# Neural Approximators for Low-Thrust Trajectory Transfer Cost and Reachability

arXiv: https://arxiv.org/abs/2508.02911 · HTML: https://mlsanity.com/paper/2508.02911/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 41 references that are in the map.
- First posted on arXiv 4 Aug 2025.

## Builds on (most cited first, 5 of 5)

- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Neural representation of a time optimal, constant acceleration rendezvous](https://mlsanity.com/paper/2203.15490/) (2022)
- [Deep Networks as Approximators of Optimal Transfers Solutions in Multitarget Missions](https://mlsanity.com/paper/1902.00250/) (2019)
- [Analytical Shaping Method for Low-Thrust Rendezvous Trajectory Using Cubic Spline Functions](https://mlsanity.com/paper/2201.00101/) (2022)
- [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)

## Abstract (arXiv)

In trajectory design, fuel consumption and trajectory reachability are two key performance indicators for low-thrust missions. This paper proposes general-purpose pretrained neural networks to predict these metrics. The contributions of this paper are as follows: Firstly, based on the confirmation of the Scaling Law applicable to low-thrust trajectory approximation, the largest dataset is constructed using the proposed homotopy ray method, which aligns with mission-design-oriented data requirements. Secondly, the data are transformed into a self-similar space, enabling the neural network to adapt to arbitrary semi-major axes, inclinations, and central bodies. This extends the applicability beyond existing studies and can generalize across diverse mission scenarios without retraining. Thirdly, to the best of our knowledge, this work presents the current most general and accurate low-thrust trajectory approximator, with implementations available in C++, Python, and MATLAB. The resulting neural network achieves a relative error of 0.78% in predicting velocity increments and 0.63% in minimum transfer time estimation. The models have also been validated on a third-party dataset, multi-flyby mission design problem, and mission analysis scenario, demonstrating their generalization capability, predictive accuracy, and computational efficiency.