# Pretrained Approximators for Low-Thrust Trajectory Cost and Reachability

arXiv: https://arxiv.org/abs/2605.26790 · HTML: https://mlsanity.com/paper/2605.26790/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 70 references that are in the map.
- First posted on arXiv 26 May 2026.

## Builds on (most cited first, 17 of 17)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Real-time optimal control via Deep Neural Networks: study on landing problems](https://mlsanity.com/paper/1610.08668/) (2016)
- [Real-Time Optimal Control for Irregular Asteroid Landings Using Deep Neural Networks](https://mlsanity.com/paper/1901.02210/) (2019)
- [On the stability analysis of deep neural network representations of an optimal state-feedback](https://mlsanity.com/paper/1812.02532/) (2018)
- [Neural representation of a time optimal, constant acceleration rendezvous](https://mlsanity.com/paper/2203.15490/) (2022)
- [Learning the optimal state-feedback via supervised imitation learning](https://mlsanity.com/paper/1901.02369/) (2019)
- [Deep Networks as Approximators of Optimal Transfers Solutions in Multitarget Missions](https://mlsanity.com/paper/1902.00250/) (2019)
- [Adaptive Guidance and Integrated Navigation with Reinforcement Meta-Learning](https://mlsanity.com/paper/1904.09865/) (2019)
- [Solar-Sail Trajectory Design for Multiple Near Earth Asteroid Exploration Based on Deep Neural Networks](https://mlsanity.com/paper/1901.02172/) (2019)
- [Optimality Principles in Spacecraft Neural Guidance and Control](https://mlsanity.com/paper/2305.13078/) (2023)
- [How Many Impulses Redux](https://mlsanity.com/paper/1906.01839/) (2019)
- [Asteroid Flyby Cycler Trajectory Design Using Deep Neural Networks](https://mlsanity.com/paper/2111.11858/) (2021)
- [Closing the Gap Between SGP4 and High-Precision Propagation via Differentiable Programming](https://mlsanity.com/paper/2402.04830/) (2024)
- [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)
- [Global Optimality in Multi-Flyby Asteroid Trajectory Optimization: Theory and Application Techniques](https://mlsanity.com/paper/2508.02904/) (2025)

## Abstract (arXiv)

Low-thrust trajectory design relies heavily on repeated evaluations of fuel consumption and transfer feasibility, which require expensive optimal control solutions. In this work, we show these quantities can be accurately approximated by machine learning surrogates, enabling fast and scalable evaluation across a wide range of scenarios. By increasing both dataset size and model capacity, we observe that low-thrust trajectory optimization follows a scaling law, with performance improving linearly with the logarithm of training data and network parameters, and no evidence of saturation within the explored regime. Guided by this observation, we construct a large-scale dataset using the proposed homotopy-ray strategy tailored to mission design requirements. A key is the introduction of a self-similar transformation, which allows generalization across semi-major axes, inclinations, and central bodies avoiding retraining. As a result, the same neural approximator can be applied to diverse orbital environments and mission classes. The proposed models accurately predict optimal fuel consumption and minimum transfer time for single- and multi-revolution transfers. Their performance and generalization are demonstrated on a public dataset, a multi-asteroid flyby problem from the Global Trajectory Optimization Competition, and an asteroid rendezvous mission design. The models and datasets are released as open-source to support the space community.