Paper Citation Record · LEDGER

The Finite Element Neural Network Method: One Dimensional Study

As of 20 August 2026, this Paper Citation Record lists 34 of 34 outbound references and 0 inbound Pith citation observations for arXiv:2501.12508.

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

pith.paper-citation-record.v1
2501.12508 v1

Coverage vector

measured 34 of 34 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-10T17:15:58.424882Z

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 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

34 of 34 outbound references displayed

verified exact2
verified fuzzy22
unresolved10
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 43bfca17-98cb-403b-9748-45616c187d2d · outbound

This paper cites an unresolved cited work.

The Finite Element Neural Network Method: One Dimensional Study Unresolved cited work

Reference 1

Resolution: unresolved; raw_fallback, observed 2026-08-10T17:15:58.956997Z

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 d6703ea3-6906-478e-9aef-64429cd275ec · outbound

This paper cites Reddy, An Introduction to the Finite Element Method.

The Finite Element Neural Network Method: One Dimensional Study Reddy, An Introduction to the Finite Element Method

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T17:15:58.941299Z

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 e3cd7793-da24-41c5-9a66-dc103e157893 · outbound

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

The Finite Element Neural Network Method: One Dimensional Study Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations,

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-10T17:15:58.275734Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 451001f0-6dab-4f5b-8c34-73c2f57d85ab · outbound

This paper cites From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learning.

The Finite Element Neural Network Method: One Dimensional Study From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learning

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-10T17:15:58.280502Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 55ab9ce4-0812-4de0-9138-877f55eae2f1 · outbound

This paper cites Neural-network-based approximations for solv- ing partial differential equations,.

The Finite Element Neural Network Method: One Dimensional Study Neural-network-based approximations for solv- ing partial differential equations,

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T17:15:58.917574Z

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 9667a201-dd86-41cc-953a-7965cee9d15d · outbound

This paper cites Nonlinear approximation and (deep) relu networks,.

The Finite Element Neural Network Method: One Dimensional Study Nonlinear approximation and (deep) relu networks,

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T17:15:58.902638Z

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 5ecaea39-43ba-4886-b72f-7b41ddd4037c · outbound

This paper cites Function approximation by deep networks.

The Finite Element Neural Network Method: One Dimensional Study Function approximation by deep networks

Reference 7

Resolution: verified exact; local_arxiv, observed 2026-08-10T17:15:58.578037Z

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 fb3ff727-4622-404d-b4c9-99b4b800115b · outbound

This paper cites Conservative physics-informed neural networks on discrete domains for conservation laws: Applications to forward and inverse problems,.

The Finite Element Neural Network Method: One Dimensional Study Conservative physics-informed neural networks on discrete domains for conservation laws: Applications to forward and inverse problems,

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T17:15:58.888480Z

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 e23ada9f-5cac-4163-bebb-7aa1e48adf92 · outbound

This paper cites hp-vpinns: Variational physics-informed neural networks with domain decomposition,.

The Finite Element Neural Network Method: One Dimensional Study hp-vpinns: Variational physics-informed neural networks with domain decomposition,

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T17:15:58.874219Z

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 8b811bca-9934-450a-a318-13c0081735c5 · outbound

This paper cites Variational Physics-Informed Neural Networks For Solving Partial Differential Equations.

The Finite Element Neural Network Method: One Dimensional Study Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-10T17:15:58.312040Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f961ec4b-7e50-4051-ab5d-1d76390fa8d1 · outbound

This paper cites Hidden physics models: Machine learning of nonlinear partial differential equations,.

The Finite Element Neural Network Method: One Dimensional Study Hidden physics models: Machine learning of nonlinear partial differential equations,

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T17:15:58.860389Z

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 bfdae471-1e08-49c4-9656-992429cafd4c · outbound

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

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T17:15:58.845319Z

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 c296385e-8fc9-489a-b6b9-395dc020993f · outbound

This paper cites Self-adaptive physics-informed neural networks,.

The Finite Element Neural Network Method: One Dimensional Study Self-adaptive physics-informed neural networks,

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T17:15:58.829476Z

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 90bb76d4-8115-4dbc-83d6-f81e035284a1 · outbound

This paper cites Understanding and mitigating gradient pathologies in physics-informed neural networks.

The Finite Element Neural Network Method: One Dimensional Study Understanding and mitigating gradient pathologies in physics-informed neural networks

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-10T17:15:58.331151Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation acd7d1e4-3744-4019-9501-1f1070739f68 · outbound

This paper cites cv-pinn: Efficient learning of variational physics-informed neural network with domain decomposition,.

The Finite Element Neural Network Method: One Dimensional Study cv-pinn: Efficient learning of variational physics-informed neural network with domain decomposition,

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T17:15:58.815250Z

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 5d12695d-7f74-4e54-b411-e7cb9608fe98 · outbound

This paper cites FastVPINNs: Tensor-Driven Acceleration of VPINNs for Complex Geometries.

The Finite Element Neural Network Method: One Dimensional Study FastVPINNs: Tensor-Driven Acceleration of VPINNs for Complex Geometries

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-10T17:15:58.340488Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9b36ad77-096a-4b4c-bda3-ef971ca06ab1 · outbound

This paper cites Nonlinear approximation,.

The Finite Element Neural Network Method: One Dimensional Study Nonlinear approximation,

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T17:15:58.801224Z

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 6ae77f86-8254-4c03-88b5-0ee3e328db24 · outbound

This paper cites Nonlinear approximation and its applications,.

The Finite Element Neural Network Method: One Dimensional Study Nonlinear approximation and its applications,

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T17:15:58.787213Z

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 4040a8d6-89fe-441f-8d81-4c46c8094f5a · outbound

This paper cites Approximation using scattered shifts of a multivariate function,.

The Finite Element Neural Network Method: One Dimensional Study Approximation using scattered shifts of a multivariate function,

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T17:15:58.773627Z

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 aa8a757d-48fa-4806-8032-9db79e98ae5b · outbound

This paper cites Greedy Deep Dictionary Learning.

The Finite Element Neural Network Method: One Dimensional Study Greedy Deep Dictionary Learning

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-10T17:15:58.359114Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 92c49ab8-570d-467c-9b1c-16283055ff42 · outbound

This paper cites Self-Adaptive Physics-Informed Neural Networks using a Soft Attention Mechanism.

The Finite Element Neural Network Method: One Dimensional Study Self-Adaptive Physics-Informed Neural Networks using a Soft Attention Mechanism

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-10T17:15:58.364917Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5f69c396-27af-4aba-874f-d5e9e82a2951 · outbound

This paper cites Training a 3-node neural network is np-complete,.

The Finite Element Neural Network Method: One Dimensional Study Training a 3-node neural network is np-complete,

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T17:15:58.759526Z

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 f8c28736-29ee-4106-9aec-7ee86e2ce781 · outbound

This paper cites Numerical analysis,.

The Finite Element Neural Network Method: One Dimensional Study Numerical analysis,

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T17:15:58.745356Z

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 b12e8169-343f-477e-941b-21cbeab6546c · outbound

This paper cites A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks,.

The Finite Element Neural Network Method: One Dimensional Study A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks,

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T17:15:58.731293Z

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 c173da10-5158-43e8-8081-5beb67bd8e0f · outbound

This paper cites Physics-informed neural networks with residual/gradient-based adaptive sampling methods for solving PDEs with sharp solutions.

The Finite Element Neural Network Method: One Dimensional Study Physics-informed neural networks with residual/gradient-based adaptive sampling methods for solving PDEs with sharp solutions

Reference 25

Resolution: verified exact; local_arxiv, observed 2026-08-10T17:15:58.484095Z

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 7458db54-1342-424e-9807-bff7062df447 · outbound

This paper cites Extended physics-informed neural networks (xpinns): A generalized space-time domain decomposition based deep learning framework for nonlinear partial differential equations,.

The Finite Element Neural Network Method: One Dimensional Study Extended physics-informed neural networks (xpinns): A generalized space-time domain decomposition based deep learning framework for nonlinear partial differential equations,

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T17:15:58.717272Z

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 8d6c6c5c-0a06-43e6-ab85-97d9a4739372 · outbound

This paper cites Varnet: Variational neural networks for the solution of partial differential equations,.

The Finite Element Neural Network Method: One Dimensional Study Varnet: Variational neural networks for the solution of partial differential equations,

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T17:15:58.701778Z

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 4e521235-210f-4c4c-a529-e83026de779f · outbound

This paper cites Variational physics informed neural networks: the role of quadratures and test functions,.

The Finite Element Neural Network Method: One Dimensional Study Variational physics informed neural networks: the role of quadratures and test functions,

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T17:15:58.686912Z

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 3e5bb1ee-99f2-4143-9a68-ce7335a30617 · outbound

This paper cites Automatic differen- tiation in machine learning: a survey,.

The Finite Element Neural Network Method: One Dimensional Study Automatic differen- tiation in machine learning: a survey,

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T17:15:58.670543Z

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 ba1b2bdd-531a-47fa-9b85-f80a7d7e79b1 · outbound

This paper cites Adam: A Method for Stochastic Optimization.

The Finite Element Neural Network Method: One Dimensional Study Adam: A Method for Stochastic Optimization

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-10T17:15:58.406192Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c719684c-8dba-4bfa-9ca9-b1b0212b7f7f · outbound

This paper cites On the limited memory bfgs method for large scale optimiza- tion,.

The Finite Element Neural Network Method: One Dimensional Study On the limited memory bfgs method for large scale optimiza- tion,

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T17:15:58.654758Z

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 3e4c1f40-6688-41be-a585-943a363bc4ce · outbound

This paper cites A dual-dimer method for training physics-constrained neural net- works with minimax architecture,.

The Finite Element Neural Network Method: One Dimensional Study A dual-dimer method for training physics-constrained neural net- works with minimax architecture,

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T17:15:58.639503Z

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 3790b9a5-2109-4335-b4cf-72994413d5df · outbound

This paper cites Fluid flow and heat transfer of liquid-liquid two phase flow in microchannels: A review,.

The Finite Element Neural Network Method: One Dimensional Study Fluid flow and heat transfer of liquid-liquid two phase flow in microchannels: A review,

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T17:15:58.624508Z

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 bab20a36-a89e-4080-aa28-fe875a7103f3 · outbound

This paper cites an unresolved cited work.

The Finite Element Neural Network Method: One Dimensional Study Unresolved cited work

Reference 34

Resolution: unresolved; raw_fallback, observed 2026-08-10T17:15:58.609546Z

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

No inbound Pith citation observations are available.