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Direct Poisson neural networks: learning non-symplectic mechanical systems

Martin Šípka, Michal Pavelka, Oğul Esen and Miroslav Grmela

Article (2023)

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Abstract

In this paper, we present neural networks learning mechanical systems that are both symplectic (for instance particle mechanics) and non-symplectic (for instance rotating rigid body). Mechanical systems have Hamiltonian evolution, which consists of two building blocks: a Poisson bracket and an energy functional. We feed a set of snapshots of a Hamiltonian system to our neural network models which then find both the two building blocks. In particular, the models distinguish between symplectic systems (with non-degenerate Poisson brackets) and non-symplectic systems (degenerate brackets). In contrast with earlier works, our approach does not assume any further a priori information about the dynamics except its Hamiltonianity, and it returns Poisson brackets that satisfy Jacobi identity. Finally, the models indicate whether a system of equations is Hamiltonian or not.

Uncontrolled Keywords

machine learning; Hamiltonian mechanics; non-symplectic; neural networks; Poisson

Department: Department of Chemical Engineering
Funders: Grantová Agentura České Republiky
Grant number: 23-05736S
PolyPublie URL: https://publications.polymtl.ca/56705/
Journal Title: Journal of Physics A (vol. 56, no. 49)
Publisher: Institute of Physics
DOI: 10.1088/1751-8121/ad0803
Official URL: https://doi.org/10.1088/1751-8121/ad0803
Date Deposited: 15 Dec 2023 15:39
Last Modified: 10 Apr 2024 03:16
Cite in APA 7: Šípka, M., Pavelka, M., Esen, O., & Grmela, M. (2023). Direct Poisson neural networks: learning non-symplectic mechanical systems. Journal of Physics A, 56(49), 495201 (25 pages). https://doi.org/10.1088/1751-8121/ad0803

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