Paper Citation Record · LEDGER

Kolmogorov-Arnold Representation for Symplectic Learning: Advancing Hamiltonian Neural Networks

As of 10 August 2026, this Paper Citation Record lists 32 of 32 outbound references and 0 inbound Pith citation observations for arXiv:2508.19410.

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

pith.paper-citation-record.v1
2508.19410 v1

Coverage vector

measured 32 of 32 reference resolution

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Source: paper_references, paper_reference_links, observed 2026-08-05T15:51:30.033855Z

measured 32 of 32 standing notices

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Pith citing papers itemized under the disclosed page cap.

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Reference resolution

32 of 32 outbound references displayed

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External citation measurements

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Outbound references

Observation b1e4fc36-0ea3-4acc-be14-c5c0a170578a · outbound

This paper cites Hairer, C.

Kolmogorov-Arnold Representation for Symplectic Learning: Advancing Hamiltonian Neural Networks Hairer, C

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T15:51:30.379044Z

Source-reported events for the cited work

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Observation f1da069c-cf23-4235-9089-af4a71ece672 · outbound

This paper cites On the use of canonical transformations and symplectic integrators for hamiltonian systems,.

Kolmogorov-Arnold Representation for Symplectic Learning: Advancing Hamiltonian Neural Networks On the use of canonical transformations and symplectic integrators for hamiltonian systems,

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T15:51:30.371928Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 947ae6f2-4dab-464f-b69d-31d74266678b · outbound

This paper cites Symplectic neural net- works in continuous and discrete time,.

Kolmogorov-Arnold Representation for Symplectic Learning: Advancing Hamiltonian Neural Networks Symplectic neural net- works in continuous and discrete time,

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T15:51:30.364908Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 13e63550-d44c-4b3b-9469-0f1f255ba639 · outbound

This paper cites Velocity-Inferred Hamiltonian Neural Networks: Learning Energy-Conserving Dynamics from Position-Only Data.

Kolmogorov-Arnold Representation for Symplectic Learning: Advancing Hamiltonian Neural Networks Velocity-Inferred Hamiltonian Neural Networks: Learning Energy-Conserving Dynamics from Position-Only Data

Reference 4

Resolution: verified exact; local_arxiv, observed 2026-08-05T15:51:30.198019Z

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Observation e7ac3030-d55d-45f5-a27c-0ba7055c1d9f · outbound

This paper cites Neural ordinary differential equations,.

Kolmogorov-Arnold Representation for Symplectic Learning: Advancing Hamiltonian Neural Networks Neural ordinary differential equations,

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T15:51:30.357892Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 48c9aa4f-58a6-439d-9144-bed1f65e3092 · outbound

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

Kolmogorov-Arnold Representation for Symplectic Learning: Advancing Hamiltonian Neural Networks Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear pdes,

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T15:51:30.351127Z

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Observation 41e74053-9295-44b0-bba0-13c5c5d7f860 · outbound

This paper cites Hamiltonian neural networks,.

Kolmogorov-Arnold Representation for Symplectic Learning: Advancing Hamiltonian Neural Networks Hamiltonian neural networks,

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T15:51:30.344379Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation d57c97ed-7815-4277-835d-b4249263c305 · outbound

This paper cites On the representation of continuous functions of several variables by superposition of continuous functions of one variable and addition,.

Kolmogorov-Arnold Representation for Symplectic Learning: Advancing Hamiltonian Neural Networks On the representation of continuous functions of several variables by superposition of continuous functions of one variable and addition,

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T15:51:30.337823Z

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Observation 4c643291-f4de-4168-b086-6f0ee12203d4 · outbound

This paper cites On functions of three variables,.

Kolmogorov-Arnold Representation for Symplectic Learning: Advancing Hamiltonian Neural Networks On functions of three variables,

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T15:51:30.331056Z

Source-reported events for the cited work

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Observation a18a2aa8-3f36-4366-aafa-1978bb680c9f · outbound

This paper cites Local kernel expansions for high-fidelity modeling of chaotic flows,.

Kolmogorov-Arnold Representation for Symplectic Learning: Advancing Hamiltonian Neural Networks Local kernel expansions for high-fidelity modeling of chaotic flows,

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T15:51:30.324419Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 98ddb96c-98c6-4023-a0c3-5334c336cd6f · outbound

This paper cites Radial basis function networks in physics-informed learn- ing,.

Kolmogorov-Arnold Representation for Symplectic Learning: Advancing Hamiltonian Neural Networks Radial basis function networks in physics-informed learn- ing,

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T15:51:30.317681Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation cd3ab843-7d9c-4212-8e3b-fe5cdecb8c94 · outbound

This paper cites Kolmogorov–arnold networks for high-dimensional function ap- proximation,.

Kolmogorov-Arnold Representation for Symplectic Learning: Advancing Hamiltonian Neural Networks Kolmogorov–arnold networks for high-dimensional function ap- proximation,

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T15:51:30.311037Z

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Observation 569a1e13-e56e-4cab-9ec3-a52d354427d3 · outbound

This paper cites Bayesian kernelized learning for physics discovery,.

Kolmogorov-Arnold Representation for Symplectic Learning: Advancing Hamiltonian Neural Networks Bayesian kernelized learning for physics discovery,

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T15:51:30.304198Z

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Observation 3ce4d2ea-8916-4437-b5cd-8229aa299716 · outbound

This paper cites an unresolved cited work.

Kolmogorov-Arnold Representation for Symplectic Learning: Advancing Hamiltonian Neural Networks Unresolved cited work

Reference 14

Resolution: unresolved; raw_fallback, observed 2026-08-05T15:51:30.297504Z

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Observation 07c99aee-4887-415a-bbb7-55df65872e8a · outbound

This paper cites an unresolved cited work.

Kolmogorov-Arnold Representation for Symplectic Learning: Advancing Hamiltonian Neural Networks Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-08-05T15:51:30.291004Z

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Observation 8788b189-882c-4346-bb0e-b3b21dd192ee · outbound

This paper cites Survey of physics-informed neural networks for scientific computing,.

Kolmogorov-Arnold Representation for Symplectic Learning: Advancing Hamiltonian Neural Networks Survey of physics-informed neural networks for scientific computing,

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T15:51:30.284285Z

Source-reported events for the cited work

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Observation 2e3468d5-c148-403d-bacc-aa11eee887cf · outbound

This paper cites Active learning based sampling for high- dimensional nonlinear partial differential equations,.

Kolmogorov-Arnold Representation for Symplectic Learning: Advancing Hamiltonian Neural Networks Active learning based sampling for high- dimensional nonlinear partial differential equations,

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T15:51:30.277491Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 6c7e6d2f-0698-4df9-8861-593b0083e91e · outbound

This paper cites Coordinate transform fourier neural operators for symmetries in physical modelings,.

Kolmogorov-Arnold Representation for Symplectic Learning: Advancing Hamiltonian Neural Networks Coordinate transform fourier neural operators for symmetries in physical modelings,

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T15:51:30.270588Z

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Observation 7b6a545a-6fa5-4c61-afb7-9ab780877ef2 · outbound

This paper cites Complex Physics-Informed Neural Network.

Kolmogorov-Arnold Representation for Symplectic Learning: Advancing Hamiltonian Neural Networks Complex Physics-Informed Neural Network

Reference 19

Resolution: verified exact; local_arxiv, observed 2026-08-05T15:51:30.187615Z

Source-reported events for the cited work

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Observation 5e155385-2f11-4239-8d65-1cffc12d6cc2 · outbound

This paper cites Initialization-enhanced physics-informed neural net- work with domain decomposition (idpinn),.

Kolmogorov-Arnold Representation for Symplectic Learning: Advancing Hamiltonian Neural Networks Initialization-enhanced physics-informed neural net- work with domain decomposition (idpinn),

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T15:51:30.263392Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 7edc6ded-223c-4de2-8c29-c2f0be27f48c · outbound

This paper cites Neural krylov iteration for accelerating linear system solving,.

Kolmogorov-Arnold Representation for Symplectic Learning: Advancing Hamiltonian Neural Networks Neural krylov iteration for accelerating linear system solving,

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T15:51:30.256525Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 229ee2d3-73d7-4d43-9a85-a1118b3c9b68 · outbound

This paper cites Convolution-weighting method for the physics-informed neural network: A Primal-Dual Optimization Perspective.

Kolmogorov-Arnold Representation for Symplectic Learning: Advancing Hamiltonian Neural Networks Convolution-weighting method for the physics-informed neural network: A Primal-Dual Optimization Perspective

Reference 22

Resolution: verified exact; local_arxiv, observed 2026-08-05T15:51:30.178129Z

Source-reported events for the cited work

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Observation 715f34b6-ce0f-4ca0-9708-100bbb930711 · outbound

This paper cites Graph neural operators for multi-scale physical simulations,.

Kolmogorov-Arnold Representation for Symplectic Learning: Advancing Hamiltonian Neural Networks Graph neural operators for multi-scale physical simulations,

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T15:51:30.249660Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 15983aaf-43a4-42d1-ba56-9d66095496b5 · outbound

This paper cites Dynamic schwartz- fourier neural operator for enhanced expressive power,.

Kolmogorov-Arnold Representation for Symplectic Learning: Advancing Hamiltonian Neural Networks Dynamic schwartz- fourier neural operator for enhanced expressive power,

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T15:51:30.242627Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 95b1457e-6450-4f38-b918-37b2975ce50c · outbound

This paper cites Holistic Physics Solver: Learning PDEs in a Unified Spectral-Physical Space.

Kolmogorov-Arnold Representation for Symplectic Learning: Advancing Hamiltonian Neural Networks Holistic Physics Solver: Learning PDEs in a Unified Spectral-Physical Space

Reference 25

Resolution: verified exact; local_arxiv, observed 2026-08-05T15:51:30.168548Z

Source-reported events for the cited work

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Observation f7179271-2395-4bf5-9b41-2c5e62984184 · outbound

This paper cites Deltaphi: Learning physical trajectory residual for pde solving,.

Kolmogorov-Arnold Representation for Symplectic Learning: Advancing Hamiltonian Neural Networks Deltaphi: Learning physical trajectory residual for pde solving,

Reference 26

Resolution: verified exact; raw_fallback, observed 2026-08-05T15:51:30.158036Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation e8ae4707-3fdc-42b8-971c-36137fb9f615 · outbound

This paper cites Discretization-invariance? on the discretization mismatch errors in neural operators,.

Kolmogorov-Arnold Representation for Symplectic Learning: Advancing Hamiltonian Neural Networks Discretization-invariance? on the discretization mismatch errors in neural operators,

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T15:51:30.235704Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation b47939b3-8d5f-4863-ab10-3fb06623867e · outbound

This paper cites APOD: Adaptive PDE-observation diffusion for physics-constrained sampling,.

Kolmogorov-Arnold Representation for Symplectic Learning: Advancing Hamiltonian Neural Networks APOD: Adaptive PDE-observation diffusion for physics-constrained sampling,

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T15:51:30.228000Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 746c68d5-4466-4210-9dc9-675db7ceff6d · outbound

This paper cites Symbolic learning of dynamical systems using mixed integer programming and neural approximations,.

Kolmogorov-Arnold Representation for Symplectic Learning: Advancing Hamiltonian Neural Networks Symbolic learning of dynamical systems using mixed integer programming and neural approximations,

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T15:51:30.220653Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation d45195e0-6d89-49d2-97ef-92a39e58c290 · outbound

This paper cites Deep coordinate descent: Training neural networks with lagrangian mechanics,.

Kolmogorov-Arnold Representation for Symplectic Learning: Advancing Hamiltonian Neural Networks Deep coordinate descent: Training neural networks with lagrangian mechanics,

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T15:51:30.213383Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 0b76d5b8-76a2-4ebd-8463-ec4d64f7b106 · outbound

This paper cites Improved hamiltonian neural networks with extended energy conservation,.

Kolmogorov-Arnold Representation for Symplectic Learning: Advancing Hamiltonian Neural Networks Improved hamiltonian neural networks with extended energy conservation,

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T15:51:30.205821Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation a37622f5-32e9-426a-bd81-34464c75e150 · outbound

This paper cites The Impact of Move Schemes on Simulated Annealing Performance.

Kolmogorov-Arnold Representation for Symplectic Learning: Advancing Hamiltonian Neural Networks The Impact of Move Schemes on Simulated Annealing Performance

Reference 32

Resolution: verified exact; local_arxiv, observed 2026-08-05T15:51:30.059105Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Pith citing papers

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