This paper demonstrates how artificial neural networks can be used to alleviate common problems encountered when creating a large database of Poincar´e map responses.A general architecture is developed using a co...This paper demonstrates how artificial neural networks can be used to alleviate common problems encountered when creating a large database of Poincar´e 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 Poincar´e 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 Poincar´e 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.展开更多
基金This work utilized the RMACC Summit supercomputer,which is supported by the National Science Foundation(awards ACI-1532235 and ACI-1532236)the University of Colorado Boulder,and Colorado State University.
文摘This paper demonstrates how artificial neural networks can be used to alleviate common problems encountered when creating a large database of Poincar´e 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 Poincar´e 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 Poincar´e 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.
