학술논문
Learning Poisson Systems and Trajectories of Autonomous Systems via Poisson Neural Networks
Document Type
Periodical
Author
Source
IEEE Transactions on Neural Networks and Learning Systems IEEE Trans. Neural Netw. Learning Syst. Neural Networks and Learning Systems, IEEE Transactions on. 34(11):8271-8283 Nov, 2023
Subject
Language
ISSN
2162-237X
2162-2388
2162-2388
Abstract
We propose the Poisson neural networks (PNNs) to learn Poisson systems and trajectories of autonomous systems from data. Based on the Darboux–Lie theorem, the phase flow of a Poisson system can be written as the composition of: 1) a coordinate transformation; 2) an extended symplectic map; and 3) the inverse of the transformation. In this work, we extend this result to the unknotted trajectories of autonomous systems. We employ structured neural networks with physical priors to approximate the three aforementioned maps. We demonstrate through several simulations that PNNs are capable of handling very accurately several challenging tasks, including the motion of a particle in the electromagnetic potential, the nonlinear Schrödinger equation, and pixel observations of the two-body problem.