论文标题
验证基准的开发和实现
Development and Realization of Validation Benchmarks
论文作者
论文摘要
在建模领域,单词验证是指模型输出与实验数据之间的简单比较。通常,此比较构成了模型结果与相同轴上的数据绘制的结果,以提供对一致性或缺乏协议的视觉评估。但是,如此天真的比较存在许多担忧。首先,这些比较倾向于提供定性的,而不是定量评估,并且显然不足以做出有关模型有效性的决策。其次,他们通常会无视或仅部分考虑实验观察中现有的不确定性或模型输入参数。第三,这种比较无法揭示该模型是否适合预期目的,因为它们主要集中于可观察数量的协议。 这些陷阱导致需要一个不确定性感知的框架,其中包括验证度量。该指标应提供一个措施,以比较实验的系统响应量与计算模型的实验响应量,同时考虑了这两者的不确定性。为了满足这一需求,我们开发了一个统计框架,该框架结合了使用完全贝叶斯方法的概率建模技术。贝叶斯的观点可以针对实验数据产生最佳的偏见差异权衡权衡,并为模型验证提供了一个集成性指标,该指标结合了参数和概念不确定性。此外,为了加快多孔介质中计算苛刻的流量和运输模型的分析,该框架配备了模型还原技术,即贝叶斯稀疏多项式混沌扩展。我们通过将其应用于验证应用程序以及对断裂的多孔介质中流体流量的不确定性量化,证明了上述贝叶斯验证框架的功能。
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.