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

• Published in: Journal of computational and applied mathematics 2021-08, Vol.392, p.113420, Article 113420
• Main Authors: Vasilyeva, Maria, Tyrylgin, Aleksei, Brown, Donald L., Mondal, Anirban
• Format: Article
• Language: English
• Subjects: GMsFEM; Heterogeneous media; Machine learning; Multiscale method; Poroelastic model; Two Stage Markov Chain Monte Carlo method
• ISSN: 0377-0427; 1879-1778
• DOI: 10.1016/j.cam.2021.113420

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–Loéve expansion is used to represent the realization of the stochastic field. Numerical results are presented for two- and three-dimensional model examples.