Deep Neural Network-Based High-Precision Identification of Weak Stability Boundary Structures

Weak stability boundary structures have been widely applied to the analysis on ballistic capture and the construction of low-energy transfers. The first step of this application is to compute/identify weak stability boundary structures. Conventional numerical and analytical methods cannot simultaneously achieve computational efficiency and identification precision. In this article, we propose an efficient and precise method to identify weak stability boundary structures in the Earth–Moon planar circular restricted three-body problem based on deep neural network. The geometric and dynamical properties of weak stability boundary structures are first analyzed, which provides further insights into the training of the deep neural network models. Then, the optimal hyperparameter combinations of the DNN model are determined by prioritizing the identification precision while ensuring the recall. The performance of the models with the optimal hyperparameter combinations is further validated using the representative test datasets, achieving a precision of 97.26$\%$ to 99.91$\%$. The trained models are applied to constructing weak stability boundary structures, improving the computational efficiency over the conventional numerical method. Finally, the identified weak stability boundary structures are applied to the construction of ballistic capture trajectories with respect to the Moon.