Paper Citation Record · LEDGER

Neural Network Element Method for Partial Differential Equations

As of 21 August 2026, this Paper Citation Record lists 33 of 33 outbound references and 1 inbound Pith citation observation for arXiv:2504.16862.

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

pith.paper-citation-record.v1
2504.16862 v1

Coverage vector

measured 33 of 33 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-16T11:00:39.806178Z

measured 34 of 34 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-20T06:33:59.587034+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-05-12T03:51:30.313597Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-12T06:51:30.431600Z

Reference resolution

33 of 33 outbound references displayed

verified exact0
verified fuzzy5
unresolved28
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation bd2d5365-c223-4e07-96e0-0e2c8abc34eb · outbound

This paper cites Brenner and R.

Neural Network Element Method for Partial Differential Equations Brenner and R

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:00:40.605796Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 42ff9b4f-0353-402b-9b2a-911b141f8188 · outbound

This paper cites an unresolved cited work.

Neural Network Element Method for Partial Differential Equations Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-08-16T11:00:40.587144Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 17965f7b-db07-446a-b653-d1a91e2adb41 · outbound

This paper cites an unresolved cited work.

Neural Network Element Method for Partial Differential Equations Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-08-16T11:00:40.565734Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 5e7817bd-67ae-4fa8-9905-8fd56dab987e · outbound

This paper cites an unresolved cited work.

Neural Network Element Method for Partial Differential Equations Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-08-16T11:00:40.541036Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation f197782e-3653-4d74-bcb6-1fed36004a54 · outbound

This paper cites an unresolved cited work.

Neural Network Element Method for Partial Differential Equations Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-08-16T11:00:40.520013Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation e3fb1446-67ab-44a5-9a18-a5f698540f46 · outbound

This paper cites an unresolved cited work.

Neural Network Element Method for Partial Differential Equations Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-08-16T11:00:40.497879Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation f9834e8a-f40b-4d11-ad8c-3671a93b0add · outbound

This paper cites an unresolved cited work.

Neural Network Element Method for Partial Differential Equations Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-16T11:00:40.475238Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 9246a919-12ab-4b12-bd84-3aff0b15b0d4 · outbound

This paper cites Grisvard, Elliptic Problems in Nonsmooth Domains, Society for Industrial and Applied Mathematics, 2011.

Neural Network Element Method for Partial Differential Equations Grisvard, Elliptic Problems in Nonsmooth Domains, Society for Industrial and Applied Mathematics, 2011

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:00:40.454968Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 671e0df3-98b4-4f98-8ced-2b949731c598 · outbound

This paper cites an unresolved cited work.

Neural Network Element Method for Partial Differential Equations Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-16T11:00:40.434226Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation b491e506-354e-4373-8123-9c9c91eb2479 · outbound

This paper cites an unresolved cited work.

Neural Network Element Method for Partial Differential Equations Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-16T11:00:40.413587Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 759b04df-b84e-4b9b-8b90-d950ccc23126 · outbound

This paper cites Huang, Q.

Neural Network Element Method for Partial Differential Equations Huang, Q

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:00:40.392401Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 53a465c6-e235-4257-abde-fe0fed5f8127 · outbound

This paper cites Huang and R.

Neural Network Element Method for Partial Differential Equations Huang and R

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-16T11:00:39.666316Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 30947077-675b-4070-bcd9-0f04a21dfc48 · outbound

This paper cites Adam: A Method for Stochastic Optimization.

Neural Network Element Method for Partial Differential Equations Adam: A Method for Stochastic Optimization

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-16T11:00:39.673577Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ac9282e7-96ed-48e4-99aa-94782e46fcd7 · outbound

This paper cites an unresolved cited work.

Neural Network Element Method for Partial Differential Equations Unresolved cited work

Reference 14

Resolution: unresolved; raw_fallback, observed 2026-08-16T11:00:40.353606Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation c52c95e1-1c0f-4972-ab6a-f73966a930c4 · outbound

This paper cites an unresolved cited work.

Neural Network Element Method for Partial Differential Equations Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-08-16T11:00:40.331136Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 3d90e636-e1fa-44c9-80cf-94ac616b9155 · outbound

This paper cites an unresolved cited work.

Neural Network Element Method for Partial Differential Equations Unresolved cited work

Reference 16

Resolution: unresolved; raw_fallback, observed 2026-08-16T11:00:40.312024Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 9373e673-591d-4db2-8bac-b1e4c58a6ff4 · outbound

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

Neural Network Element Method for Partial Differential Equations Local Randomized Neural Networks Methods for Interface Problems

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-16T11:00:39.698551Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 735275a1-5742-4f58-a823-a17f5672cd78 · outbound

This paper cites Adaptive Neural Network Subspace Method for Solving Partial Differential Equations with High Accuracy.

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

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-16T11:00:39.704324Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3d47219e-92a5-4104-9e69-d1135756fa1e · outbound

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

Neural Network Element Method for Partial Differential Equations Subspace method based on neural networks for solving the partial differential equation in weak form

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-16T11:00:39.710577Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 53e374ec-742b-41aa-a35a-1e0727aeae1c · outbound

This paper cites an unresolved cited work.

Neural Network Element Method for Partial Differential Equations Unresolved cited work

Reference 20

Resolution: unresolved; raw_fallback, observed 2026-08-16T11:00:40.293516Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation ed7e64e9-7b99-45e1-b0f9-1b4a5e7a01bd · outbound

This paper cites an unresolved cited work.

Neural Network Element Method for Partial Differential Equations Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-08-16T11:00:40.272243Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 30a107f2-100f-4cbf-93fc-ddffbe44b4cd · outbound

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

Neural Network Element Method for Partial Differential Equations Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-16T11:00:39.728514Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5676d094-c1dc-4e23-940f-57a7a3fba80f · outbound

This paper cites Shang, F.

Neural Network Element Method for Partial Differential Equations Shang, F

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:00:40.248080Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation f598d1b5-e8e3-443c-be67-53a7562b6336 · outbound

This paper cites Sirignano and K.

Neural Network Element Method for Partial Differential Equations Sirignano and K

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:00:40.227513Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 3e40b5f6-3977-4f31-ac85-17be3446fbdc · outbound

This paper cites an unresolved cited work.

Neural Network Element Method for Partial Differential Equations Unresolved cited work

Reference 25

Resolution: unresolved; raw_fallback, observed 2026-08-16T11:00:40.208657Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation a2200963-878a-4233-80e0-f800268cfd70 · outbound

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

Neural Network Element Method for Partial Differential Equations Tensor neural networks for high-dimensional Fokker-Planck equations

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-16T11:00:39.759098Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 710d0a99-956b-4762-b4e9-d3aadca869f7 · outbound

This paper cites an unresolved cited work.

Neural Network Element Method for Partial Differential Equations Unresolved cited work

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-16T11:00:39.765143Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d4f2ebd2-d4b0-4ec8-9dcd-cc0a702debf3 · outbound

This paper cites Tensor Neural Network and Its Numerical Integration.

Neural Network Element Method for Partial Differential Equations Tensor Neural Network and Its Numerical Integration

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-16T11:00:39.770855Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 59404edc-16d5-4ebd-a673-e5e489b46c48 · outbound

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

Neural Network Element Method for Partial Differential Equations Solving Schr\"{o}dinger Equation Using Tensor Neural Network

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-16T11:00:39.777419Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8c190c90-fde0-4afd-a49b-2052eb829f73 · outbound

This paper cites an unresolved cited work.

Neural Network Element Method for Partial Differential Equations Unresolved cited work

Reference 30

Resolution: unresolved; raw_fallback, observed 2026-08-16T11:00:40.189701Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation cbc6948e-2958-4389-a00c-6e5ca123eade · outbound

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

Neural Network Element Method for Partial Differential Equations Computing Multi-Eigenpairs of High-Dimensional Eigenvalue Problems Using Tensor Neural Networks

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-16T11:00:39.788409Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 86f16fa8-bcf9-47ad-843d-00fb6a470095 · outbound

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

Neural Network Element Method for Partial Differential Equations Subspace method based on neural networks for solving the partial differential equation

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-16T11:00:39.800564Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 17996990-59ee-4534-b3f4-89e5ca574692 · outbound

This paper cites an unresolved cited work.

Neural Network Element Method for Partial Differential Equations Unresolved cited work

Reference 33

Resolution: unresolved; raw_fallback, observed 2026-08-16T11:00:40.170088Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Pith citing papers

Observation 23d692d8-5129-4cf2-85ed-6c9525ba2bbe · inbound

Neural enrichment finite element method: A hybrid framework for problems with strong oscillations or interface problems cites this paper.

Neural enrichment finite element method: A hybrid framework for problems with strong oscillations or interface problems Neural Network Element Method for Partial Differential Equations

Reference 61

Resolution: verified exact; arxiv_id, observed 2026-05-12T06:51:30.437347Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.