# Deep Networks as Approximators of Optimal Transfers Solutions in Multitarget Missions

## TL;DR

This paper demonstrates that deep neural networks can accurately estimate optimal transfer solutions in multitarget interplanetary missions, significantly speeding up preliminary mission design processes.

## Contribution

The study introduces a deep learning approach to estimate optimal transfer parameters, outperforming traditional methods in speed and accuracy for complex space mission trajectory optimization.

## Key findings

- Deep networks achieve less than 0.5% error for low-thrust transfer estimates.
- Deep networks achieve less than 4% error for multi-impulse transfer estimates.
- Deep learning models outperform other machine learning algorithms in this context.

## Abstract

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.