验证基准的开发与实现
Development and Realization of Validation Benchmarks
摘要：
在建模领域，验证一词指的是模型输出和实验数据之间的简单比较。通常，这种比较包括将模型结果与相同轴上的数据作图，以提供一致性或不一致性的视觉评估。然而，这种天真的比较存在一些问题。首先，这些比较往往提供定性而非定量评估，显然不足以就模型的有效性作出决定。第二，他们往往忽视或只部分考虑现有的不确定性，在实验观测或模型输入参数。第三，这种比较不能揭示模型是否适合预期目的，因为它们主要集中在可观察量的一致性上。这些缺陷导致需要一个包含验证度量的不确定性感知框架。该指标应提供一种测量方法，用于比较实验的系统响应量与计算模型的系统响应量，同时考虑两者的不确定性。为了满足这一需求，我们已经开发了一个统计框架，采用完全贝叶斯方法的概率建模技术。贝叶斯的观点产生一个最佳的偏差方差权衡对实验数据，并提供了一个综合指标模型验证，包括参数和概念的不确定性。此外，为了加速多孔介质中计算要求较高的流动和输运模型的分析，该框架配备了模型简化技术，即贝叶斯稀疏多项式混沌扩展。我们证明了上述贝叶斯验证框架的能力，通过将其应用于验证以及裂缝性多孔介质中流体流动的不确定性量化。
英文摘要：
In the field of modeling, the word validation refers to simple comparisons between model outputs and experimental data. Usually, this comparison constitutes plotting the model results against data on the same axes to provide a visual assessment of agreement or lack thereof. However, there are a number of concerns with such naive comparisons. First, these comparisons tend to provide qualitative rather than quantitative assessments and are clearly insufficient for making decisions regarding model validity. Second, they often disregard or only partly account for existing uncertainties in the experimental observations or the model input parameters. Third, such comparisons can not reveal whether the model is appropriate for the intended purposes, as they mainly focus on the agreement in the observable quantities. These pitfalls give rise to the need for an uncertainty-aware framework that includes a validation metric. This metric shall provide a measure for comparison of the system response quantities of an experiment with the ones from a computational model, while accounting for uncertainties in both. To address this need, we have developed a statistical framework that incorporates a probabilistic modeling technique using a fully Bayesian approach. A Bayesian perspective yields an optimal bias-variance trade-off against the experimental data and provide an integrative metric for model validation that incorporates parameter and conceptual uncertainty. Additionally, to accelerate the analysis for computationally demanding flow and transport models in porous media, the framework is equipped with a model reduction technique, namely Bayesian Sparse Polynomial Chaos Expansion. We demonstrate the capabilities of the aforementioned Bayesian validation framework by applying it to an application for validation as well as uncertainty quantification of fluid flow in fractured porous media.
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