Autoencoder Neural Networks for Representations of Periodic Orbit Families

Traditional methods for parameterizing and storing periodic orbit families use discretized representations of the family. In this work, continuous parameterizations of periodic orbit families in the Earth/Moon system are developed using techniques from machine learning. Autoencoder neural networks are used to parameterize periodic orbit families in terms of a single, continuous parameter and a discrete angle. The recovered one-dimensional latent space is monotonic and allows for the unique identification of an orbit throughout a family. This work also demonstrates the ability of a single autoencoder neural network to generate orbits across multiple families in the Circular Restricted Three-Body Problem (CR3BP) connected using a bifurcation diagram. The approach allows for a versatile and efficient method to generate orbits in the CR3BP and can be applied to mission design and trajectory optimization.