Latent Lie-Poisson Neural Networks (LLPNNs): Discovering the motion of Lie-Poisson systems through observable data and latent dynamics | Paper Citation Record

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This paper cites Physics-informed machine learning.Nature Reviews Physics, 3(6):422–440, 2021.

Latent Lie-Poisson Neural Networks (LLPNNs): Discovering the motion of Lie-Poisson systems through observable data and latent dynamics Physics-informed machine learning.Nature Reviews Physics, 3(6):422–440, 2021

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This paper cites Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next.

Latent Lie-Poisson Neural Networks (LLPNNs): Discovering the motion of Lie-Poisson systems through observable data and latent dynamics Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next

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Latent Lie-Poisson Neural Networks (LLPNNs): Discovering the motion of Lie-Poisson systems through observable data and latent dynamics Neural Ordinary Differential Equations

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This paper cites Learning nonlinear operators via deeponet based on the universal approximation theorem of operators.Nature machine intelli- gence, 3(3):218–229, 2021.

Latent Lie-Poisson Neural Networks (LLPNNs): Discovering the motion of Lie-Poisson systems through observable data and latent dynamics Learning nonlinear operators via deeponet based on the universal approximation theorem of operators.Nature machine intelli- gence, 3(3):218–229, 2021

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This paper cites Hamiltonian neural networks.Advances in neural information processing systems, 32, 2019.

Latent Lie-Poisson Neural Networks (LLPNNs): Discovering the motion of Lie-Poisson systems through observable data and latent dynamics Hamiltonian neural networks.Advances in neural information processing systems, 32, 2019

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This paper cites Adaptable Hamiltonian neural networks.Physical Review Research, 3(2):023156, 2021.

Latent Lie-Poisson Neural Networks (LLPNNs): Discovering the motion of Lie-Poisson systems through observable data and latent dynamics Adaptable Hamiltonian neural networks.Physical Review Research, 3(2):023156, 2021

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This paper cites Symplectic Learning for Hamiltonian Neural Networks.

Latent Lie-Poisson Neural Networks (LLPNNs): Discovering the motion of Lie-Poisson systems through observable data and latent dynamics Symplectic Learning for Hamiltonian Neural Networks

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Latent Lie-Poisson Neural Networks (LLPNNs): Discovering the motion of Lie-Poisson systems through observable data and latent dynamics Lagrangian Neural Networks

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Latent Lie-Poisson Neural Networks (LLPNNs): Discovering the motion of Lie-Poisson systems through observable data and latent dynamics Direct Poisson neural networks: Learning non-symplectic mechanical systems

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This paper cites A global structure- preserving kernel method for the learning of poisson systems.Journal of Nonlinear Science, 35(4):79, 2025.

Latent Lie-Poisson Neural Networks (LLPNNs): Discovering the motion of Lie-Poisson systems through observable data and latent dynamics A global structure- preserving kernel method for the learning of poisson systems.Journal of Nonlinear Science, 35(4):79, 2025

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This paper cites Discrete mechanics and varia- tional integrators.Acta numerica, 10:357–514, 2001.

Latent Lie-Poisson Neural Networks (LLPNNs): Discovering the motion of Lie-Poisson systems through observable data and latent dynamics Discrete mechanics and varia- tional integrators.Acta numerica, 10:357–514, 2001

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This paper cites General techniques for constructing variational integrators.Frontiers of Mathematics in China, 7:273–303, 2012.

Latent Lie-Poisson Neural Networks (LLPNNs): Discovering the motion of Lie-Poisson systems through observable data and latent dynamics General techniques for constructing variational integrators.Frontiers of Mathematics in China, 7:273–303, 2012

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This paper cites Spectral variational integrators.Nu- merische Mathematik, 130:681–740, 2015.

Latent Lie-Poisson Neural Networks (LLPNNs): Discovering the motion of Lie-Poisson systems through observable data and latent dynamics Spectral variational integrators.Nu- merische Mathematik, 130:681–740, 2015

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This paper cites Springer Science & Business Media, 2013.

Latent Lie-Poisson Neural Networks (LLPNNs): Discovering the motion of Lie-Poisson systems through observable data and latent dynamics Springer Science & Business Media, 2013

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This paper cites Marsden and T.

Latent Lie-Poisson Neural Networks (LLPNNs): Discovering the motion of Lie-Poisson systems through observable data and latent dynamics Marsden and T

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Latent Lie-Poisson Neural Networks (LLPNNs): Discovering the motion of Lie-Poisson systems through observable data and latent dynamics Springer, 2025

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This paper cites Symplectic recurrent neural networks.International Conference on Learning Representations, 2020.

Latent Lie-Poisson Neural Networks (LLPNNs): Discovering the motion of Lie-Poisson systems through observable data and latent dynamics Symplectic recurrent neural networks.International Conference on Learning Representations, 2020

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This paper cites Nonseparable Symplectic Neural Networks.

Latent Lie-Poisson Neural Networks (LLPNNs): Discovering the motion of Lie-Poisson systems through observable data and latent dynamics Nonseparable Symplectic Neural Networks

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This paper cites Explicit symplectic approximation of nonseparable Hamil- tonians: Algorithm and long time performance.Physical Review E, 94(4):043303, 2016.

Latent Lie-Poisson Neural Networks (LLPNNs): Discovering the motion of Lie-Poisson systems through observable data and latent dynamics Explicit symplectic approximation of nonseparable Hamil- tonians: Algorithm and long time performance.Physical Review E, 94(4):043303, 2016

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This paper cites Symplectic Neural Networks for Learning Non-Separable Hamiltonians.

Latent Lie-Poisson Neural Networks (LLPNNs): Discovering the motion of Lie-Poisson systems through observable data and latent dynamics Symplectic Neural Networks for Learning Non-Separable Hamiltonians

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Latent Lie-Poisson Neural Networks (LLPNNs): Discovering the motion of Lie-Poisson systems through observable data and latent dynamics Unresolved cited work

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This paper cites Variational neural networks for observable thermodynamics (v-nots).arXiv preprint arXiv:2509.09899, 2025.

Latent Lie-Poisson Neural Networks (LLPNNs): Discovering the motion of Lie-Poisson systems through observable data and latent dynamics Variational neural networks for observable thermodynamics (v-nots).arXiv preprint arXiv:2509.09899, 2025

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This paper cites SympNets: Intrinsic structure-preserving symplectic net- works for identifying Hamiltonian systems.Neural Networks, 132:166– 179, 2020.

Latent Lie-Poisson Neural Networks (LLPNNs): Discovering the motion of Lie-Poisson systems through observable data and latent dynamics SympNets: Intrinsic structure-preserving symplectic net- works for identifying Hamiltonian systems.Neural Networks, 132:166– 179, 2020

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Latent Lie-Poisson Neural Networks (LLPNNs): Discovering the motion of Lie-Poisson systems through observable data and latent dynamics Data-driven prediction of general Hamil- tonian dynamics via learning exactly-symplectic maps

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Latent Lie-Poisson Neural Networks (LLPNNs): Discovering the motion of Lie-Poisson systems through observable data and latent dynamics Fast neural Poincaré maps for toroidal magnetic fields.Plasma Physics and Controlled Fu- sion, 63(2):024001, 2020

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This paper cites Lie–Poisson Neural Networks (LPNets): Data-Based Com- puting of Hamiltonian Systems with Symmetries.Neural Networks, 173:106162, 2024.

Latent Lie-Poisson Neural Networks (LLPNNs): Discovering the motion of Lie-Poisson systems through observable data and latent dynamics Lie–Poisson Neural Networks (LPNets): Data-Based Com- puting of Hamiltonian Systems with Symmetries.Neural Networks, 173:106162, 2024

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Latent Lie-Poisson Neural Networks (LLPNNs): Discovering the motion of Lie-Poisson systems through observable data and latent dynamics Clpnets: Coupledlie–poissonneuralnetworksformulti-parthamiltonian systems with symmetries.Neural Networks, 189:107441, 2025

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This paper cites Structure-preserving learning and prediction in optimal control of collective motion.arXiv preprint arXiv:2601.06770, 2026.

Latent Lie-Poisson Neural Networks (LLPNNs): Discovering the motion of Lie-Poisson systems through observable data and latent dynamics Structure-preserving learning and prediction in optimal control of collective motion.arXiv preprint arXiv:2601.06770, 2026

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Latent Lie-Poisson Neural Networks (LLPNNs): Discovering the motion of Lie-Poisson systems through observable data and latent dynamics Springer, 01 2013

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Latent Lie-Poisson Neural Networks (LLPNNs): Discovering the motion of Lie-Poisson systems through observable data and latent dynamics Learning Poisson systems and trajectories of autonomous sys- tems via Poisson neural networks.IEEE Transactions on Neural Net- works and Learning Systems, 2022

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Latent Lie-Poisson Neural Networks (LLPNNs): Discovering the motion of Lie-Poisson systems through observable data and latent dynamics StatisticalmechanicsofArakawa’s discretizations.Journal of Computational Physics, 227(2):1286–1305, 2007

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Latent Lie-Poisson Neural Networks (LLPNNs): Discovering the motion of Lie-Poisson systems through observable data and latent dynamics Designing Poisson Integrators Through Machine Learning

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Latent Lie-Poisson Neural Networks (LLPNNs): Discovering the motion of Lie-Poisson systems through observable data and latent dynamics Symmetry preservation in hamiltonian systems: Simulation and learning.Journal of Nonlinear Science, 34(6):115, 2024

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Latent Lie-Poisson Neural Networks (LLPNNs): Discovering the motion of Lie-Poisson systems through observable data and latent dynamics Locally-symplectic neural networks for learning volume- preserving dynamics.Journal of Computational Physics, 476:111911, 2023

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Latent Lie-Poisson Neural Networks (LLPNNs): Discovering the motion of Lie-Poisson systems through observable data and latent dynamics Learning to predict 3d rotational dynamics from images of a rigid body with unknown mass distribution.Aerospace, 10(11):921, 2023

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Latent Lie-Poisson Neural Networks (LLPNNs): Discovering the motion of Lie-Poisson systems through observable data and latent dynamics Springer Science & Business Media, 2013

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Latent Lie-Poisson Neural Networks (LLPNNs): Discovering the motion of Lie-Poisson systems through observable data and latent dynamics Bloch.Nonholonomic Mechanics and Control, volume 24

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Latent Lie-Poisson Neural Networks (LLPNNs): Discovering the motion of Lie-Poisson systems through observable data and latent dynamics Extremal collective behavior

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Latent Lie-Poisson Neural Networks (LLPNNs): Discovering the motion of Lie-Poisson systems through observable data and latent dynamics Optimality, reduction and collec- tive motion.Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 471(2177):20140606, 2015

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Latent Lie-Poisson Neural Networks (LLPNNs): Discovering the motion of Lie-Poisson systems through observable data and latent dynamics Cambridge University Press, 2022

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Latent Lie-Poisson Neural Networks (LLPNNs): Discovering the motion of Lie-Poisson systems through observable data and latent dynamics Springer, 2006

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Observation 909a3246-084b-4561-9264-c55d48c8fab8 · outbound

This paper cites Universal ap- proximation of an unknown mapping and its derivatives using multilayer feedforward networks.Neural networks, 3(5):551–560, 1990.

Latent Lie-Poisson Neural Networks (LLPNNs): Discovering the motion of Lie-Poisson systems through observable data and latent dynamics Universal ap- proximation of an unknown mapping and its derivatives using multilayer feedforward networks.Neural networks, 3(5):551–560, 1990

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Resolution: unresolved; no resolver link, observed 2026-08-03T16:56:07.130893Z

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Observation 21c0e4b3-34cd-412a-9136-9e805a522d8c · outbound

This paper cites CUP Archive, 1964.

Latent Lie-Poisson Neural Networks (LLPNNs): Discovering the motion of Lie-Poisson systems through observable data and latent dynamics CUP Archive, 1964

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Resolution: unresolved; no resolver link, observed 2026-08-03T16:56:07.267846Z

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This paper cites Springer Science & Business Media, 2013.

Latent Lie-Poisson Neural Networks (LLPNNs): Discovering the motion of Lie-Poisson systems through observable data and latent dynamics Springer Science & Business Media, 2013

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Resolution: unresolved; no resolver link, observed 2026-08-03T16:56:07.353074Z

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Observation 03530a3e-1f6c-4e53-b962-611515f83c87 · outbound

This paper cites Stability of a bottom-heavy underwater vehicle.

Latent Lie-Poisson Neural Networks (LLPNNs): Discovering the motion of Lie-Poisson systems through observable data and latent dynamics Stability of a bottom-heavy underwater vehicle

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Resolution: unresolved; no resolver link, observed 2026-08-03T16:56:07.412328Z

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Observation 841299cd-9b67-4491-8a71-b574ce6b54ac · outbound

This paper cites Stability and drift of underwater vehicle dynamics: mechanical systems with rigid motion symmetry.Physica D: Nonlinear Phenomena, 105(1-3):130–162, 1997.

Latent Lie-Poisson Neural Networks (LLPNNs): Discovering the motion of Lie-Poisson systems through observable data and latent dynamics Stability and drift of underwater vehicle dynamics: mechanical systems with rigid motion symmetry.Physica D: Nonlinear Phenomena, 105(1-3):130–162, 1997

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Resolution: unresolved; no resolver link, observed 2026-08-03T16:56:07.511035Z

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Observation d1cdb6a2-9059-4293-9190-1d0862e6936a · outbound

This paper cites Dynamics of the Kirchhoff equations i: Coincident centers of gravity and buoyancy.

Latent Lie-Poisson Neural Networks (LLPNNs): Discovering the motion of Lie-Poisson systems through observable data and latent dynamics Dynamics of the Kirchhoff equations i: Coincident centers of gravity and buoyancy

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Resolution: unresolved; no resolver link, observed 2026-08-03T16:56:07.573261Z

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Observation 185a9a1d-109b-4f66-8be6-02d10c65d624 · outbound

This paper cites The Euler– Poincaré equations and semidirect products with applications to contin- uum theories.Advances in Mathematics, 137(1):1–81, 1998.

Latent Lie-Poisson Neural Networks (LLPNNs): Discovering the motion of Lie-Poisson systems through observable data and latent dynamics The Euler– Poincaré equations and semidirect products with applications to contin- uum theories.Advances in Mathematics, 137(1):1–81, 1998

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Resolution: unresolved; no resolver link, observed 2026-08-03T16:56:07.665980Z

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Observation 0538e458-53bd-4710-8c62-6ac0eebe3a18 · outbound

This paper cites Oxford University Press, 2009.

Latent Lie-Poisson Neural Networks (LLPNNs): Discovering the motion of Lie-Poisson systems through observable data and latent dynamics Oxford University Press, 2009

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Resolution: unresolved; no resolver link, observed 2026-08-03T16:56:07.750166Z

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Observation 11f47f93-eb66-4383-be19-4d8ea0d8c762 · outbound

This paper cites Springer Science & Business Media, 2013.

Latent Lie-Poisson Neural Networks (LLPNNs): Discovering the motion of Lie-Poisson systems through observable data and latent dynamics Springer Science & Business Media, 2013

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Resolution: unresolved; no resolver link, observed 2026-08-03T16:56:07.847490Z

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Observation f1531379-db8c-491c-a721-6ec028d377f8 · outbound

This paper cites Optimal control problems with symmetry breaking cost functions.

Latent Lie-Poisson Neural Networks (LLPNNs): Discovering the motion of Lie-Poisson systems through observable data and latent dynamics Optimal control problems with symmetry breaking cost functions

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Resolution: unresolved; no resolver link, observed 2026-08-03T16:56:07.921636Z

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Observation 2f4ddd9a-5b4b-4ce5-b5c6-ab73e6b20318 · outbound

This paper cites Structure- preserving learning of nonholonomic dynamics.arXiv preprint arXiv:2603.27580, 2026.

Latent Lie-Poisson Neural Networks (LLPNNs): Discovering the motion of Lie-Poisson systems through observable data and latent dynamics Structure- preserving learning of nonholonomic dynamics.arXiv preprint arXiv:2603.27580, 2026

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Resolution: unresolved; no resolver link, observed 2026-08-03T16:56:08.012741Z

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Observation ecca129b-5c5d-4226-8738-345422a68a5e · outbound

This paper cites an unresolved cited work.

Latent Lie-Poisson Neural Networks (LLPNNs): Discovering the motion of Lie-Poisson systems through observable data and latent dynamics Unresolved cited work

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Resolution: unresolved; no resolver link, observed 2026-08-03T16:56:08.063197Z

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Observation d86f01e4-3cad-4ffd-ad3d-b80321452d0f · outbound

This paper cites an unresolved cited work.

Latent Lie-Poisson Neural Networks (LLPNNs): Discovering the motion of Lie-Poisson systems through observable data and latent dynamics Unresolved cited work

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Resolution: unresolved; no resolver link, observed 2026-08-03T16:56:08.133490Z

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Observation aa0e0ace-f5c0-4c44-972b-16acf6416a29 · outbound

This paper cites As shown below, the tangent space at the identity is naturally endowed with a commutator bracket.

Latent Lie-Poisson Neural Networks (LLPNNs): Discovering the motion of Lie-Poisson systems through observable data and latent dynamics As shown below, the tangent space at the identity is naturally endowed with a commutator bracket

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Resolution: unresolved; no resolver link, observed 2026-08-03T16:56:08.200447Z

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