In this work, we develop Non-Intrusive Reduced Order Models (NIROMs) that combine Proper Orthogonal Decomposition (POD) with a Radial Basis Function (RBF) interpolation method to construct efficient reduced order models for time-dependent problems arising in large scale environmental flow applications. The performance of the POD-RBF NIROM is compared with a traditional nonlinear POD (NPOD) model by evaluating the accuracy and robustness for test problems representative of riverine flows. Different greedy algorithms are studied in order to determine a near-optimal distribution of interpolation points for the RBF approximation. A new power-scaled residual greedy (psr-greedy) algorithm is proposed to address some of the primary drawbacks of the existing greedy approaches. The relative performances of these greedy algorithms are studied with numerical experiments using realistic two-dimensional (2D) shallow water flow applications involving coastal and riverine dynamics.

在这项工作中，我们开发了非侵入式降阶模型（NIROM），该模型将适当的正交分解（POD）与径向基函数（RBF）插值方法相结合，以构造有效的降阶模型，以解决大规模环境流动中与时间相关的问题应用程序。通过评估代表河流流量的测试问题的准确性和鲁棒性，将POD-RBF NIROM的性能与传统的非线性POD（NPOD）模型进行了比较。为了确定用于RBF近似的插值点的最佳分布，研究了不同的贪婪算法。一个新的幂级残差贪婪（psr-greedy提出了一种算法来解决现有贪婪方法的一些主要缺点。这些贪婪算法的相对性能通过使用涉及海岸和河流动力学的逼真的二维（2D）浅水流应用程序的数值实验进行了数值研究。