[论文解读] 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 0

一句话总结

本论文基于地震与流体压力数据，在动态地下含水层流动模型中对后验分布的估计，比较了 ADVI、SVGD、sSVGD、PSVI 与 Metropolis-Hastings MCMC 的变分推理与蒙特卡洛方法。

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.

研究动机与目标

• 为动态地下渗流的准确贝叶斯反演提供动机，以在不同情景下预测油藏性能。
• 利用地震与流体压力观测值估计后验渗透率分布。
• 在非线性贝叶斯反演中比较变分推理方法与蒙特卡洛采样的表现。
• 研究空间参数相关性如何影响遥感问题中的后验近似。

提出的方法

• 应用自动微分变分推理（ADVI）和 Stein 变分梯度下降（SVGD）以估计后验分布。
• 引入一种物理结构化变分推理（PSVI）变体，仅估计参数之间的局部空间相关性。
• 使用名为随机 SVGD（sSVGD）的蒙特卡洛方法进行后验近似。
• 在受 Endurance 田场启发的二维与三维二氧化碳封存问题上，将所有方法与 Metropolis-Hastings MCMC 进行基准比较。

实验结果

研究问题

• RQ1 ADVI、SVGD、sSVGD 与 PSVI 在动态地下渗流模型的贝叶斯反演中，其准确性和计算效率的对比如何？
• RQ2 在此背景下，PSVI 能否在平均场与全秩变分方法之间提供良好的平衡？
• RQ3 哪种方法最有效地减轻后验中的模态坍缩和虚假相关性？
• RQ4 在地震与流体压力数据约束下，变分方法与 MCMC 的后验估计相对性能如何？

主要发现

• PSVI 在准确性与效率上实现了平均场与全秩变分方法之间的良好平衡。
• SVGD 与 sSVGD 提供更准确的后验近似，但计算成本较高。
• 在 SVGD 的变体中，sSVGD 在计算效率和抑制模态坍缩及虚假相关性方面优于 SVGD。
• 所有方法在二维与三维二氧化碳封存问题上均与 Metropolis-Hastings MCMC 进行基准比较。
• 结果显示存在不同的权衡：PSVI 在效率与可接受的准确性之间；SVGD/sSVGD 在更高保真度但成本更高。