Manifold-informed state vector subset for reduced-order modeling
Manifold-informed state vector subset for reduced-order modeling
复制标题
用于降阶建模的流形通知状态向量子集
DOI：
10.1016/j.proci.2022.06.019
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发表时间：
2022
影响因子：
3.4
通讯作者：
Parente, Alessandro
中科院分区：
文献类型：
--
作者：
Zdybał, Kamila;Sutherland, James C.;Parente, Alessandro
湍流燃烧的降阶模型依赖于识别能够有效描述反应流动复杂性的少量参数。随着数据驱动方法的出现，可以在简单反应系统中表示热化学状态空间的数据集上训练ROM。对于低马赫数流，作为训练数据集的完整状态向量通常由温度和化学成分组成。数据集被投影到低维基础上，并且复杂系统的演变在低维流形上被跟踪。这种方法可以大幅减少燃烧模拟中需要求解的传输方程的数量，但歧管拓扑的质量是成功建模的一个决定性因素。为了缓解多重挑战，几位作者主张在训练ROM时将状态向量减少到主要变量的子集。然而，这种简化通常是杂乱无章的，没有给出删除某些变量对结果低维数据投影的影响的详细见解。在这项工作中，我们提出了一种定量的流形信息方法来选择状态变量的子集，以最小化流形拓扑中不需要的行为。虽然过去许多作者都专注于选择主要物种，但我们表明，主要物种和次要物种的混合有助于提高低维数据表示的质量。期望的效果包括减少因变量空间中的非唯一性和空间梯度。最后，我们证明了从最优状态向量子集而不是整个状态向量建立的流形的可回归性的改进。
Reduced-order models (ROMs) for turbulent combustion rely on identifying a small number of parameters that can effectively describe the complexity of reacting flows. With the advent of data-driven approaches, ROMs can be trained on datasets representing the thermo-chemical state-space in simple reacting systems. For low-Mach flows, the full state vector that serves as a training dataset is typically composed of temperature and chemical composition. The dataset is projected onto a lower-dimensional basis and the evolution of the complex system is tracked on a lower-dimensional manifold. This approach allows for substantial reduction of the number of transport equations to solve in combustion simulations, but the quality of the manifold topology is a decisive aspect in successful modeling. To mitigate manifold challenges, several authors advocate reducing the state vector to only a subset of major variables when training ROMs. However, this reduction is often donead hocand without giving detailed insights into the effect of removing certain variables on the resulting low-dimensional data projection. In this work, we present a quantitative manifold-informed method for selecting the subset of state variables that minimizes unwanted behaviors in manifold topologies. While many authors in the past have focused on selecting major species, we show that a mixture of major and minor species can be beneficial to improving the quality of low-dimensional data representations. The desired effects include reducing non-uniqueness and spatial gradients in the dependent variable space. Finally, we demonstrate improvements in regressibility of manifolds built from the optimal state vector subset as opposed to the full state vector.
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