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Hidden physics model for parameter estimation of elastic wave equations
Computer Methods in Applied Mechanics and Engineering ( IF 7.2 ) Pub Date : 2021-04-18 , DOI: 10.1016/j.cma.2021.113814
Yijie Zhang , Xueyu Zhu , Jinghuai Gao

A numerical approach based on the hidden physics model to estimate the model parameters of elastic wave equations with the sparse and noisy data is presented in this paper. Through discretizing the time derivatives of elastic wave equations and placing the priors of the state variables as Gaussian process, the model parameters and structure of elastic wave equations are encoded in the kernel function of a multi-output Gaussian process. In the learning stage, a parameter bound constraint condition is incorporated to enforce the physical bound of the model parameters. The numerical results from several benchmark problems, including homogeneous media, layer media, anisotropic media, and homogeneous model with an inclusion, demonstrate the feasibility and performance of the hidden physics model.



中文翻译:

弹性波方程参数估计的隐藏物理模型

本文提出了一种基于隐藏物理模型的数值方法,用稀疏和嘈杂的数据来估计弹性波方程的模型参数。通过离散化弹性波方程的时间导数并将状态变量的先验值作为高斯过程,将弹性波方程的模型参数和结构编码到多输出高斯过程的核函数中。在学习阶段,合并参数约束条件以强制模型参数的物理边界。来自几个基准问题的数值结果,包括均质介质,层介质,各向异性介质和包含一个均质模型,证明了隐藏物理模型的可行性和性能。

更新日期:2021-04-19
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