Preconditioning Markov Chain Monte Carlo Method for Geomechanical Subsidence using multiscale method and machine learning technique

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:392

Article

Vasilyeva, Maria^1,2  Tyrylgin, Aleksei²  Brown, Donald L.³  Mondal, Anirban⁴ 

[1] Texas A&M Univ, Inst Sci Computat ISC, College Stn, TX 77843 USA

[2] North Eastern Fed Univ, Inst Math & Informat, Yakutsk 677980, Republic Of Sak, Russia

[3] Equ Engn Grp, Shaker Hts, OH 44122 USA

[4] Case Western Reserve Univ, Dept Math Appl Math & Stat, Cleveland, OH 44106 USA

关键词: Poroelastic model;    Heterogeneous media;    Two Stage Markov Chain Monte Carlo method;    Multiscale method;    Machine learning;    GMsFEM;   

DOI  :  10.1016/j.cam.2021.113420

来源: Elsevier

【 摘 要 】

In this paper, we consider the numerical solution of the poroelasticity problem with stochastic properties. We present a Two-stage Markov Chain Monte Carlo method for geomechanical subsidence. In this work, we study two techniques of preconditioning: (MS) multiscale method for model order reduction and (ML) machine learning technique. The purpose of preconditioning is the fast sampling, where a new proposal is first tested by a cheap multiscale solver or using fast prediction of the neural network and the full fine grid computations will be conducted only if the proposal passes the first step. To construct a reduced order model, we use the Generalized Multiscale Finite Element Method and present construction of the multiscale basis functions for pressure and displacements in stochastic fields. In order to construct a machine learning based preconditioning, we generate a dataset using a multiscale solver and use it to train neural networks. The Karhunen-Loeve expansion is used to represent the realization of the stochastic field. Numerical results are presented for two-and three-dimensional model examples. (C) 2021 Elsevier B.V. All rights reserved.

【 授权许可】

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