DDDAS-Collaborative Proposal: Multiscale Data-Driven POD-Based Prediction of the Ocean

该项目将在利用多变量海洋的多尺度动力学的低维随机建模的基础上，开发和验证一种新的真正动态的方法来预测海洋状况和相关的不确定性。其主要思想是使用几个时间演化的POD(真正交分解)模式来参数化慢流形，然后使用无Galerkin/无方程的方法以大的时间步长推进解。这种方法从根本上不同于标准的Galerkin方法，该方法通常用于生成用于降阶建模的演化方程。具体地说，新方法只使用基于区域海洋模式系统(ROMS)和现有实验数据的一连串完整模拟，本质上提供了一种“按需关闭”，以便执行无方程的时间演化。在这种多尺度方法中，通过ROMS进行的完全模拟解决了细尺度问题，而粗略分量Galerkin-Free/POD方法以大的时间步长传播了最高能量的速度、温度和盐度模式以及相应的不确定性场。使用马萨诸塞湾的真实数据进行的初步模拟表明，只有少数几个模式足以描述最有趣的海洋动力学，在Galerkin-Free过程中可以使用几个小时的时间步长，而不是秒或分钟。这些结果证明了该方法的可行性，并表明这种只需要很小的计算量和通信量的快速预测确实可以在自主水下航行器(AUV)上执行。因此，这些AUV被赋予导航智能和真正的自主性。该方法将通过全ROMS模拟进行验证，并将通过在科德角海湾进行的三个现场实验进行验证。该计划第三年的最后实验将演示海洋预报中的DDDAS概念。该项目将利用AUV舰队和其他测量资源，以及麻省理工学院海洋赠款这类任务的独特专业知识。该项目的总体贡献是在实时预测海洋状态方面的一个新范式。基本的具体贡献包括构建获得随时间演变的POD模式所需的依赖时间的协方差核；对无Galerkin多尺度程序中涉及的投影时间积分进行数值分析；通过用于不确定性预测的自适应广义多项式混沌来表示随机性；以及本着DDDAS的精神在海洋中收集数据的严格协议。

The project will develop and validate with field experiments a new truly dynamic approach in forecasting the ocean state and associated uncertainties based on low-dimensional stochastic modeling that exploits the multiscale dynamics of the multivariate ocean. The main idea is to employ a few time-evolving POD (proper orthogonal decomposition) modes to parametrize the slow manifold, and subsequently to advance the solutionwith a large time step using a Galerkin-free/equation-free procedure. This approach is fundamentally different from the standard Galerkin method used often to produce evolution equations for reduced order modeling. Specifically, the new method uses only bursts of full simulations based on the Regional Ocean Model System (ROMS) and available experimental data, providing in essence a "closure-on-demand", in order to perform an equation-free time evolution. In such multiscale approach, the full simulation through ROMS resolves the fine scales whereas the Galerkin-free/POD method - the coarse component - propagates with large time steps the most energetic modes of velocity, temperature and salinity and corresponding uncertainty fields.Preliminary simulations using realistic data for the Massachusetts Bay suggest thatonly a few modes are sufficient in describing the most interesting ocean dynamics, and that time steps of a few hours, instead of seconds or minutes, can be used in the Galerkin- free procedure. These results demonstrate feasibility of the proposed approach and imply that such fast predictions requiring very small computational cost and communications can indeed be performed on board of autonomous underwater vehicles (AUVs). Hence, these AUVs are endowed with navigation intelligence and true autonomy. This approach will be verified with full ROMS simulations and will be validated with three field experiments in the Cape Cod Bay. The final experiment in the third year of theprogram will demonstrate the DDDAS concept in ocean forecasting. The project willleverage the AUV fleet and other measurement resources as well as unique expertise for such missions of the MIT Sea Grant. The overall contribution of this project is a new paradigm in predicting the ocean state in real-time. Fundamental specific contributions include construction of time-dependent covariance kernels required in obtaining time-evolving POD modes; numerical analysis of the projective time-integration involved in the Galerkin-free multiscale procedure; representation of stochasticity via adaptive generalized polynomial chaos for uncertainty predictions; and rigorous protocols for data gathering in the ocean in the spirit of DDDAS.