Title: Forecasting the evolution of three-dimensional turbulent recirculating flows from sparse sensor data Show Chinese title

Title: 从稀疏传感器数据预测三维湍流回流流动的演变

Abstract: A data-driven algorithm is proposed that employs sparse data from velocity and/or scalar sensors to forecast the future evolution of three dimensional turbulent flows. The algorithm combines time-delayed embedding together with Koopman theory and linear optimal estimation theory. It consists of 3 steps; dimensionality reduction (currently POD), construction of a linear dynamical system for current and future POD coefficients and system closure using sparse sensor measurements. In essence, the algorithm establishes a mapping from current sparse data to the future state of the dominant structures of the flow over a specified time window. The method is scalable (i.e.\ applicable to very large systems), physically interpretable, and provides sequential forecasting on a sliding time window of prespecified length. It is applied to the turbulent recirculating flow over a surface-mounted cube (with more than $10^8$ degrees of freedom) and is able to forecast accurately the future evolution of the most dominant structures over a time window at least two orders of magnitude larger that the (estimated) Lyapunov time scale of the flow. Most importantly, increasing the size of the forecasting window only slightly reduces the accuracy of the estimated future states. Extensions of the method to include convolutional neural networks for more efficient dimensionality reduction and moving sensors are also discussed. Show Chinese abstract

Abstract: 提出了一种基于数据驱动的算法，该算法利用来自速度和/或标量传感器的稀疏数据来预测三维湍流的未来演化。 该算法结合了时延嵌入以及Koopman理论和线性最优估计理论。 它由3个步骤组成；降维（目前为POD），构建用于当前和未来POD系数的线性动力系统，以及使用稀疏传感器测量值进行系统闭合。 本质上，该算法建立了从当前稀疏数据到指定时间窗口内流的主要结构未来状态的映射。 该方法具有可扩展性（即适用于非常大的系统）、物理可解释，并且能够在预设长度的滑动时间窗口上提供序列化的预测。 该方法应用于表面安装立方体上的湍流回流流动（具有超过$10^8$个自由度），并且能够准确预测最主导结构在未来窗口中的演化，该窗口至少比流的（估计）李雅普诺夫时间尺度大两个数量级。 最重要的是，增加预测窗口的大小只会略微降低对未来状态估计的准确性。 文中还讨论了将该方法扩展以包括卷积神经网络以实现更高效的降维和移动传感器的应用。