# Multiscale model reduction method for Bayesian inverse problems of subsurface flow

@article{Jiang2017MultiscaleMR, title={Multiscale model reduction method for Bayesian inverse problems of subsurface flow}, author={Lijian Jiang and Na Ou}, journal={J. Comput. Appl. Math.}, year={2017}, volume={319}, pages={188-209} }

This work presents a model reduction approach to the inverse problem in the application of subsurface flows. For the Bayesian inverse problem, the forward model needs to be repeatedly computed for a large number of samples to get a stationary chain. This requires large computational efforts. To significantly improve the computation efficiency, we use generalized multiscale finite element method and least-squares stochastic collocation method to construct a reduced computational model. To avoid…

## Figures, Tables, and Topics from this paper

## 12 Citations

Inverse modeling of tracer flow via a mass conservative generalized multiscale finite volume/element method and stochastic collocation

- Computer ScienceComputational and Applied Mathematics
- 2018

A reduced stochastic model is incorporated (that combines GMsFEM-FV and sparse-grid collocation) in order to present a suitable alternative for determining input permeability distributions conditioned to available tracer cut data.

Bayesian Inference Using Intermediate Distribution Based on Coarse Multiscale Model for Time Fractional Diffusion Equations

- Mathematics, Computer ScienceMultiscale Model. Simul.
- 2018

A strategy for accelerating posterior inference for unknown inputs in time fractional diffusion models with lower gPC order is presented, which gives the approximate posterior as accurate as the the surrogate model directly based on the original prior.

An efficient algorithm for a class of stochastic forward and inverse Maxwell models in R3

- Computer ScienceJ. Comput. Phys.
- 2019

The efficiency of the Bayesian inverse algorithm for reconstruction of the electromagnetic parameters of an unbounded dielectric medium from noisy cross section data induced by a point source in R 3 is described.

A two-stage ensemble Kalman filter based on multiscale model reduction for inverse problems in time fractional diffusion-wave equations

- Computer Science, MathematicsJ. Comput. Phys.
- 2018

The two-stage EnkF can achieve a better estimation than standard EnKF, and significantly improve the efficiency to update the ensemble analysis (posterior exploration), and is extended to enhance the applicability and flexibility in Bayesian inverse problems.

A conservative generalized multiscale finite volume/element method for modeling two-phase flow with capillary pressure

- Computer Science, MathematicsJ. Comput. Appl. Math.
- 2021

This paper divides the coupled system into three subsystems: the elliptic, the hyperbolic, and the parabolic pieces, and proposes a mass-conservative generalized multiscale finite element method (GMsFEM-FV), which allows for the use of respective numerical discretizations for each type of equation, and accounts for the scale-dependent exchange of information between them.

Fast sampling of parameterised Gaussian random fields

- Computer Science, MathematicsComputer Methods in Applied Mechanics and Engineering
- 2019

A reduced basis surrogate built from snapshots of Karhunen–Loeve eigenvectors is constructed and a linearisation of the covariance function is suggested and described and the associated online–offline decomposition is described.

A Bayesian framework for inverse problems for quantitative biology

- Computer Science
- 2019

A novel combination of the Bayesian approach to inverse problems, suitable for infinite-dimensional problems, with a parallel, scalable Markov Chain Monte Carlo algorithm to approximate the posterior distribution is presented.

Continuous data assimilation for two-phase flow: analysis and simulations

- Computer Science, MathematicsArXiv
- 2021

A stability estimate is obtained which illustrates an exponential decay of the residual error between the reference and approximate solution, until the error hits a threshold depending on the order of data resolution.

Identification of the degradation coefficient for an anomalous diffusion process in hydrology

- Mathematics
- 2018

In hydrology, the degradation coefficient is one of the key parameters to describe the water quality change and to determine the water carrying capacity. This paper is devoted to identify the…

## References

SHOWING 1-10 OF 38 REFERENCES

Stochastic Collocation Algorithms Using l1-Minimization for Bayesian Solution of Inverse Problems

- Mathematics, Computer ScienceSIAM J. Sci. Comput.
- 2015

This paper presents an efficient technique for constructing stochastic surrogate models to accelerate the Bayesian inference approach for statistical inverse problems.

A stochastic collocation approach to Bayesian inference in inverse problems

- Mathematics
- 2009

We present an efficient numerical strategy for the Bayesian solution of inverse problems. Stochastic collocation methods, based on generalized polynomial chaos (gPC), are used to construct a…

Dimensionality reduction and polynomial chaos acceleration of Bayesian inference in inverse problems

- Mathematics, Computer ScienceJ. Comput. Phys.
- 2009

This work considers a Bayesian approach to nonlinear inverse problems in which the unknown quantity is a spatial or temporal field, endowed with a hierarchical Gaussian process prior, and introduces truncated Karhunen-Loeve expansions, based on the prior distribution, to efficiently parameterize the unknown field.

A Bayesian approach to multiscale inverse problems using the sequential Monte Carlo method

- Mathematics
- 2011

A new Bayesian computational approach is developed to estimate spatially varying parameters. The sparse grid collocation method is adopted to parameterize the spatial field. Based on a hierarchically…

A Stochastic Newton MCMC Method for Large-Scale Statistical Inverse Problems with Application to Seismic Inversion

- Computer Science, MathematicsSIAM J. Sci. Comput.
- 2012

This work addresses the solution of large-scale statistical inverse problems in the framework of Bayesian inference with a so-called Stochastic Monte Carlo method.

Sparse grid collocation schemes for stochastic natural convection problems

- Mathematics, Computer ScienceJ. Comput. Phys.
- 2007

The sparse grid collocation method based on the Smolyak algorithm offers a viable alternate method for solving high-dimensional stochastic partial differential equations and an extension of the collocation approach to include adaptive refinement in important stochastically dimensions is utilized to further reduce the numerical effort necessary for simulation.

A Bayesian inference approach to the inverse heat conduction problem

- Mathematics
- 2004

Abstract A Bayesian inference approach is presented for the solution of the inverse heat conduction problem. The posterior probability density function (PPDF) of the boundary heat flux is computed…

Reduced-order model tracking and interpolation to solve PDE-based Bayesian inverse problems

- Mathematics
- 2013

This work presents a computationally efficient probabilistic framework that enables the identification of model parameters from noisy measurements of the response. We consider transient PDE-based…

A markov random field model of contamination source identification in porous media flow

- Mathematics
- 2006

Abstract A contamination source identification problem in constant porous media flow is addressed by solving the advection–dispersion equation (ADE) with a hierarchical Bayesian computation method…

Stochastic spectral methods for efficient Bayesian solution of inverse problems

- Mathematics, Computer ScienceJ. Comput. Phys.
- 2007

This work presents a reformulation of the Bayesian approach to inverse problems, that seeks to accelerate Bayesian inference by using polynomial chaos expansions to represent random variables, and evaluates the utility of this technique on a transient diffusion problem arising in contaminant source inversion.