论文标题
在机器学习和数据同化的交集时，地球物理流的无方程式替代建模
Equation-free surrogate modeling of geophysical flows at the intersection of machine learning and data assimilation
论文作者
论文摘要
人们对开发数据驱动的减少阶模型的兴趣越来越大，以用于大气和海洋流，这些模型是根据从高分辨率模拟或卫星观测值获得的数据进行培训的。与大规模数值模型相比，数据驱动的模型本质上是非侵入性的，并提供了可观的计算节省。这些低维模型可用于减少产生预测和估算模型不确定性的计算负担，而不会丢失数据同化所需的关键信息以产生准确的状态估计。本文旨在在地球系统建模中机器学习和数据同化的交集中探索一种无方程式的替代建模方法。有了这个目标，我们引入了一个端到端的非渗透降低建模（NIROM）框架，该框架配备了模态分解，时间序列预测，最佳传感器放置和顺序数据同化的贡献。具体而言，我们使用适当的正交分解（POD）来识别流量的主要结构，并使用长期的短期存储网络来建模POD模式的动力学。 NIROM集成在确定性的集合Kalman滤波器（DENKF）中，以在通过QR枢纽获得的最佳传感器位置上合并稀疏和嘈杂的观测值。对于NOAA最佳插值海面温度（SST）V2数据集证明了所提出的框架的可行性和好处。我们的结果表明，NIROM对于长期预测是稳定的，并且可以以合理的准确性对SST的动力学进行建模。此外，DENKF算法通过一个数量级提高了NIROM的预测准确性。这项工作为将这些方法转移到从地球系统模型和观察结果中融合信息以实现准确的预测提供了前进的方向。
There is a growing interest in developing data-driven reduced-order models for atmospheric and oceanic flows that are trained on data obtained either from high-resolution simulations or satellite observations. The data-driven models are non-intrusive in nature and offer significant computational savings compared to large-scale numerical models. These low-dimensional models can be utilized to reduce the computational burden of generating forecasts and estimating model uncertainty without losing the key information needed for data assimilation to produce accurate state estimates. This paper aims at exploring an equation-free surrogate modeling approach at the intersection of machine learning and data assimilation in Earth system modeling. With this objective, we introduce an end-to-end non-intrusive reduced-order modeling (NIROM) framework equipped with contributions in modal decomposition, time series prediction, optimal sensor placement, and sequential data assimilation. Specifically, we use proper orthogonal decomposition (POD) to identify the dominant structures of the flow, and a long short-term memory network to model the dynamics of the POD modes. The NIROM is integrated within the deterministic ensemble Kalman filter (DEnKF) to incorporate sparse and noisy observations at optimal sensor locations obtained through QR pivoting. The feasibility and the benefit of the proposed framework are demonstrated for the NOAA Optimum Interpolation Sea Surface Temperature (SST) V2 dataset. Our results indicate that the NIROM is stable for long-term forecasting and can model dynamics of SST with a reasonable level of accuracy. Furthermore, the prediction accuracy of the NIROM gets improved by one order of magnitude by the DEnKF algorithm. This work provides a way forward toward transitioning these methods to fuse information from Earth system models and observations to achieve accurate forecasts.
