Representing dynamics in the eccentric Hill system using a neural network architecture

摘要

This paper demonstrates how artificial neural networks can be used to alleviate common problems encountered when creating a large database of Poincare map responses. A general architecture is developed using a combination of regression and classification feedforward neural networks. This allows one to predict the response of the Poincare map, as well as to identify anomalies, such as impact or escape. Furthermore, this paper demonstrates how an artificial neural network can be used to predict the error between a more complex and a simpler dynamical system. As an example application, the developed architecture is implemented on the Sun-Mars eccentric Hill system. Error statistics of the entire architecture are computed for both one Poincare map and for iterated maps. The neural networks are then applied to study the long-term impact and escape stability of trajectories in this system.