Ultra-fast Unscented Kalman Inversion for the Calibration of Expensive Reduced Chaotic Models

Abstract. The high-fidelity computer models traditionally used for weather and climate prediction have extremely high computational costs. While reduced models exist, their utility is limited in part because their calibration poses a host of difficulties, including chaotic dynamics that prevent the use of adjoint methods, computational costs that become unreasonable when sampling approaches require many forward runs with long ergodic trajectories, and large existing code bases in legacy languages that necessitate black-box approaches. Recently, unscented Kalman inversion (UKI) methods have shown promise for such models by providing approximate derivatives of parameters in order to reach convergence using relatively few forward model runs through the use of gradient approximation. However, previous UKI applications have required expensive ergodic trajectories. Inspired by recent work in consistency testing for climate models, multi-fidelity methods, and multiple-shooting techniques in controls theory, we present a new approach that instead samples many ultra-short model trajectories to reduce calibration cost and greatly increase opportunities for parallelism. Numerical examples include calibration of a canonical chaotic test case and a simplified climate model.