Paper Citation Record · LEDGER

Neural Multiscale Decomposition for Solving The Nonlinear Klein-Gordon Equation with Time Oscillation

As of 7 August 2026, this Paper Citation Record lists 12 of 12 outbound references and 0 inbound Pith citation observations for arXiv:2512.00266.

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

pith.paper-citation-record.v1
2512.00266 v7

Coverage vector

measured 12 of 12 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-03T19:36:17.508809Z

measured 12 of 12 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-07T06:34:17.273281+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

12 of 12 outbound references displayed

verified exact0
verified fuzzy0
unresolved12
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation b00c7c59-b8a0-4741-8744-1b1bbd69737f · outbound

This paper cites SetPINNs: Set-based Physics-informed Neural Networks.

Neural Multiscale Decomposition for Solving The Nonlinear Klein-Gordon Equation with Time Oscillation SetPINNs: Set-based Physics-informed Neural Networks

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-03T19:36:17.280806Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e5db429d-5544-4323-9dc6-0becf2f82fbc · outbound

This paper cites On the Role of Fixed Points of Dynamical Systems in Training Physics-Informed Neural Networks.

Neural Multiscale Decomposition for Solving The Nonlinear Klein-Gordon Equation with Time Oscillation On the Role of Fixed Points of Dynamical Systems in Training Physics-Informed Neural Networks

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-03T19:36:17.332012Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f4d6945c-66fd-4849-9435-b534874845e4 · outbound

This paper cites Respecting causality is all you need for training physics-informed neural networks.

Neural Multiscale Decomposition for Solving The Nonlinear Klein-Gordon Equation with Time Oscillation Respecting causality is all you need for training physics-informed neural networks

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-03T19:36:17.376295Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a99250dc-590d-4181-85d2-780bcf29453e · outbound

This paper cites ProPINN: Demystifying Propagation Failures in Physics-Informed Neural Networks.

Neural Multiscale Decomposition for Solving The Nonlinear Klein-Gordon Equation with Time Oscillation ProPINN: Demystifying Propagation Failures in Physics-Informed Neural Networks

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-03T19:36:17.421647Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0204f235-39d4-46ae-947f-777fec22b1f1 · outbound

This paper cites KAN: Kolmogorov-Arnold Networks.

Neural Multiscale Decomposition for Solving The Nonlinear Klein-Gordon Equation with Time Oscillation KAN: Kolmogorov-Arnold Networks

Reference 1989

Resolution: unresolved; no resolver link, observed 2026-08-03T19:36:17.195374Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5076e08e-0129-4579-b58c-ad888ba30ed2 · outbound

This paper cites Adam: A Method for Stochastic Optimization.

Neural Multiscale Decomposition for Solving The Nonlinear Klein-Gordon Equation with Time Oscillation Adam: A Method for Stochastic Optimization

Reference 1990

Resolution: unresolved; no resolver link, observed 2026-08-03T19:36:17.151908Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b68b7176-20eb-4410-b50e-e29f7a027ed0 · outbound

This paper cites Quadratic residual networks: A new class of neural networks for solving forward and inverse problems in physics involving pdes.

Neural Multiscale Decomposition for Solving The Nonlinear Klein-Gordon Equation with Time Oscillation Quadratic residual networks: A new class of neural networks for solving forward and inverse problems in physics involving pdes

Reference 2009

Resolution: unresolved; no resolver link, observed 2026-08-03T19:36:16.982233Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6f024dbb-dcff-4d05-8fc1-2c96cc8381ab · outbound

This paper cites Momentum Diminishes the Effect of Spectral Bias in Physics-Informed Neural Networks.

Neural Multiscale Decomposition for Solving The Nonlinear Klein-Gordon Equation with Time Oscillation Momentum Diminishes the Effect of Spectral Bias in Physics-Informed Neural Networks

Reference 2013

Resolution: unresolved; no resolver link, observed 2026-08-03T19:36:17.114347Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 279c71bc-85dc-4158-90f7-f0dbbc9888f0 · outbound

This paper cites Multi-scale Deep Neural Networks for Solving High Dimensional PDEs.

Neural Multiscale Decomposition for Solving The Nonlinear Klein-Gordon Equation with Time Oscillation Multi-scale Deep Neural Networks for Solving High Dimensional PDEs

Reference 2021

Resolution: unresolved; no resolver link, observed 2026-08-03T19:36:17.053466Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d2223b3e-6dd1-48d0-85b7-c5569fc65994 · outbound

This paper cites PINNsFormer: A Transformer-Based Framework For Physics-Informed Neural Networks.

Neural Multiscale Decomposition for Solving The Nonlinear Klein-Gordon Equation with Time Oscillation PINNsFormer: A Transformer-Based Framework For Physics-Informed Neural Networks

Reference 2022

Resolution: unresolved; no resolver link, observed 2026-08-03T19:36:17.508809Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0f32f1e4-9563-4d4b-a95c-6fc81066a839 · outbound

This paper cites Multi-scale Deep Neural Network (MscaleDNN) for Solving Poisson-Boltzmann Equation in Complex Domains.

Neural Multiscale Decomposition for Solving The Nonlinear Klein-Gordon Equation with Time Oscillation Multi-scale Deep Neural Network (MscaleDNN) for Solving Poisson-Boltzmann Equation in Complex Domains

Reference 2024

Resolution: unresolved; no resolver link, observed 2026-08-03T19:36:17.238153Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fb632feb-d47b-4d15-a5e3-a7be04ed6e60 · outbound

This paper cites Sub-Sequential Physics-Informed Learning with State Space Model.

Neural Multiscale Decomposition for Solving The Nonlinear Klein-Gordon Equation with Time Oscillation Sub-Sequential Physics-Informed Learning with State Space Model

Reference 2025

Resolution: unresolved; no resolver link, observed 2026-08-03T19:36:17.466777Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.