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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.
MSC:
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
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