  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
dv of minimum-dv J2-perturbed multi-impulse transfers. To generate the training
data, low-thrust trajectories are optimized using the indirect method and
J2-perturbed multi-impulse trajectories are optimized using J2 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.
