Abstract
Abstract
Diffusion models trained on pre-computed optimal trajectories
have recently been shown to accelerate direct-method spacecraft
trajectory optimization by generating high-quality warm starts,
reducing the number of solver attempts needed. However, a
diffusion-generated candidate's dynamical feasibility is currently
either checked entirely by the downstream nonlinear program (NLP)
solver or not checked at all prior to that refinement step. This
work proposes and demonstrates a generate-then-verify framework
that pairs a diffusion model with an independent, computationally
cheap consistency check based on a quadrature-based Extended
Dynamic Mode Decomposition (qEDMD) Koopman operator, applied to a
stationkeeping correction scenario in the Circular Restricted
Three-Body Problem (CR3BP). A dataset of 10,000 fuel-conscious
correction trajectories was generated via a direct-method NLP with
homotopy continuation, used to train a diffusion model, and
independently verified via a Koopman-based residual and
minimum-movement check. Negative-control testing, using four
categories of deliberately corrupted candidate trajectories,
confirmed the verifier reliably discriminates invalid from valid
trajectories (100% detection, 0% false-positive rate on held-out
real data). Applied to 200 diffusion-generated candidates, only one
was flagged by the verifier; an independent constraint-violation
check confirmed this flagged candidate exhibited a mean deviation
from true dynamics roughly 14.7x larger than the average across
unflagged candidates. The Koopman check is best understood not as a
feasibility guarantee, but as an inexpensive consistency screen
capable of identifying grossly inconsistent candidates before
expensive downstream refinement.