Improving the efficiency of dynamic completeness calculations for exoplanet direct imaging

Direct exoplanet imaging mission studies use dynamic completeness, the probability of detecting a planet given prior observations, to guide scheduling and estimate yield. Computing it is challenging: brute-force Monte Carlo is expensive, and common approximations often miss the true evolution of detectability. We analyze the numerical behavior of dynamic completeness, identifying cost- and accuracy-dominant steps, including repeated Kepler-equation solves and the mapping from orbital elements to observables. We further introduce a reduced-order uncertainty-propagation framework that carries orbital and photometric uncertainties through parameter distributions, enabling efficient, uncertainty-aware completeness estimates for the Roman Space Telescope Coronagraph Instrument.