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

该项目将开发并通过实地实验验证一种新的真正动态的方法，以利用多变量海洋的多尺度动态的低维随机建模为基础，预测海洋状况和相关的不确定性。其主要思想是采用几个时间演变的POD（适当的正交分解）模式参数化的慢流形，并随后推进solutionwith一个大的时间步长使用Galerkin自由/方程自由的程序。这种方法是从根本上不同于标准的Galerkin方法经常使用的降阶建模产生的发展方程。具体而言，新方法仅使用基于区域海洋模型系统和现有实验数据的全面模拟的突发，实质上提供了“按需关闭”，以便进行无方程的时间演变。在这种多尺度方法中，通过ROMS的完整模拟解决了精细尺度，而Galerkin自由/POD方法-粗分量-以大的时间步长传播速度，温度和盐度以及相应的不确定性场的最具活力的模式。使用马萨诸塞州湾的实际数据进行的初步模拟表明，只有少数模式足以描述最有趣的海洋动力学，并且在无伽辽金过程中可以使用几小时的时间步长，而不是几秒或几分钟。这些结果表明，所提出的方法的可行性，并意味着这种快速的预测需要非常小的计算成本和通信，确实可以在船上的自主水下航行器（AUV）。因此，这些AUV具有导航智能和真正的自主性。这种方法将得到验证，充分的ROMS模拟，并将在科德角湾的三个现场实验进行验证。该计划第三年的最后一次实验将展示DDDAS在海洋预报中的概念。 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的独特专业知识进行此类任务。该项目的总体贡献是实时预测海洋状态的新范式。基本的具体贡献包括建设所需的随时间变化的协方差内核获得时间演变的POD模式;数值分析的投影时间积分参与的Galerkin自由多尺度程序;表示随机性通过自适应广义多项式混沌的不确定性预测;和严格的协议，在海洋中的DDDAS的精神，数据收集。

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.