Abstract In monitoring subsurface aquifer contamination, we want to predict quantities—fractional flow curves of pollutant concentration—using subsurface fluid flow models with expertise and limited data. A Bayesian approach is considered here and the complexity associated with the simulation study presents an ongoing practical challenge. We use a Karhunen–Loeve expansion for the permeability field in conjunction with GPU computing within a two–stage Markov Chain Monte Carlo (MCMC) method. Further reduction in computing costs is addressed by running several MCMC chains. We compare convergence criteria to quantify the uncertainty of predictions. Our contributions are two-fold: we first propose a fitting procedure for the Multivariate Potential Scale Reduction Factor (MPSRF) data that allows us to estimate the number of iterations for convergence. Then we present a careful analysis of ensembles of fractional flow curves suggesting that, for the problem at hand, the number of iterations required for convergence through the MPSRF analysis is excessive. Thus, for practical applications, our results provide an indication that an analysis of the posterior distributions of quantities of interest provides a reliable criterion to terminate MCMC simulations for quantifying uncertainty.

中文翻译：

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使用贝叶斯框架进行地下污染物迁移预测

摘要 在监测地下含水层污染时，我们希望使用具有专业知识和有限数据的地下流体流动模型来预测数量——污染物浓度的分流曲线。这里考虑了贝叶斯方法，与模拟研究相关的复杂性提出了持续的实际挑战。我们在两阶段马尔可夫链蒙特卡罗 (MCMC) 方法中结合 GPU 计算对渗透场使用 Karhunen-Loeve 扩展。通过运行多个 MCMC 链可以进一步降低计算成本。我们比较收敛标准来量化预测的不确定性。我们的贡献有两个方面：我们首先提出了一个适用于多元潜在尺度缩减因子 (MPSRF) 数据的拟合程序，该程序使我们能够估计收敛的迭代次数。然后我们对分数流曲线的集合进行了仔细分析，表明对于手头的问题，通过 MPSRF 分析收敛所需的迭代次数过多。因此，对于实际应用，我们的结果表明，对感兴趣量的后验分布的分析提供了终止 MCMC 模拟以量化不确定性的可靠标准。