Most ab initio simulation packages based on Density Functional Theory (DFT) use the Superposition of Atomic Densities (SAD) as a starting point of the self-consistent fi eld (SCF) iteration. However, this trial charge density without modeling atomic iterations nonlinearly may lead to a relatively slow or even failed convergence. This thesis proposes a machine learning-based scheme to improve the initial guess. We train a 3-Dimensional Convolutional Neural Network (3D CNN) to map the SAD initial guess to the corresponding converged charge density with simple structures. We show that the 3D CNN-processed charge density reduces the number of required SCF iterations at different unit cell complexity levels.

This concept of calculating, optimizing, and utilizing a trajectory known as a ``Free Return Trajectory" to facilitate spacecraft rendezvous with Near-Earth Asteroids is presented in this dissertation. A Free Return Trajectory may be defined as a trajectory that begins and ends near the same point, relative to some central body, without performing any deterministic velocity maneuvers (i.e., no maneuvers are planned in a theoretical sense for the nominal mission to proceed). Free Return Trajectories have been utilized previously for other purposes in astrodynamics, but they have not been previously applied to the problem of Near-Earth Asteroid rendezvous. Presented here is a series of descriptions, algorithms, and results related to trajectory initial guess calculation and optimal trajectory convergence. First, Earth-centered Free Return Trajectories are described in a general manner, and these trajectories are classified into several families based on common characteristics. Next, these trajectories are used to automatically generate initial conditions in the three-body problem for the purpose of Near-Earth Asteroid rendezvous. For several bodies of interest, example initial conditions are automatically generated, and are subsequently converged, resulting in feasible, locally-optimal, round-trip trajectories to Near-Earth Asteroids utilizing Free Return Trajectories. Subsequently, a study is performed on using an unpowered flyby of the Moon to lower the overall DV cost for a nominal round-trip voyage to a Near-Earth Asteroid. Using the Moon is shown to appreciably decrease the overall mission cost. In creating the formulation and algorithms for the Lunar flyby problem, an initial guess routine for generic planetary and lunar flyby tours was developed. This continuation algorithm is presented next, and details a novel process by which ballistic trajectories in a simplistic two-body force model may be iteratively converged in progressively more realistic dynamical models until a final converged ballistic trajectory is found in a full-ephemeris, full-dynamics model. This procedure is useful for constructing interplanetary transfers and moon tours in a realistic dynamical framework; an interplanetary and an inter-moon example are both shown. To summarize, the material in this dissertation consists of: novel algorithms to compute Free Return Trajectories, and application of the concept to Near-Earth Asteroid rendezvous; demonstration of cost-savings by using a Lunar flyby; and a novel routine to transfer trajectories from a simplistic model to a more realistic dynamical representation. / text