Paper Citation Record · LEDGER

Learning Hamiltonian Dynamics at Scale: A Differential-Geometric Approach

As of 5 August 2026, this Paper Citation Record lists 49 of 49 outbound references and 0 inbound Pith citation observations for arXiv:2509.24627.

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

pith.paper-citation-record.v1
2509.24627 v2

Coverage vector

measured 49 of 49 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-04T13:54:17.897051Z

measured 49 of 49 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-05T06:32:48.257954+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

49 of 49 outbound references displayed

verified exact3
verified fuzzy0
unresolved45
parse uncertain0
malformed identifier1
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation ada11a83-f4fb-4dfb-b19d-a15d03286f83 · outbound

This paper cites an unresolved cited work.

Learning Hamiltonian Dynamics at Scale: A Differential-Geometric Approach Unresolved cited work

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-04T13:54:08.484927Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 22b59924-9452-4369-9916-121104d4f88e · outbound

This paper cites Optimization Algorithms on Matrix Manifolds.

Learning Hamiltonian Dynamics at Scale: A Differential-Geometric Approach Optimization Algorithms on Matrix Manifolds

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-04T13:54:08.789820Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c97d8c98-4111-452a-ac12-37533b365639 · outbound

This paper cites Riemannian adaptive optimization methods.

Learning Hamiltonian Dynamics at Scale: A Differential-Geometric Approach Riemannian adaptive optimization methods

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-04T13:54:09.001086Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7970d4a7-1fb3-47a9-bdbe-c9bd9ba1011b · outbound

This paper cites Geometric optimization for structure-preserving model reduction of hamiltonian systems.

Learning Hamiltonian Dynamics at Scale: A Differential-Geometric Approach Geometric optimization for structure-preserving model reduction of hamiltonian systems

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-04T13:54:09.464810Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 591b13cf-69c7-4738-ba58-2c6fb07c988d · outbound

This paper cites Which priors matter? B enchmarking models for learning latent dynamics.

Learning Hamiltonian Dynamics at Scale: A Differential-Geometric Approach Which priors matter? B enchmarking models for learning latent dynamics

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-04T13:54:09.928569Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2db887d7-f49a-4e0c-ab06-ae370c3206ba · outbound

This paper cites An introduction to optimization on smooth manifolds.

Learning Hamiltonian Dynamics at Scale: A Differential-Geometric Approach An introduction to optimization on smooth manifolds

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-04T13:54:10.104639Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1421b9b1-1a9c-4fd5-8c6c-f78792816805 · outbound

This paper cites Brunton, Joshua L.

Learning Hamiltonian Dynamics at Scale: A Differential-Geometric Approach Brunton, Joshua L

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-04T13:54:10.285567Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation eb24cf10-1ea6-4b25-ae6e-b65c1c18c9e2 · outbound

This paper cites Symplectic model reduction of H amiltonian systems on nonlinear manifolds and approximation with weakly symplectic autoencoder.

Learning Hamiltonian Dynamics at Scale: A Differential-Geometric Approach Symplectic model reduction of H amiltonian systems on nonlinear manifolds and approximation with weakly symplectic autoencoder

Reference 8

Resolution: verified exact; doi, observed 2026-08-04T13:58:39.634740Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation db1e5f57-6cbd-4944-840f-e964ff80fabf · outbound

This paper cites Model reduction on manifolds: A differential geometric framework.

Learning Hamiltonian Dynamics at Scale: A Differential-Geometric Approach Model reduction on manifolds: A differential geometric framework

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-04T13:54:10.544980Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 307ac885-6168-4754-a0c2-71f97721a66c · outbound

This paper cites Nathan Kutz, and Steven L.

Learning Hamiltonian Dynamics at Scale: A Differential-Geometric Approach Nathan Kutz, and Steven L

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-04T13:54:10.703708Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 07db2837-e32b-43fd-9f33-2c610ec773ed · outbound

This paper cites Neural symplectic form: Learning H amiltonian equations on general coordinate systems.

Learning Hamiltonian Dynamics at Scale: A Differential-Geometric Approach Neural symplectic form: Learning H amiltonian equations on general coordinate systems

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-04T13:54:11.067743Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0508dc96-d58b-49e9-a9b7-7731c0fd3309 · outbound

This paper cites Symplectic recurrent neural networks.

Learning Hamiltonian Dynamics at Scale: A Differential-Geometric Approach Symplectic recurrent neural networks

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-04T13:54:11.280609Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation df8b6b89-46c5-49ea-9211-56e8cd5b1e49 · outbound

This paper cites Lagrangian Neural Networks.

Learning Hamiltonian Dynamics at Scale: A Differential-Geometric Approach Lagrangian Neural Networks

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-04T13:54:11.462932Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f9951404-123d-4304-b912-424cc70a50cf · outbound

This paper cites Fernandes, and Waldyr M.

Learning Hamiltonian Dynamics at Scale: A Differential-Geometric Approach Fernandes, and Waldyr M

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-04T13:54:11.734614Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation dee694f0-1327-4ecf-9e42-7ddc2ef3752d · outbound

This paper cites H amiltonian -based neural ODE networks on the SE (3) manifold for dynamics learning and control.

Learning Hamiltonian Dynamics at Scale: A Differential-Geometric Approach H amiltonian -based neural ODE networks on the SE (3) manifold for dynamics learning and control

Reference 15

Resolution: verified exact; doi, observed 2026-08-04T13:58:36.865511Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 8d44a448-b87c-403f-9bc6-60cd9d3c85c9 · outbound

This paper cites Geometries and interpolations for symmetric positive definite matrices, pp.\ 85--113.

Learning Hamiltonian Dynamics at Scale: A Differential-Geometric Approach Geometries and interpolations for symmetric positive definite matrices, pp.\ 85--113

Reference 16

Resolution: verified exact; doi, observed 2026-08-04T13:58:36.204804Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation e3393a7a-6bb0-405d-b50f-aa616a05fb08 · outbound

This paper cites A R iemannian framework for learning reduced-order L agrangian dynamics.

Learning Hamiltonian Dynamics at Scale: A Differential-Geometric Approach A R iemannian framework for learning reduced-order L agrangian dynamics

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-04T13:54:12.266338Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3e407039-1b27-4f77-a1e1-1ecb3079c67d · outbound

This paper cites H amiltonian neural networks.

Learning Hamiltonian Dynamics at Scale: A Differential-Geometric Approach H amiltonian neural networks

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-04T13:54:12.460466Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 40cd8fc4-d9b9-4d0d-8513-97fcdfbbb59d · outbound

This paper cites Hamilton.

Learning Hamiltonian Dynamics at Scale: A Differential-Geometric Approach Hamilton

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-04T13:54:12.614466Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 47f63250-f73b-4126-a3fb-86a9e5657ec8 · outbound

This paper cites Sympnets: Intrinsic structure-preserving symplectic networks for identifying H amiltonian systems.

Learning Hamiltonian Dynamics at Scale: A Differential-Geometric Approach Sympnets: Intrinsic structure-preserving symplectic networks for identifying H amiltonian systems

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-04T13:54:12.834505Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b78bb767-1d64-4fdd-a27b-d07ab6bfc995 · outbound

This paper cites Riemann tensor neural networks: Learning conservative systems with physics-constrained networks.

Learning Hamiltonian Dynamics at Scale: A Differential-Geometric Approach Riemann tensor neural networks: Learning conservative systems with physics-constrained networks

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-04T13:54:13.034672Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fc76d973-77ce-4988-93f1-957aced53c22 · outbound

This paper cites Kevrekidis, Lu Lu, Paris Perdikaris, Sifan Wang, and Liu Yang.

Learning Hamiltonian Dynamics at Scale: A Differential-Geometric Approach Kevrekidis, Lu Lu, Paris Perdikaris, Sifan Wang, and Liu Yang

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-04T13:54:13.204872Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b8da9e48-05dc-45cc-9b07-c195ea6a7687 · outbound

This paper cites Geoopt: Riemannian Optimization in PyTorch.

Learning Hamiltonian Dynamics at Scale: A Differential-Geometric Approach Geoopt: Riemannian Optimization in PyTorch

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-04T13:54:13.362270Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 88f177a4-6f81-4bc4-ba34-a166111afdb0 · outbound

This paper cites an unresolved cited work.

Learning Hamiltonian Dynamics at Scale: A Differential-Geometric Approach Unresolved cited work

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-04T13:54:13.539205Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 68868a57-5d9b-4bdb-8b02-3de5e55842d0 · outbound

This paper cites Simulating Hamiltonian Dynamics.

Learning Hamiltonian Dynamics at Scale: A Differential-Geometric Approach Simulating Hamiltonian Dynamics

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-04T13:54:13.706169Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation efecdd5d-af9c-4d76-b6cc-8164eae62a8a · outbound

This paper cites Neural autoencoder-based structure-preserving model order reduction and control design for high-dimensional physical systems.

Learning Hamiltonian Dynamics at Scale: A Differential-Geometric Approach Neural autoencoder-based structure-preserving model order reduction and control design for high-dimensional physical systems

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-04T13:54:13.848787Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 46f1f3f9-5026-429a-bee2-04e6950bba1f · outbound

This paper cites Harnessing the power of neural operators with automatically encoded conservation laws.

Learning Hamiltonian Dynamics at Scale: A Differential-Geometric Approach Harnessing the power of neural operators with automatically encoded conservation laws

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-04T13:54:14.033324Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2a0b9da5-197a-4739-91da-0f2b8750b378 · outbound

This paper cites Combining physics and deep learning to learn continuous-time dynamics models.

Learning Hamiltonian Dynamics at Scale: A Differential-Geometric Approach Combining physics and deep learning to learn continuous-time dynamics models

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-04T13:54:14.166040Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 51a93d4b-baac-44b4-b443-d18e3bd8e88e · outbound

This paper cites Otto, Gregory R.

Learning Hamiltonian Dynamics at Scale: A Differential-Geometric Approach Otto, Gregory R

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-04T13:54:14.313149Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cdb3629d-5682-497d-b257-08e9aab7a4fc · outbound

This paper cites Symplectic model reduction of H amiltonian systems.

Learning Hamiltonian Dynamics at Scale: A Differential-Geometric Approach Symplectic model reduction of H amiltonian systems

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-04T13:54:14.459848Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 07c32fb3-5ff0-4682-bc13-be71abcf2f85 · outbound

This paper cites A R iemannian framework for tensor computing.

Learning Hamiltonian Dynamics at Scale: A Differential-Geometric Approach A R iemannian framework for tensor computing

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-04T13:54:14.607883Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d9ade356-7e4b-48d4-a55d-042ae7df4e6d · outbound

This paper cites Hamiltonian fluid mechanics.

Learning Hamiltonian Dynamics at Scale: A Differential-Geometric Approach Hamiltonian fluid mechanics

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-04T13:54:14.790010Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9a721588-0b9e-4141-bb48-538ef896a15f · outbound

This paper cites an unresolved cited work.

Learning Hamiltonian Dynamics at Scale: A Differential-Geometric Approach Unresolved cited work

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-04T13:54:15.042692Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ffa08cf7-c75e-41d9-8725-318b5930a69c · outbound

This paper cites Quantisierung als eigenwertproblem.

Learning Hamiltonian Dynamics at Scale: A Differential-Geometric Approach Quantisierung als eigenwertproblem

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-04T13:54:15.198272Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b3609104-befb-4604-9be3-3262d7fbec6e · outbound

This paper cites Preserving lagrangian structure in data-driven reduced-order modeling of large-scale dynamical systems.

Learning Hamiltonian Dynamics at Scale: A Differential-Geometric Approach Preserving lagrangian structure in data-driven reduced-order modeling of large-scale dynamical systems

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-04T13:54:15.337375Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3f505326-7f6a-4e7e-ba97-ad842b24369f · outbound

This paper cites Symplectic model reduction of H amiltonian systems using data-driven quadratic manifolds.

Learning Hamiltonian Dynamics at Scale: A Differential-Geometric Approach Symplectic model reduction of H amiltonian systems using data-driven quadratic manifolds

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-04T13:54:15.582809Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6ebc9990-81f5-468c-8e9c-30daf64784a1 · outbound

This paper cites Najera-Flores, Michael D.

Learning Hamiltonian Dynamics at Scale: A Differential-Geometric Approach Najera-Flores, Michael D

Reference 37

Resolution: unresolved; no resolver link, observed 2026-08-04T13:54:15.788357Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d3e0a14b-bc25-4691-aac3-ba71fec69b4b · outbound

This paper cites Dissipative Hamiltonian Neural Networks: Learning Dissipative and Conservative Dynamics Separately.

Learning Hamiltonian Dynamics at Scale: A Differential-Geometric Approach Dissipative Hamiltonian Neural Networks: Learning Dissipative and Conservative Dynamics Separately

Reference 38

Resolution: unresolved; no resolver link, observed 2026-08-04T13:54:15.995251Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 49d90e36-8054-4ca2-8f39-68c90d0fc639 · outbound

This paper cites Explicit symplectic approximation of nonseparable H amiltonians: Algorithm and long time performance.

Learning Hamiltonian Dynamics at Scale: A Differential-Geometric Approach Explicit symplectic approximation of nonseparable H amiltonians: Algorithm and long time performance

Reference 39

Resolution: unresolved; no resolver link, observed 2026-08-04T13:54:16.175271Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 156d8920-5ade-4f26-830d-cc14d2892bb0 · outbound

This paper cites Mujoco: A physics engine for model-based control.

Learning Hamiltonian Dynamics at Scale: A Differential-Geometric Approach Mujoco: A physics engine for model-based control

Reference 40

Resolution: unresolved; no resolver link, observed 2026-08-04T13:54:16.410532Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 12655260-afef-405a-9606-b6f93744bc2c · outbound

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

Learning Hamiltonian Dynamics at Scale: A Differential-Geometric Approach Understanding and mitigating gradient flow pathologies in physics-informed neural networks

Reference 41

Resolution: unresolved; no resolver link, observed 2026-08-04T13:54:16.551452Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 44853645-45fb-443e-a402-64653d48c0a1 · outbound

This paper cites Nonseparable symplectic neural networks.

Learning Hamiltonian Dynamics at Scale: A Differential-Geometric Approach Nonseparable symplectic neural networks

Reference 42

Resolution: unresolved; no resolver link, observed 2026-08-04T13:54:16.732154Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5f2b5af0-f5fd-4124-97f2-2ebf920440ee · outbound

This paper cites Dissipative SymODEN : Encoding H amiltonian dynamics with dissipation and control into deep learning.

Learning Hamiltonian Dynamics at Scale: A Differential-Geometric Approach Dissipative SymODEN : Encoding H amiltonian dynamics with dissipation and control into deep learning

Reference 43

Resolution: unresolved; no resolver link, observed 2026-08-04T13:54:16.895729Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6b51363d-9d46-4c3a-969c-8b01c53f9621 · outbound

This paper cites Symplectic ODE -net: Learning H amiltonian dynamics with control.

Learning Hamiltonian Dynamics at Scale: A Differential-Geometric Approach Symplectic ODE -net: Learning H amiltonian dynamics with control

Reference 44

Resolution: unresolved; no resolver link, observed 2026-08-04T13:54:17.066535Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7b6f6c52-d607-4381-af75-28091e99ec48 · outbound

This paper cites Extending L agrangian and H amiltonian neural networks with differentiable contact models.

Learning Hamiltonian Dynamics at Scale: A Differential-Geometric Approach Extending L agrangian and H amiltonian neural networks with differentiable contact models

Reference 45

Resolution: unresolved; no resolver link, observed 2026-08-04T13:54:17.265790Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1527dca1-f4f1-43c0-a2fa-582405eaeb11 · outbound

This paper cites write newline.

Learning Hamiltonian Dynamics at Scale: A Differential-Geometric Approach write newline

Reference 46

Resolution: unresolved; no resolver link, observed 2026-08-04T13:54:17.388749Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2b376fdc-920a-4505-8e15-bc91b61660cc · outbound

This paper cites @esa (Ref.

Learning Hamiltonian Dynamics at Scale: A Differential-Geometric Approach @esa (Ref

Reference 47

Resolution: unresolved; no resolver link, observed 2026-08-04T13:54:17.573520Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0307e834-f87d-443d-85c1-020a2381a1a6 · outbound

This paper cites an unresolved cited work.

Learning Hamiltonian Dynamics at Scale: A Differential-Geometric Approach Unresolved cited work

Reference 48

Resolution: unresolved; no resolver link, observed 2026-08-04T13:54:17.728633Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d5509a83-9f72-4b12-b6a9-d944e5ca1f95 · outbound

This paper cites ^iziK W;x^.^ m mx xi _ ׵^Sq× = ޟik_K; ڞ I||]˚h緯u ,gx^ضڃ0ل 4s ! q^`K )Okْ.

Learning Hamiltonian Dynamics at Scale: A Differential-Geometric Approach ^iziK W;x^.^ m mx xi _ ׵^Sq× = ޟik_K; ڞ I||]˚h緯u ,gx^ضڃ0ل 4s ! q^`K )Okْ

Reference 49

Resolution: malformed identifier; no resolver link, observed 2026-08-04T13:54:17.897051Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.