FINITE DIMENSIONAL MODELS FOR RANDOM MICROSTRUCTURES
FINITE DIMENSIONAL MODELS FOR RANDOM MICROSTRUCTURES
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随机微观结构的有限维模型
DOI：
10.1090/tpms/1168
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发表时间：
2022
影响因子：
0.9
通讯作者：
M. Grigoriu
中科院分区：
文献类型：
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作者：
M. Grigoriu
有限维（FD）模型，即依赖于有限组随机变量的空间确定性函数，广泛应用于生成随机场样本和构造随机系数依赖于的常微分方程或偏微分方程解的近似，FD模型和构成这些随机场的代理，其目标是各种属性，例如均值/相关函数或样本属性。本文建立了FD模型的样本可以代替两类随机场和一个简单随机方程的样本的条件。这些条件中的一些数值例子说明。
Finite dimensional (FD) models, ie, deterministic functions of space depending on finite sets of random variables, are used extensively in applications to generate samples of random fieldsand construct approximations of solutionsof ordinary or partial differential equations whose random coefficients depend on. FD models ofandconstitute surrogates of these random fields which target various properties, eg, mean/correlation functions or sample properties. We establish conditions under which samples of FD models can be used as substitutes for samples ofandfor two types of random fieldsand a simple stochastic equation. Some of these conditions are illustrated by numerical examples.