Data-driven discovery of the governing equations for transport in heterogeneous media by symbolic regression and stochastic optimization
Data-driven discovery of the governing equations for transport in heterogeneous media by symbolic regression and stochastic optimization
复制标题
通过符号回归和随机优化，以数据驱动的方式发现异质介质中传输的控制方程
DOI：
10.1103/physreve.107.l013301
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发表时间：
2023
影响因子：
2.4
通讯作者：
Ziff, Robert M.
中科院分区：
文献类型：
--
作者：
Im, Jinwoo;de Barros, Felipe P.;Masri, Sami;Sahimi, Muhammad;Ziff, Robert M.
随着仪器的进步和计算能力的巨大增加，大量的数据变得可用于宏观异质介质中的许多复杂现象，特别是涉及流动和传输过程的那些，这些是发生在各种物理系统中的基本问题。没有一个长度尺度，超过这个尺度，这些系统可以被认为是均匀的，这意味着传统的体积或系综平均的连续介质力学方程的异质性不再有效，因此，发现流动和运输过程的控制方程的问题是一个悬而未决的问题。我们提出了一个数据驱动的方法，使用随机优化和符号回归发现的流动和运输过程中的非均匀介质的控制方程。这些数据可以是实验性的，也可以通过微观模拟获得。作为一个例子，我们发现了临界渗流团簇在渗流阈值处的反常扩散控制方程，它是分数阶偏微分方程的形式，与以前提出的一致.
With advances in instrumentation and the tremendous increase in computational power, vast amounts of data are becoming available for many complex phenomena in macroscopically heterogeneous media, particularly those that involve flow and transport processes, which are problems of fundamental interest that occur in a wide variety of physical systems. The absence of a length scale beyond which such systems can be considered as homogeneous implies that the traditional volume or ensemble averaging of the equations of continuum mechanics over the heterogeneity is no longer valid and, therefore, the issue of discovering the governing equations for flow and transport processes is an open question. We propose a data-driven approach that uses stochastic optimization and symbolic regression to discover the governing equations for flow and transport processes in heterogeneous media. The data could be experimental or obtained by microscopic simulation. As an example, we discover the governing equation for anomalous diffusion on the critical percolation cluster at the percolation threshold, which is in the form of a fractional partial differential equation, and agrees with what has been proposed previously.