Learning Poisson systems and trajectories of autonomous systems via Poisson neural networks

Code that ran

We have not lifted any functions out of this paper's repositories yet, so there is nothing we have run. If it links a repository, it is listed below.

Repositories linked to this paper

jpzxshi/learner — marked official in Papers with Code

Some links come from the archived Papers with Code dataset (CC BY-SA 4.0): attribution and licence.

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 Schr{ö}dinger equation, and pixel observations of the two-body problem.

For agents

The same record, over MCP at https://syntology.ai/mcp:

get_harvested_code_for_paper("2012.03133")
get_code_for_paper("2012.03133")
have("2012.03133")

Connect an agent — have() is free.