标题： 随机 Proper Orthogonal 分解用于两层准地转海洋模型的数据驱动降阶建模 显示英文标题

标题： Randomized Proper Orthogonal Decomposition for data-driven reduced order modeling of a two-layer quasi-geostrophic ocean model

摘要： 两层准地转方程（2QGE）作为一种简化模型，用于模拟风驱动的分层海洋流动。然而，由于需要高分辨率网格来捕捉广泛的湍流尺度，其数值模拟仍然计算成本高昂。当由于参数设置的不确定性等原因需要运行多次模拟时，这个问题尤为突出。 为了解决这一挑战，我们提出了一种基于数据驱动的2QGE降阶模型（ROM），该模型利用了随机化主成分分解（rPOD）和长短期记忆网络（LSTM）。 为了高效生成构建模型所需的快照数据，我们应用了一种非线性滤波稳定技术，与直接数值模拟（DNS）相比，这种方法允许使用更大的网格尺寸。 由于使用rPOD从快照矩阵中提取主导模态，我们的方法相比确定性POD实现了高达700倍的速度提升。在在线阶段，通过训练与快照相关的模态系数的LSTM网络，可以预测时间及参数依赖的模态系数，这比DNS快数十万倍。 我们通过扩展一个著名的基准测试——双涡旋风力驱动测试，来评估我们的rPOD-LSTM ROM的准确性和效率。在这个测试中，参数空间的维度从二维增加到四维。 显示英文摘要

摘要： The two-layer quasi-geostrophic equations (2QGE) serve as a simplified model for simulating wind-driven, stratified ocean flows. However, their numerical simulation remains computationally expensive due to the need for high-resolution meshes to capture a wide range of turbulent scales. This becomes especially problematic when several simulations need to be run because of, e.g., uncertainty in the parameter settings. To address this challenge, we propose a data-driven reduced order model (ROM) for the 2QGE that leverages randomized proper orthogonal decomposition (rPOD) and long short-term memory (LSTM) networks. To efficiently generate the snapshot data required for model construction, we apply a nonlinear filtering stabilization technique that allows for the use of larger mesh sizes compared to a direct numerical simulations (DNS). Thanks to the use of rPOD to extract the dominant modes from the snapshot matrices, we achieve up to 700 times speedup over the use of deterministic POD. LSTM networks are trained with the modal coefficients associated with the snapshots to enable the prediction of the time- and parameter-dependent modal coefficients during the online phase, which is hundreds of thousands of time faster than a DNS. We assess the accuracy and efficiency of our rPOD-LSTM ROM through an extension of a well-known benchmark called double-gyre wind forcing test. The dimension of the parameter space in this test is increased from two to four.