Physics informed generative design of invariant manifolds in the circular restricted three body problem

Abstract

The increasing prevalence of small spacecraft platforms in Cis-Lunar space has underscored the need for computationally efficient and fuel-optimal trajectory design methods. Invariant manifolds in multi-body gravitational systems provide natural, low-energy pathways for space missions, but their computation remains reliant on numerically intensive techniques that require integration of the variational equations and sampling across large families of periodic orbits. These methods are poorly suited for onboard computation or rapid preliminary analysis. This thesis proposes a physics-informed generative framework for invariant manifold design in the Circular Restricted Three Body Problem (CR3BP), using a Vector Quantised Variational Autoencoder (VQ-VAE) trained on trajectory data associated with Earth–Moon L1 halo orbits. The model learns a discrete latent representation of the manifold geometry conditioned on physical parameters such as Jacobi constant and manifold branch. A physics-consistent loss is introduced to enforce compliance with the CR3BP dynamics during training. The results presented in this work demonstrate the feasibility of using generative deep learning models to approximate invariant manifold structures in the CR3BP. By learning a discrete latent representation of manifold trajectories directly from trajectory data, the proposed model provides a novel, data-driven perspective on a classic problem in astrodynamics. This work represents an initial step toward the use of generative models in astrodynamics. It offers a foundation for further exploration of latent-space representations, and highlights the potential for deep learning to support manifold discovery, low-energy transfer design, and the generation of physically consistent trajectories without reliance on traditional generating orbit methods.