Bayesian optimization for tuning chaotic systems

In this work, we consider the Bayesian optimization (BO) approach for tuning parameters of complex chaotic systems. Such problems arise, for instance, in tuning the sub-grid scale parameterizations in weather and climate models. For such problems, the tuning procedure is generally based on a performance metric which measures how well the tuned model fits the data. This tuning is often a computationally expensive task. We show that BO, as a tool for finding the extrema of computationally expensive objective functions, is suitable for such tuning tasks. In the experiments, we consider tuning parameters of two systems: a simplified atmospheric model and a low-dimensional chaotic system. We show that BO is able to tune parameters of both the systems with a low number of objective function evaluations and without the need of any gradient information.