Port-Hamiltonian system: structure recognition and applications

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Abstract

In this paper, we continue to consider the problem of recovering the port-Hamiltonian structure for an arbitrary system of differential equations. We complement our previous study on this topic by explaining the choice of machine learning algorithms and discussing some details of their application. We also consider the possibility provided by this approach for a potentially new definition of canonical forms and classification of systems of differential equations.

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About the authors

V. N. Salnikov

University of La Rochelle

Author for correspondence.
Email: vladimir.salnikov@univ-lr.fr
France, Av. Michel Crépeau, La Rochelle, 17042, Paris

References

  1. Salnikov V., Hamdouni A., Loziienko D., Generalized and graded geometry for mechanics: a comprehensive introduction // Mathematics and Mechanics of Complex Systems. 2021. V. 9. № 1. 2021.
  2. Salnikov V., Hamdouni A. Geometric integrators in mechanics: The need for computer algebra tools, Tr. Tret’ei Mezhdun. Konf. “Computer algebra” (Proc. 3rd Int. Conf. Computer Algebra), Moscow, 2019.
  3. Salnikov V.N., Hamdouni A. Differential geometry and mechanics: A source for computer algebra problems // Program. Comput. Software. 2020. V. 46. P. 126–132.
  4. Salnikov V., Falaize A., Lozienko D. Learning port-Hamiltonian systems: Algorithms // Comput. Math. Math. Phys. 2023. V. 63. P. 126–134.
  5. Paynter H.M. Analysis and Design of Engineering Systems // MIT Press, Cambridge, Massachusetts, 1961.
  6. A. van der Schaft. Port-Hamiltonian systems: an introductory survey // Proceedings of the International Congress of Mathematicians, Madrid, 2006.
  7. Sage Manifolds – Differential geometry and tensor calculus with SageMath, https://sagemanifolds.obspm.fr
  8. Falaize A. Modélisation, simulation, génération de code et correction de systèmes multi-physiques audios: Approche par réseau de composants et formulation hamiltonienne à ports, // PhD thesis, Télécommunication et Électronique de Paris, Université Pierre et Marie Curie, 2016.
  9. Modeling, simulation and code-generation of multiphysical Port-Hamiltonian Systems in Python: https://github.com/pyphs/pyphs
  10. Edler D., Holmgren A. Rosvall M., Infomap – Network community detection using the MapEquation framework, https://www.mapequation.org/infomap/
  11. Hairer E., Lubich C., Wanner G., Geometric Numerical Integration // Springer Series in Computational Mathematics, 2006.
  12. Razafindralandy D., Hamdouni A., Chhay M., A review of some geometric integrators // Advanced Modeling and Simulation in Engineering Sciences, SpringerOpen. 2018. V. 5 № 1. P. 16.
  13. Razafindralandy D., Salnikov V., Hamdouni A., Deeb A. Some robust integrators for large time dynamics // Advanced Modeling and Simulation in Engineering Sciences. 2019. V. 6. № 5.
  14. Cosserat O., Symplectic groupoids for Poisson integrators // Journal of Geometry and Physics, 2023. V. 186.
  15. Cosserat O., Laurent-Gengoux C., Salnikov V. // Numerical Methods in Poisson Geometry and their Application to Mechanics, Preprint: arXiv:2303.15883.

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