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首页> 美国政府科技报告 >Adaptive Sparse-Grid High-Order Stochastic Collocation Method for Bayesian Inference in Groundwater Reactive Transport Modeling.
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Adaptive Sparse-Grid High-Order Stochastic Collocation Method for Bayesian Inference in Groundwater Reactive Transport Modeling.

机译：地下水反应传输模型中贝叶斯推断的自适应稀疏网格高阶随机配点法。

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摘要

Although Bayesian analysis has become vital to the quantification of prediction uncertainty in groundwater modeling, its application has been hindered due to the computational cost associated with numerous model executions needed for exploring the posterior probability density function (PPDF) of model parameters. This is particularly the case when the PPDF is estimated using Markov Chain Monte Carlo (MCMC) sampling. In this study, we develop a new approach that improves computational efficiency of Bayesian inference by constructing a surrogate system based on an adaptive sparse-grid high-order stochastic collocation (aSG-hSC) method. Unlike previous works using first-order hierarchical basis, we utilize a compactly supported higher-order hierarchical basis to construct the surrogate system, resulting in a significant reduction in the number of computational simulations required. In addition, we use hierarchical surplus as an error indicator to determine adaptive sparse grids. This allows local refinement in the uncertain domain and/or anisotropic detection with respect to the random model parameters, which further improves computational efficiency. Finally, we incorporate a global optimization technique and propose an iterative algorithm for building the surrogate system for the PPDF with multiple significant modes. Once the surrogate system is determined, the PPDF can be evaluated by sampling the surrogate system directly with very little computational cost.

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