In the design of multitarget interplanetary missions, there are always many options available, making it often impractical to optimize in detail each transfer trajectory in a preliminary search phase. Fast and accurate estimation methods for optimal transfers are thus of great value. In this paper, deep feed-forward neural networks are employed to estimate solutions to three types of optimization problems: the transfer time of time-optimal low-thrust transfers, fuel consumption of fuel-optimal low-thrust transfers, and the total ∆v of minimum-∆v J 2 -perturbed multi-impulse transfers. To generate the training data, low-thrust trajectories are optimized using the indirect method and J 2 -perturbed multi-impulse trajectories are optimized using J 2 homotopy and particle swarm optimization. The hyper-parameters of our deep networks are searched by grid search, random search, and the tree-structured Parzen estimators approach. Results show that deep networks are capable of estimating the final mass or time of optimal transfers with extremely high accuracy; resulting into a mean relative error of less than 0.5% for low-thrust transfers and less than 4% for multi-impulse transfers. Our results are also compared with other off-the-shelf machine-learning algorithms and investigated with respect to their capability of predicting cases well outside of the training data. Nomenclature a = semi-major axis e = eccentricity i = inclination Ω = right ascension of ascending node * PhD Candidate, School of Aerospace Engineering, lihy15@mails.tsinghua.edu.cn. † Graduate Student, School of Aerospace Engineering, chen-sy16@mails.tsinghua.edu.cn.
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