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

by   Maria Vasilyeva, et al.

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 testes 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.



There are no comments yet.


page 14

page 15

page 16

page 17

page 24

page 25

page 31

page 33


Mixed Generalized Multiscale Finite Element Method for Flow Problem in Thin Domains

In this paper, we construct a class of Mixed Generalized Multiscale Fini...

Machine learning for accelerating effective property prediction for poroelasticity problem in stochastic media

In this paper, we consider a numerical homogenization of the poroelastic...

A probabilistic model for fast-to-evaluate 2D crack path prediction in heterogeneous materials

This paper is devoted to the construction of a new fast-to-evaluate mode...

Learning Algorithms for Coarsening Uncertainty Space and Applications to Multiscale Simulations

In this paper, we investigate and design multiscale simulations for stoc...

Maximal couplings of the Metropolis-Hastings algorithm

Couplings play a central role in the analysis of Markov chain Monte Carl...

Smooth Shells: Multi-Scale Shape Registration with Functional Maps

We propose a novel 3D shape correspondence method based on the iterative...

Multiscale Inverse Reinforcement Learning using Diffusion Wavelets

This work presents a multiscale framework to solve an inverse reinforcem...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.