用Transformer自动求解地月三体问题的边界值问题。
A Prefixed Patch Time Series Transformer for Two-Point Boundary Value Problems in Three-Body Problems
- 用前缀标记终端条件，让Transformer直接生成轨迹。
- 训练数据来自前向传播，无需手动求解边界值。
- 适合地月任务初轨设计，效率高于传统方法。
地月轨道的两点边界值问题在限制性三体模型中极具挑战，传统解析方法如Lambert问题不再适用。本文提出一种基于前缀补丁的时间序列Transformer模型，可自动求解从月球飞越到任意终端条件的边界值问题。通过在深度生成模型中引入终端条件的前缀标记，实现了三体动力学中边界值问题的端到端求解。训练数据由前向传播生成的轨迹构成，而非直接求解边界值问题。该模型在地月任务初步轨迹设计中展现出实际应用潜力。
原文摘要 · Abstract (English)
Two-point boundary value problems for cislunar trajectories present significant challenges in circler restricted three body problem, making traditional analytical methods like Lambert's problem inapplicable. This study proposes a novel approach using a prefixed patch time series Transformer model that automates the solution of two-point boundary value problems from lunar flyby to arbitrary terminal conditions. Using prefix tokens of terminal conditions in our deep generative model enables solving boundary value problems in three-body dynamics. The training dataset consists of trajectories obtained through forward propagation rather than solving boundary value problems directly. The model demonstrates potential practical utility for preliminary trajectory design in cislunar mission scenarios.
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