejchodsk` y, Complementarity based a posteriori error estimates and their properties, Math

Reference 28

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Observation 6dcd0019-01a8-46fc-b49c-d78dfeb19bf8 · outbound

This paper cites Tensor neural networks for high-dimensional Fokker-Planck equations.

Adaptive Neural Network Subspace Method for Solving Partial Differential Equations with High Accuracy Tensor neural networks for high-dimensional Fokker-Planck equations

Reference 29

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Observation ac93cfa4-17a0-4f44-847d-a65ca8ae1b2b · outbound

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Adaptive Neural Network Subspace Method for Solving Partial Differential Equations with High Accuracy Tensor Neural Network and Its Numerical Integration

Reference 30

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Adaptive Neural Network Subspace Method for Solving Partial Differential Equations with High Accuracy Solving Schr\"{o}dinger Equation Using Tensor Neural Network

Reference 31

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This paper cites Solving High Dimensional Partial Differential Equations Using Tensor Neural Network and A Posteriori Error Estimators.

Adaptive Neural Network Subspace Method for Solving Partial Differential Equations with High Accuracy Solving High Dimensional Partial Differential Equations Using Tensor Neural Network and A Posteriori Error Estimators

Reference 32

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This paper cites Computing Multi-Eigenpairs of High-Dimensional Eigenvalue Problems Using Tensor Neural Networks.

Adaptive Neural Network Subspace Method for Solving Partial Differential Equations with High Accuracy Computing Multi-Eigenpairs of High-Dimensional Eigenvalue Problems Using Tensor Neural Networks

Reference 33

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Adaptive Neural Network Subspace Method for Solving Partial Differential Equations with High Accuracy Wu and B

Reference 34

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Adaptive Neural Network Subspace Method for Solving Partial Differential Equations with High Accuracy Unresolved cited work

Reference 35

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Observation 21d32535-a94f-429f-ab78-08393492c733 · outbound

This paper cites Subspace method based on neural networks for solving the partial differential equation.

Adaptive Neural Network Subspace Method for Solving Partial Differential Equations with High Accuracy Subspace method based on neural networks for solving the partial differential equation

Reference 36

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Adaptive Neural Network Subspace Method for Solving Partial Differential Equations with High Accuracy Unresolved cited work

Reference 37

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Adaptive Neural Network Subspace Method for Solving Partial Differential Equations with High Accuracy Unresolved cited work

Reference 38

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This paper cites Improved randomized neural network methods with boundary processing for solving elliptic equations.

Adaptive Neural Network Subspace Method for Solving Partial Differential Equations with High Accuracy Improved randomized neural network methods with boundary processing for solving elliptic equations

Reference 39

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Pith citing papers

Observation 2371d7c4-c0a3-4370-a849-1cce78dcd11c · inbound

Lower Bound on the Representation Complexity of Antisymmetric Tensor Product Functions cites this paper.

Lower Bound on the Representation Complexity of Antisymmetric Tensor Product Functions Adaptive Neural Network Subspace Method for Solving Partial Differential Equations with High Accuracy

Reference 38

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Observation 264b420e-962c-4032-8d28-05ca2a65d87e · inbound

Domain Decomposition Subspace Neural Network Method for Solving Linear and Nonlinear Partial Differential Equations cites this paper.

Domain Decomposition Subspace Neural Network Method for Solving Linear and Nonlinear Partial Differential Equations Adaptive Neural Network Subspace Method for Solving Partial Differential Equations with High Accuracy

Reference 21

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Observation 5d2de342-b54f-406e-97c6-7a0cedee451d · inbound

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

Adaptive feature capture method for solving partial differential equations with near singular solutions Adaptive Neural Network Subspace Method for Solving Partial Differential Equations with High Accuracy

Reference 19

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