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arXiv · 2305.05540

Direct Poisson neural networks: Learning non-symplectic mechanical systems

Martin Šípka·Michal Pavelka·Oğul Esen·Miroslav Grmela
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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.

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Martin Šípka, Michal Pavelka, Oğul Esen, Miroslav Grmela. 2023-05-07. Direct Poisson neural networks: Learning non-symplectic mechanical systems. https://arxiv.org/abs/2305.05540

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