[論文レビュー] Variational and Monte Carlo Methods for Bayesian Inversion of Dynamic Subsurface Flow Simulations Using Seismic and Fluid Pressure Data

Zhen Zhang, Xuebin Zhao+1 more|arXiv (Cornell University)|Feb 3, 2026

Reservoir Engineering and Simulation Methods被引用数 0

ひとこと要約

The paper benchmarks variational inference and Monte Carlo methods for estimating posterior distributions of reservoir permeability from seismic and fluid pressure data in dynamic subsurface flow models, comparing ADVI, SVGD, sSVGD, PSVI, and Metropolis-Hastings MCMC.

ABSTRACT

In order to predict future performance of subsurface fluid reservoirs under possible operating scenarios, a dynamic, porous-medium flow simulation model must be tuned to include representative properties of the reservoir. Estimating subsurface reservoir properties given remotely sensed or borehole-based observations typically involves finding the solution to a challenging inverse problem. We compare Monte Carlo random sampling to variational inference methods which use optimisation to constrain parametrised uncertainties in nonlinear Bayesian inversions. We use them to estimate the posterior probability distribution of reservoir permeability given fluid pressure and seismic measurements. The methods include automatic differentiation variational inference (ADVI), Stein variational gradient descent (SVGD), and a Monte Carlo method called stochastic SVGD (sSVGD), all of which we benchmark against results from Metropolis-Hastings McMC. We also test an ADVI variant called physically structured variational inference (PSVI): in our implementation this method estimates only spatially-local correlations between model parameters based on the intuition that such correlations are strong in remote sensing problems in which data only inform about spatial-averages of local dynamics. We apply the methods to two- and three-dimensional inverse problems of carbon dioxide storage, inspired by the Endurance field, located in the UK North Sea. Results show that PSVI achieves a good balance between mean-field ADVI and full-rank ADVI in terms of accuracy of the posterior approximation and computational efficiency. SVGD and sSVGD offer more accurate approximations of the target posterior distribution, but at far higher computational cost. Between them, sSVGD outperforms SVGD, exhibiting better computational efficiency and mitigating the problems of mode collapse and spurious correlations.

研究の動機と目的

• Motivate accurate Bayesian inversion for dynamic subsurface flow to predict reservoir performance under different scenarios.
• Estimate posterior permeability distributions using seismic and fluid pressure observations.
• Compare variational inference methods with Monte Carlo sampling in nonlinear Bayesian inversions.
• Investigate how spatial parameter correlations affect posterior approximation in remote sensing problems.

提案手法

• Apply automatic differentiation variational inference (ADVI) and Stein variational gradient descent (SVGD) to estimate posteriors.
• Introduce a physically structured variational inference (PSVI) variant that estimates only spatially-local correlations between parameters.
• Use a Monte Carlo method called stochastic SVGD (sSVGD) for posterior approximation.
• Benchmark all methods against Metropolis-Hastings MCMC on 2D and 3D CO2 storage problems inspired by the Endurance field.

実験結果

リサーチクエスチョン

• RQ1 How do ADVI, SVGD, sSVGD, and PSVI compare in accuracy and computational efficiency for Bayesian inversion of dynamic subsurface flow models?
• RQ2 Can PSVI provide a good balance between mean-field and full-rank variational approaches in this context?
• RQ3 Which method most effectively mitigates mode collapse and spurious correlations in the posterior?
• RQ4 What is the relative performance of variational methods versus MCMC for posterior estimation under seismic and fluid pressure data constraints?

主な発見

• PSVI achieves a good balance between mean-field and full-rank variational approaches in accuracy and efficiency.
• SVGD and sSVGD yield more accurate posterior approximations but with higher computational cost.
• Between SVGD variants, sSVGD outperforms SVGD in computational efficiency and in mitigating mode collapse and spurious correlations.
• All methods are benchmarked against Metropolis-Hastings MCMC on two- and three-dimensional CO2 storage problems.
• Results indicate varying trade-offs: PSVI for efficiency and reasonable accuracy; SVGD/sSVGD for higher fidelity at cost.