论文标题
使用人工神经网络对PDE的降低订购建模方法的比较
A Comparison of Reduced-Order Modeling Approaches Using Artificial Neural Networks for PDEs with Bifurcating Solutions
论文作者
论文摘要
本文着重于为有效处理的PDE构建的降低阶模型（ROM），该PDE具有分叉的解决方案，因为多个输入参数的值会改变。首先，我们考虑一种称为局部ROM的方法，该方法使用K-均值算法聚集快照并构造本地吊舱碱基，每个群集一个。我们研究了这种方法的一个关键要素：局部基础选择标准。比较了几个标准，发现基于回归人工神经网络（ANN）的标准为表现出超临界干草叉分叉的通道流问题提供了最准确的结果。然后，使用相同的基准测试将局部ROM方法与回归ANN选择标准与已建立的基于全球投影的ROM和最近提出的基于ANN的方法POD-NN进行比较。我们表明，与全球投影的ROM相比，我们本地的ROM方法的准确性超过了数量级。但是，与基于局部投影的ROM相比，POD-NN提供的近似值始终如一。
This paper focuses on reduced-order models (ROMs) built for the efficient treatment of PDEs having solutions that bifurcate as the values of multiple input parameters change. First, we consider a method called local ROM that uses k-means algorithm to cluster snapshots and construct local POD bases, one for each cluster. We investigate one key ingredient of this approach: the local basis selection criterion. Several criteria are compared and it is found that a criterion based on a regression artificial neural network (ANN) provides the most accurate results for a channel flow problem exhibiting a supercritical pitchfork bifurcation. The same benchmark test is then used to compare the local ROM approach with the regression ANN selection criterion to an established global projection-based ROM and a recently proposed ANN based method called POD-NN. We show that our local ROM approach gains more than an order of magnitude in accuracy over the global projection-based ROM. However, the POD-NN provides consistently more accurate approximations than the local projection-based ROM.
