论文标题
基于时间依赖的复合系统的基于分类的随机减少阶模型
Pre-classification based stochastic reduced-order model for time-dependent complex system
论文作者
论文摘要
我们通过结合聚类和分类策略，为复杂系统提出了一种新型的随机减少阶模型（SROM）。具体而言，根据适当的正交分解（POD）的最佳性，重新定义了质心伏罗尼二核（CVT）的距离和质心，从而获得了时间依赖性的广义CVT，并且每个类都可以生成一组基于群集的POD（CPOD）基础功能。为了了解随机输入的分类机制，应用了幼稚的贝叶斯前分类剂和聚类结果。然后，对于新输入，与预测标签相关的CPOD基础函数集用于减少相应的模型。显示了严格的错误分析，并在随机Navier-Stokes方程中进行了讨论，以提供该模型应用的上下文。数值实验验证了与标准POD方法相比，SROM的准确性得到提高。
We propose a novel stochastic reduced-order model (SROM) for complex systems by combining clustering and classification strategies. Specifically, the distance and centroid of centroidal Voronoi tessellation (CVT) are redefined according to the optimality of proper orthogonal decomposition (POD), thereby obtaining a time-dependent generalized CVT, and each class can generate a set of cluster-based POD (CPOD) basis functions. To learn the classification mechanism of random input, the naive Bayes pre-classifier and clustering results are applied. Then for a new input, the set of CPOD basis functions associated with the predicted label is used to reduce the corresponding model. Rigorous error analysis is shown, and a discussion in stochastic Navier-Stokes equation is given to provide a context for the application of this model. Numerical experiments verify that the accuracy of our SROM is improved compared with the standard POD method.
