用神经网络精准预测低推力轨道转移的燃料与可达性，无需重新训练。
Neural Approximators for Low-Thrust Trajectory Transfer Cost and Reachability
- 构建大规模数据集并转换至自相似空间，实现跨天体通用。
- 预测速度增量误差仅0.78%，最小转移时间误差0.63%。
- 支持多任务场景，适合航天任务设计与快速仿真应用。
在低推力轨道设计中，燃料消耗与可达性是关键性能指标。本文提出通用预训练神经网络以预测这些指标。首先，基于低推力轨迹近似中的尺度律验证，采用提出的同伦射线法构建了最大规模数据集，符合任务设计导向的数据需求。其次，将数据映射至自相似空间，使神经网络可适应任意半长轴、倾角及中心天体，突破现有研究局限，无需重训即可推广至多样任务场景。第三，据我们所知，这是目前最通用且最准确的低推力轨道近似器，支持C++、Python和MATLAB实现。模型在速度增量预测上相对误差为0.78%，最小转移时间估计误差为0.63%。已在第三方数据集、多飞掠任务设计与任务分析场景中验证，展现出良好泛化能力、预测精度与计算效率。
原文摘要 · Abstract (English)
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.
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