Project

Exploring Bayesian Regression Techniques

Goal: The goal is to explore modern regression techniques providing statistical inference and apply them to various problems of interest across different fields. We want to begin with understanding the Gaussian Process Regression (GPR) as a powerful ML tool and work our way to more advanced topics.

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Sandeep Singh
added a research item
A supervised machine learning approach called the Gaussian Process Regression (GPR) is applied to approximate the optimal bi-impulse rendezvous maneuvers in cis-lunar space. The use of GPR approximation of the optimal bi-impulse transfer to patch-points associated with various invariant manifolds in the cis-lunar space is demonstrated. The proposed method advances preliminary mission design operations by avoiding the computational costs associated with repeated solution of the optimal bi-impulsive Lambert transfer because the learned map is efficient to compute. This approach promises to be useful for aiding preliminary mission design. The use of invariant manifolds as part of the transfer trajectory design offers unique features in reducing propellant consumption while facilitating the solution of the trajectory optimization problems. Long ballistic capture coasts are also very attractive for mission guidance, navigation and control robustness. A multi-input single-output GPR model is shown to efficiently represent the fuel costs (in terms of the $\Delta$V magnitude) associated with the class of orbital transfers of interest. A multi-input multi-output GPR model is developed and shown to provide efficient approximations. Multi-resolution use of local GPRs over smaller sub domains, and their use to construct a global GPR model is also demonstrated. One of the unique features of GPRs is to provide an estimate on the quality of the approximations in the form of covariance, which is shown to provide statistical consistency to the optimal trajectories generated from the approximation process. Numerical results demonstrate a basis for optimism for the utility of the proposed method.
Sandeep Singh
added a project goal
The goal is to explore modern regression techniques providing statistical inference and apply them to various problems of interest across different fields. We want to begin with understanding the Gaussian Process Regression (GPR) as a powerful ML tool and work our way to more advanced topics.