On the Construction of Uncertain Time Series Surrogates Using Polynomial Chaos and Gaussian Processes

Abstract

The analysis of time series is a fundamental task in many flow simulations such as oceanic and atmospheric flows. A major challenge is the design of a faithful and accurate time-dependent surrogate built with a tractable sample set and a manageable number of degrees of freedom. Several techniques are implemented to handle the time-dependent aspect of the quantity of interest including uncoupled approaches, low-rank approximations, auto-regressive models and global Bayesian emulators. These approaches rely on two popular methods for uncertainty quantification: polynomial chaos and Gaussian process regression. The different techniques are tested and compared on the uncertain evolution of the sea surface height forecast at two locations exhibiting contrasting levels of variance. Two ensemble sizes are considered as well as two versions of polynomial chaos (ordinary least squares or ridge regression) and Gaussian processes (squared exponential or Matern covariance function) in order to assess their impact on the results. The conclusions focus on the advantages and the drawbacks, in terms of accuracy, flexibility and computational costs of the different techniques.