Paper Citation Record · LEDGER

On the convergence of physics informed neural networks for linear second-order elliptic and parabolic type PDEs

As of 20 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 13 inbound Pith citation observations for arXiv:2004.01806.

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

pith.paper-citation-record.v1
2004.01806 v2

Coverage vector

measured 0 of 0 reference resolution

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Source: paper_references, paper_reference_links

measured 13 of 13 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 13 of 13 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-10T21:49:17.223401Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-04T07:59:40.360688Z

Reference resolution

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External citation measurements

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Outbound references

No outbound reference observations are available for this paper version.

Pith citing papers

Observation 1150d558-5c99-4d1c-8be4-0bae2be474ed · inbound

Physics-Informed Neural Networks for microflows: Rarefied Gas Dynamics in Cylinder Arrays cites this paper.

Physics-Informed Neural Networks for microflows: Rarefied Gas Dynamics in Cylinder Arrays On the convergence of physics informed neural networks for linear second-order elliptic and parabolic type PDEs

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-10T21:49:17.223401Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6e9c2167-9dd0-420d-a6d8-8e46db542120 · inbound

XNet-Enhanced Deep BSDE Method and Numerical Analysis cites this paper.

XNet-Enhanced Deep BSDE Method and Numerical Analysis On the convergence of physics informed neural networks for linear second-order elliptic and parabolic type PDEs

Reference 30

Resolution: verified exact; arxiv_id, observed 2026-05-23T04:22:31.121277Z

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 58503be7-cad5-44d0-8021-92b65da03543 · inbound

BridgeNet: A Hybrid, Physics-Informed Machine Learning Framework for Solving High-Dimensional Fokker-Planck Equations cites this paper.

BridgeNet: A Hybrid, Physics-Informed Machine Learning Framework for Solving High-Dimensional Fokker-Planck Equations On the convergence of physics informed neural networks for linear second-order elliptic and parabolic type PDEs

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-07T10:50:50.405698Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 637ddf3e-3659-4deb-b778-c5efe0cf5706 · inbound

S-shaped Utility Maximization with VaR Constraint and Partial Information cites this paper.

S-shaped Utility Maximization with VaR Constraint and Partial Information On the convergence of physics informed neural networks for linear second-order elliptic and parabolic type PDEs

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-07T04:59:31.606230Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 319bc03a-a1cc-4dd8-b8d0-0ebf4d9b1e63 · inbound

Structure-Informed Deep Reinforcement Learning for Inventory Management cites this paper.

Structure-Informed Deep Reinforcement Learning for Inventory Management On the convergence of physics informed neural networks for linear second-order elliptic and parabolic type PDEs

Reference 2018

Resolution: unresolved; no resolver link, observed 2026-08-06T12:12:46.234443Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 23b32805-c502-4211-a89d-9f6e7077ccba · inbound

A Practitioner's Guide to Kolmogorov-Arnold Networks cites this paper.

A Practitioner's Guide to Kolmogorov-Arnold Networks On the convergence of physics informed neural networks for linear second-order elliptic and parabolic type PDEs

Reference 7

Resolution: verified exact; arxiv_id, observed 2026-05-18T03:30:50.478444Z

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 42e99c5f-d11b-4763-9623-1c526a3df420 · inbound

Universal Approximation of Nonlinear Operators and Their Derivatives cites this paper.

Universal Approximation of Nonlinear Operators and Their Derivatives On the convergence of physics informed neural networks for linear second-order elliptic and parabolic type PDEs

Reference 115

Resolution: verified exact; arxiv_id, observed 2026-05-19T16:52:40.272497Z

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 96815386-8b1c-4db6-a706-db6ccd34c977 · inbound

Universal Approximation of Nonlinear Operators and Their Derivatives cites this paper.

Universal Approximation of Nonlinear Operators and Their Derivatives On the convergence of physics informed neural networks for linear second-order elliptic and parabolic type PDEs

Reference 115

Resolution: verified exact; arxiv_id, observed 2026-06-30T20:55:04.282366Z

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 32d502e6-e918-48cd-bd75-60fa49193d2f · inbound

PINNsur: Physics-Informed Neural Networks for PDEs on Curved Surfaces cites this paper.

PINNsur: Physics-Informed Neural Networks for PDEs on Curved Surfaces On the convergence of physics informed neural networks for linear second-order elliptic and parabolic type PDEs

Reference 12

Resolution: verified exact; arxiv_id, observed 2026-06-29T14:33:30.493388Z

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 83d8b2fc-f221-439c-b303-5d53e05f3c0d · inbound

Effective Dimensionality as an Operator Invariant for Physics-Preserving Constraint Adaptation in Physics-Informed Neural Networks cites this paper.

Effective Dimensionality as an Operator Invariant for Physics-Preserving Constraint Adaptation in Physics-Informed Neural Networks On the convergence of physics informed neural networks for linear second-order elliptic and parabolic type PDEs

Reference 29

Resolution: verified exact; arxiv_id, observed 2026-07-02T15:47:06.082524Z

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 9dac4652-bc26-4ea5-ae50-c6df012c2f38 · inbound

Error Analysis of Tr-PINNs Algorithm for 2D Incompressible Navier-Stokes Equations with Non-Homogeneous Boundary Conditions cites this paper.

Error Analysis of Tr-PINNs Algorithm for 2D Incompressible Navier-Stokes Equations with Non-Homogeneous Boundary Conditions On the convergence of physics informed neural networks for linear second-order elliptic and parabolic type PDEs

Reference 21

Resolution: verified exact; arxiv_id, observed 2026-07-02T14:37:04.160153Z

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 aac4c5c0-fdd3-4450-9850-8dcaa70a8708 · inbound

Parameterized Representations via Implicit Stochastic Modulation for High-Dimensional and High-Order Neural PDE Solvers cites this paper.

Parameterized Representations via Implicit Stochastic Modulation for High-Dimensional and High-Order Neural PDE Solvers On the convergence of physics informed neural networks for linear second-order elliptic and parabolic type PDEs

Reference 27

Resolution: verified exact; arxiv_id, observed 2026-07-04T07:59:40.362054Z

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 60b0783b-a236-4d2c-ae5e-44359c22f354 · inbound

Uncertainty-aware damage identification in short-span bridges via physics-informed variational autoencoder cites this paper.

Uncertainty-aware damage identification in short-span bridges via physics-informed variational autoencoder On the convergence of physics informed neural networks for linear second-order elliptic and parabolic type PDEs

Reference 52

Resolution: unresolved; no resolver link, observed 2026-07-11T09:54:49.262236Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.