DeepAI AI Chat
Log In Sign Up

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

by   Pengzhan Jin, et al.
Brown University
Chinese Academy of Science
Johns Hopkins University

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.


page 8

page 9


Structure-preserving numerical methods for stochastic Poisson systems

We propose a class of numerical integration methods for stochastic Poiss...

Casimir preserving stochastic Lie-Poisson integrators

Casimir preserving integrators for stochastic Lie-Poisson equations with...

Poisson Integrators based on splitting method for Poisson systems

We propose Poisson integrators for the numerical integration of separabl...

Learning-based Design of Luenberger Observers for Autonomous Nonlinear Systems

The design of Luenberger observers for nonlinear systems involves state ...

Symplectic Groupoids for Poisson Integrators

We use local symplectic Lie groupoids to construct Poisson integrators f...

Towards Expressive Priors for Bayesian Neural Networks: Poisson Process Radial Basis Function Networks

While Bayesian neural networks have many appealing characteristics, curr...