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

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