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 Matérn 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.

中文翻译：

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利用多项式混沌和高斯过程构造不确定的时间序列代理

在许多流模拟中，例如海洋和大气流，时间序列分析是一项基本任务。一个主要的挑战是设计一个忠实且准确的与时间相关的替代方案，该替代方案具有易于处理的样本集和可管理的自由度。已实现多种技术来处理感兴趣量的时间相关方面，包括非耦合方法，低秩逼近，自回归模型和全局贝叶斯仿真器。这些方法依靠两种流行的不确定性量化方法：多项式混沌和高斯过程回归。测试和比较了不同的技术，以比较显示出方差相反水平的两个地点的海面高度预报的不确定演变。为了评估它们对结果的影响，考虑了两个集合大小以及两个版本的多项式混沌（普通最小二乘或岭回归）和高斯过程（平方指数或Matérn协方差函数）。结论集中于不同技术的准确性，灵活性和计算成本方面的优缺点。