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Preconditioning Markov chain Monte Carlo method for geomechanical subsidence using multiscale method and machine learning technique. (English) Zbl 1467.74096
Summary: 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.
74S60 Stochastic and other probabilistic methods applied to problems in solid mechanics
74S05 Finite element methods applied to problems in solid mechanics
74L10 Soil and rock mechanics
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
74E05 Inhomogeneity in solid mechanics
68T05 Learning and adaptive systems in artificial intelligence
Full Text: DOI
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