Statistical Modeling for Spatio-Temporal Data From Stochastic Convection-Diffusion Processes
Statistical Modeling for Spatio-Temporal Data From Stochastic Convection-Diffusion Processes
复制标题
随机对流扩散过程时空数据的统计建模
DOI：
10.1080/01621459.2020.1863223
复制
发表时间：
2020
影响因子：
3.7
通讯作者：
Siyuan Lu
中科院分区：
文献类型：
--
作者：
Xiao Liu;K. Yeo;Siyuan Lu
摘要本文提出了一种适用于一类随机对流扩散过程的时空数据的物理统计建模方法。这些过程广泛存在于科学和工程应用中，其中基础物理学对如何建模数据以及如何解释模型施加了关键约束。谱分解的思想是通过空间基函数的线性组合和谱系数的多元随机过程来逼近物理时空过程。与现有的方法假设空间和时间不变的对流扩散，本文认为一个更一般的情况下，空间变化的对流扩散和非零均值源汇。因此，频谱系数的时间动力学是相互耦合的，这可以从物理学的角度解释为跨多个尺度的非线性能量重新分布。由于对流扩散的空间变化，时空协方差在空间上是非平稳的。理论结果被集成到一个层次的动态时空模型。基于积分-差分方程建立了该模型与现有模型之间的联系。计算效率和可扩展性也进行了研究，使所提出的方法实用。所提出的方法的优点是证明了数值例子，案例研究，和全面的比较研究。计算机代码可以在GitHub上找到。本文的补充材料可在网上查阅。
Abstract This article proposes a physical-statistical modeling approach for spatio-temporal data arising from a class of stochastic convection-diffusion processes. Such processes are widely found in scientific and engineering applications where fundamental physics imposes critical constraints on how data can be modeled and how models should be interpreted. The idea of spectrum decomposition is employed to approximate a physical spatio-temporal process by the linear combination of spatial basis functions and a multivariate random process of spectral coefficients. Unlike existing approaches assuming spatially and temporally invariant convection-diffusion, this article considers a more general scenario with spatially varying convection-diffusion and nonzero-mean source-sink. As a result, the temporal dynamics of spectral coefficients is coupled with each other, which can be interpreted as the nonlinear energy redistribution across multiple scales from the perspective of physics. Because of the spatially varying convection-diffusion, the space-time covariance is nonstationary in space. The theoretical results are integrated into a hierarchical dynamical spatio-temporal model. The connection is established between the proposed model and the existing models based on integro-difference equations. Computational efficiency and scalability are also investigated to make the proposed approach practical. The advantages of the proposed methodology are demonstrated by numerical examples, a case study, and comprehensive comparison studies. Computer code is available on GitHub. Supplementary materials for this article are available online.
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DOI：
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发表时间：
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影响因子：
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