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

arXiv: https://arxiv.org/abs/1902.00250 · HTML: https://mlsanity.com/paper/1902.00250/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Feb 2019.

## Built on by (most cited first, 8 of 8)

- [Neural representation of a time optimal, constant acceleration rendezvous](https://mlsanity.com/paper/2203.15490/) (2022)
- [Asteroid Flyby Cycler Trajectory Design Using Deep Neural Networks](https://mlsanity.com/paper/2111.11858/) (2021)
- [Computing low-thrust transfers in the asteroid belt, a comparison between astrodynamical manipulations and a machine learning approach](https://mlsanity.com/paper/2405.18918/) (2024)
- [Fast solver for J2-perturbed Lambert problem using deep neural network](https://mlsanity.com/paper/2201.02942/) (2022)
- [Feasible Low-thrust Trajectory Identification via a Deep Neural Network Classifier](https://mlsanity.com/paper/2202.04962/) (2022)
- [Efficient low-thrust trajectory data generation based on generative adversarial network](https://mlsanity.com/paper/2209.06427/) (2022)
- [Neural Approximators for Low-Thrust Trajectory Transfer Cost and Reachability](https://mlsanity.com/paper/2508.02911/) (2025)
- [Pretrained Approximators for Low-Thrust Trajectory Cost and Reachability](https://mlsanity.com/paper/2605.26790/) (2026)

## Abstract (arXiv)

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.