Paper Citation Record · LEDGER

The Kuramoto Neural Operator: Learning to Solve PDEs via Coupled Oscillator Dynamics

As of 19 August 2026, this Paper Citation Record lists 37 of 37 outbound references and 0 inbound Pith citation observations for arXiv:2608.10234.

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

pith.paper-citation-record.v1
2608.10234 v1

Coverage vector

measured 37 of 37 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-14T04:16:22.548899Z

measured 37 of 37 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-18T06:34:40.430872+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

37 of 37 outbound references displayed

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verified fuzzy28
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 12854bd9-4f7d-4d0f-9c73-cbd0afb69a01 · outbound

This paper cites Iterative procedures for nonlinear integral equations.

The Kuramoto Neural Operator: Learning to Solve PDEs via Coupled Oscillator Dynamics Iterative procedures for nonlinear integral equations

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:16:24.064402Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation d15eeb60-fd6f-4955-8b84-4ede663b4e47 · outbound

This paper cites DrivAerML: High-Fidelity Computational Fluid Dynamics Dataset for Road-Car External Aerodynamics.

The Kuramoto Neural Operator: Learning to Solve PDEs via Coupled Oscillator Dynamics DrivAerML: High-Fidelity Computational Fluid Dynamics Dataset for Road-Car External Aerodynamics

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-14T04:16:22.087267Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8c2b98ca-0439-406c-ada7-f46f73c9bbb2 · outbound

This paper cites Spectral methods, volume 285.

The Kuramoto Neural Operator: Learning to Solve PDEs via Coupled Oscillator Dynamics Spectral methods, volume 285

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:16:24.045701Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation a44f2932-0d2b-4e74-be2d-b98504145974 · outbound

This paper cites Laplace neural operator for solving differential equations.

The Kuramoto Neural Operator: Learning to Solve PDEs via Coupled Oscillator Dynamics Laplace neural operator for solving differential equations

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:16:24.020023Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 8cf33480-fc5f-4842-aa4b-ed070901c3b7 · outbound

This paper cites Continuous versus discontinuous transitions in the d-dimensional generalized kuramoto model: Odd d is different.

The Kuramoto Neural Operator: Learning to Solve PDEs via Coupled Oscillator Dynamics Continuous versus discontinuous transitions in the d-dimensional generalized kuramoto model: Odd d is different

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:16:23.992334Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 25b1cdb5-ff04-4956-9325-dc931ba9b6d4 · outbound

This paper cites The finite element method for elliptic problems.

The Kuramoto Neural Operator: Learning to Solve PDEs via Coupled Oscillator Dynamics The finite element method for elliptic problems

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:16:23.968014Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation a3b0cc21-2806-46f6-8aa0-3d99d8cad534 · outbound

This paper cites A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized pdes.

The Kuramoto Neural Operator: Learning to Solve PDEs via Coupled Oscillator Dynamics A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized pdes

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:16:23.942502Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation c2ce9c9e-45f5-49da-9f89-8819fe358b1d · outbound

This paper cites On training implicit models.

The Kuramoto Neural Operator: Learning to Solve PDEs via Coupled Oscillator Dynamics On training implicit models

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:16:23.914530Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation b4c82eb2-1043-4766-aadd-a8297f07e575 · outbound

This paper cites One-dimensional lattice of oscillators coupled through power-law interactions: Continuum limit and dynamics of spatial fourier modes.

The Kuramoto Neural Operator: Learning to Solve PDEs via Coupled Oscillator Dynamics One-dimensional lattice of oscillators coupled through power-law interactions: Continuum limit and dynamics of spatial fourier modes

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:16:23.886704Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation f4417b86-5f25-4114-99a6-83f44530cfd3 · outbound

This paper cites Kuramoto oscillators and swarms on manifolds for geometry informed machine learning.

The Kuramoto Neural Operator: Learning to Solve PDEs via Coupled Oscillator Dynamics Kuramoto oscillators and swarms on manifolds for geometry informed machine learning

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:16:23.865292Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 1f7ff57b-61c8-4011-bbca-42e8367babf8 · outbound

This paper cites Rank correlation methods.

The Kuramoto Neural Operator: Learning to Solve PDEs via Coupled Oscillator Dynamics Rank correlation methods

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:16:23.833935Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation ed498609-8bf7-4907-98c1-51d307a110b0 · outbound

This paper cites Learning latent field dynamics of pdes.

The Kuramoto Neural Operator: Learning to Solve PDEs via Coupled Oscillator Dynamics Learning latent field dynamics of pdes

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:16:23.808192Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 090e5313-4838-42cc-9450-7b591bacfdcf · outbound

This paper cites Neural operator: Learning maps between function spaces with applications to pdes.

The Kuramoto Neural Operator: Learning to Solve PDEs via Coupled Oscillator Dynamics Neural operator: Learning maps between function spaces with applications to pdes

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-14T04:16:22.322405Z

Source-reported events for the cited work

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Observation dc0b4a86-3b82-4ec7-815e-b4016cc5220f · outbound

This paper cites Chemical turbulence.

The Kuramoto Neural Operator: Learning to Solve PDEs via Coupled Oscillator Dynamics Chemical turbulence

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:16:23.768843Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation f0be5769-3239-4a68-9089-1f441f804292 · outbound

This paper cites Finite difference methods for ordinary and partial differential equations: steady-state and time-dependent problems.

The Kuramoto Neural Operator: Learning to Solve PDEs via Coupled Oscillator Dynamics Finite difference methods for ordinary and partial differential equations: steady-state and time-dependent problems

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-14T04:16:22.346911Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2e79c103-6370-4643-862c-cbb3055de828 · outbound

This paper cites Fourier Neural Operator for Parametric Partial Differential Equations.

The Kuramoto Neural Operator: Learning to Solve PDEs via Coupled Oscillator Dynamics Fourier Neural Operator for Parametric Partial Differential Equations

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-14T04:16:22.352600Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b00e53ae-c431-42ee-80ac-304cfc88e694 · outbound

This paper cites Fourier neural operator with learned deformations for pdes on general geometries.

The Kuramoto Neural Operator: Learning to Solve PDEs via Coupled Oscillator Dynamics Fourier neural operator with learned deformations for pdes on general geometries

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:16:23.696834Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 4cb34a4d-79ad-486c-8162-b4a0143abe1a · outbound

This paper cites Geometry-informed neural operator for large-scale 3d pdes.

The Kuramoto Neural Operator: Learning to Solve PDEs via Coupled Oscillator Dynamics Geometry-informed neural operator for large-scale 3d pdes

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:16:23.672265Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 14db0eaa-5106-4d00-9c4b-ccc40a62c1a8 · outbound

This paper cites The kuramoto model on a sphere: Explaining its low-dimensional dynamics with group theory and hyperbolic geometry.

The Kuramoto Neural Operator: Learning to Solve PDEs via Coupled Oscillator Dynamics The kuramoto model on a sphere: Explaining its low-dimensional dynamics with group theory and hyperbolic geometry

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:16:23.584748Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 4d9a0f03-49dd-4c74-9181-c75bf4f296b4 · outbound

This paper cites Enhancing Fourier Neural Operators with Local Spatial Features.

The Kuramoto Neural Operator: Learning to Solve PDEs via Coupled Oscillator Dynamics Enhancing Fourier Neural Operators with Local Spatial Features

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-14T04:16:22.380796Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f393c691-9083-4031-8bd5-c26535d3717d · outbound

This paper cites Riesz neural operator for solving partial differential equations.

The Kuramoto Neural Operator: Learning to Solve PDEs via Coupled Oscillator Dynamics Riesz neural operator for solving partial differential equations

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:16:23.519434Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 8bc245a2-b83a-4058-9b84-bad96206e369 · outbound

This paper cites Non-abelian kuramoto models and synchronization.

The Kuramoto Neural Operator: Learning to Solve PDEs via Coupled Oscillator Dynamics Non-abelian kuramoto models and synchronization

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:16:23.473210Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 7a471e62-9bd0-433e-8a1d-98a145b1acb6 · outbound

This paper cites Learning nonlinear operators via deeponet based on the universal approximation theorem of operators.

The Kuramoto Neural Operator: Learning to Solve PDEs via Coupled Oscillator Dynamics Learning nonlinear operators via deeponet based on the universal approximation theorem of operators

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-14T04:16:22.407666Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 66e5c512-75db-4ea1-bfa0-c2b106f5c009 · outbound

This paper cites Solving partial differential equations via radon neural operator.

The Kuramoto Neural Operator: Learning to Solve PDEs via Coupled Oscillator Dynamics Solving partial differential equations via radon neural operator

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:16:23.405907Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation f79ade35-ea80-4026-9a0a-c3745ad6c854 · outbound

This paper cites Almost global convergence to practical synchronization in the generalized kuramoto model on networks over the n-sphere.

The Kuramoto Neural Operator: Learning to Solve PDEs via Coupled Oscillator Dynamics Almost global convergence to practical synchronization in the generalized kuramoto model on networks over the n-sphere

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:16:23.377863Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 436d6f03-2ec8-44c4-bfcc-1d774aef261d · outbound

This paper cites Deep equilibrium based neural operators for steady-state pdes.

The Kuramoto Neural Operator: Learning to Solve PDEs via Coupled Oscillator Dynamics Deep equilibrium based neural operators for steady-state pdes

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:16:23.358084Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 55b0ce00-1a97-4f30-8bf7-da67dc3a86df · outbound

This paper cites The continuum limit of the Kuramoto model on sparse random graphs.

The Kuramoto Neural Operator: Learning to Solve PDEs via Coupled Oscillator Dynamics The continuum limit of the Kuramoto model on sparse random graphs

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-14T04:16:22.446028Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation aaa06d3a-b80f-4886-b079-a4afc12fcc38 · outbound

This paper cites Artificial kuramoto oscillatory neurons.

The Kuramoto Neural Operator: Learning to Solve PDEs via Coupled Oscillator Dynamics Artificial kuramoto oscillatory neurons

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:16:23.308958Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation d15ca557-7354-437d-a025-b342da2fb2fb · outbound

This paper cites The finite volume method.

The Kuramoto Neural Operator: Learning to Solve PDEs via Coupled Oscillator Dynamics The finite volume method

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:16:23.213130Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 2d23f0ae-7b4d-44db-927d-a6405b7fd834 · outbound

This paper cites Convolutional neural operators for robust and accurate learning of pdes.

The Kuramoto Neural Operator: Learning to Solve PDEs via Coupled Oscillator Dynamics Convolutional neural operators for robust and accurate learning of pdes

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:16:23.169267Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 056d5191-fd73-4bac-a4af-7ba8b54b600f · outbound

This paper cites U-net: Convolutional networks for biomedical image segmentation.

The Kuramoto Neural Operator: Learning to Solve PDEs via Coupled Oscillator Dynamics U-net: Convolutional networks for biomedical image segmentation

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:16:23.110058Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation b5f8f83b-d2a3-49c8-8961-7819b1c7f436 · outbound

This paper cites Derivation of the tight-binding approximation for time-dependent nonlinear schr \"o dinger equations.

The Kuramoto Neural Operator: Learning to Solve PDEs via Coupled Oscillator Dynamics Derivation of the tight-binding approximation for time-dependent nonlinear schr \"o dinger equations

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:16:23.005259Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 06626340-9b7c-43a1-a512-18c097a04ccd · outbound

This paper cites Kuramoto orientation diffusion models.

The Kuramoto Neural Operator: Learning to Solve PDEs via Coupled Oscillator Dynamics Kuramoto orientation diffusion models

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:16:22.954734Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation ea62c142-4b61-487b-81c1-500dcc14ec67 · outbound

This paper cites 05 the continuum limit and the wave equation.

The Kuramoto Neural Operator: Learning to Solve PDEs via Coupled Oscillator Dynamics 05 the continuum limit and the wave equation

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:16:22.864091Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation e76bad9f-20c7-4abd-948a-30cfd2b35969 · outbound

This paper cites U-fno—an enhanced fourier neural operator-based deep-learning model for multiphase flow.

The Kuramoto Neural Operator: Learning to Solve PDEs via Coupled Oscillator Dynamics U-fno—an enhanced fourier neural operator-based deep-learning model for multiphase flow

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:16:22.781978Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 9e2e588c-decc-4fb4-ace6-0c7b54e2f18e · outbound

This paper cites GeoPT: Scaling Physics Simulation via Lifted Geometric Pre-Training.

The Kuramoto Neural Operator: Learning to Solve PDEs via Coupled Oscillator Dynamics GeoPT: Scaling Physics Simulation via Lifted Geometric Pre-Training

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-14T04:16:22.521169Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 823a02f1-c0d1-426e-8e81-4a13ebc6cbe3 · outbound

This paper cites Kuramoto Oscillatory Phase Encoding: Neuro-inspired Synchronization for Improved Learning Efficiency.

The Kuramoto Neural Operator: Learning to Solve PDEs via Coupled Oscillator Dynamics Kuramoto Oscillatory Phase Encoding: Neuro-inspired Synchronization for Improved Learning Efficiency

Reference 37

Resolution: unresolved; no resolver link, observed 2026-08-14T04:16:22.548899Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

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