Direct Poisson neural networks: Learning non-symplectic mechanical systems

2023/05/07 by Šípka, Martin, Pavelka, Michal, Esen, Oğul +1 · 1 citation
#Computational Physics (physics.comp-ph) #Data Analysis #FOS: Physical sciences #Mathematical Physics (math-ph) #Statistics and Probability (physics.data-an)

paper · doi:10.48550/arxiv.2305.05540

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

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