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

该项目将通过现场实验开发和验证一种新的真正的动态方法，以预测海洋状态和相关的不确定性，该方法基于低维随机建模，利用多元海洋的多尺度动力学。其主要思想是采用一些时间演化的POD（适当正交分解）模式来参数化慢流形，然后使用无伽辽金/无方程过程以大时间步进推进解。这种方法与通常用于生成降阶建模的演化方程的标准伽辽金方法有着根本的不同。具体来说，新方法仅使用基于区域海洋模式系统（ROMS）和现有实验数据的全面模拟，提供本质上的“按需关闭”，以执行无方程的时间演化。在这种多尺度方法中，通过ROMS进行的全模拟解决了精细尺度，而Galerkin-free/POD方法-粗分量-以大时间步长传播速度，温度和盐度的最高能量模式以及相应的不确定场。利用马萨诸塞湾的真实数据进行的初步模拟表明，只有几种模式足以描述最有趣的海洋动力学，并且在无伽辽金程序中可以使用几个小时的时间步长，而不是几秒或几分钟。这些结果证明了所提出方法的可行性，并意味着这种需要非常小的计算成本和通信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被赋予了导航智能和真正的自主性。该方法将通过完整的ROMS模拟进行验证，并将在科德角湾进行三次现场实验。该计划第三年的最后一个实验将展示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拨款任务的独特专业知识。该项目的总体贡献是实时预测海洋状态的新范例。基本的具体贡献包括构建时变协方差核，以获得时变POD模式；无伽辽金多尺度过程中射影时间积分的数值分析；用自适应广义多项式混沌表示不确定性预测的随机性以及遵循DDDAS精神的严格的海洋数据收集协议。

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.