Transfer Learning of Multiobjective Indirect Low-Thrust Trajectories Using Diffusion Models and Markov Chain Monte Carlo

Preliminary low-thrust spacecraft mission design is a global search problem characterized by a complex solution landscape, multiple objectives, and numerous local minima. During this phase, mission parameters are often not yet fully defined, requiring new solutions to be generated at a high cadence across varying parameter values. When combined with the indirect approach to optimal control, diffusion models can accelerate this search by learning distributions that represent high-quality initial costates. However, generating training data remains expensive, and opportunities exist to better exploit past data. We propose a transfer-learning framework that combines homotopy in a mission parameter with Markov chain Monte Carlo (MCMC) to generate training data more efficiently. The approach reformulates a multiobjective optimization problem as sampling from an unnormalized target distribution in costate space. We compare three MCMC algorithms on a planar multi-revolution transfer in the circular restricted three-body problem, with homotopy in the system mass parameter. The results show that gradient-based MCMC variants achieve the best trade-off between sample quality and computational cost. For the test transfer, the proposed framework generates 40 % more feasible solutions and achieves a higher-quality Pareto front than a state-of-the-art indirect approach based on adjoint control transformations and gradient-based optimization. Finally, the MCMC-generated samples are used to fine-tune a diffusion model conditioned on the mass parameter, enabling it to learn a global representation of the underlying solution distribution and efficiently generate new solutions. These findings establish the transfer-learning framework as a practical method for efficiently solving indirect trajectory optimization problems with varying parameters.