KDI: Multiscale Modeling and Simulation in Scientific Inference: Hierarchical Methods for Parameter Estimation in Porous Flow

Trangenstein9873275这位研究人员和他的同事们开发了多孔介质中流动的新空间模型和数值方法。这些问题的传统仿真模型需要非常高维的参数作为输入，然而这些参数的确定从根本上是不适定的。可靠和相关的额外数据来源很少。这个问题是多尺度的，因为定义参数的细微变化可能会产生关键的大尺度效应。因此，该项目将在尺度层次上开发模型和数值方法。然而，不同比例尺的子模型之间的关系超出了简单的平均。研究人员为数据合成和高维推断和预测开发统计模型、方法和计算。流体流动的计算结合了分层模拟，包括自适应网格细化和流管方法。计算的巨大规模需要分布式计算和构建运行定制软件的工作站网络。通过对随机偏微分方程解的新分析，验证了该方法的有效性。最后，将所得到的方法应用于涉及表面活性剂的污染物清除的现场研究和石油生产问题。渗流中的不确定性对社会和经济有很大的影响。例如，石油的发现和高效生产的成本影响运输和能源生产的成本。此外，地下水中污染物的定位和清除费用影响安全水资源的成本和质量。该项目的一个目标是开发新的统计和计算方法，以评估和减少多孔介质中流动建模的不确定性。这一目标需要在建模、不确定性、计算和数据测量方面进行新的研究。为了解决这一广泛的问题，这个项目涉及应用数学家、统计学家和工程师的合作。因此，这个项目是针对国家科学基金会感兴趣的知识和分布式智能领域，特别是这一倡议的新计算挑战方面。为了给计算机模拟增加信心，该项目中的统计学家开发了概念、模型和方法，以整合数据并纳入和衡量不确定性。统计学家、应用数学家和工程师一起使用各种复杂的分析和数值技术来减少计算的规模和成本。工程师将产生的方法应用于各种实地研究，并将结果传达给他们的工业附属公司。即使有了这些新的概念和算法，计算的规模也是如此之大，以至于许多计算机必须同时处理这个问题。应用数学家使用快速通信板建立了一个工作站网络来执行这些大型计算，并将这台机器专门用于这些计算和学生教学。

Trangenstein9873275The investigator and his colleagues develop new spatial models and numerical methods for flow in porous media. Conventional simulation models for these problems require very high-dimensional parameters as inputs, yet the determination of these parameters is radically ill-posed. Reliable and relevant additional data sources are scarce. The problem is multi-scaled, since fine-scale variations in the defining parameters can have key large-scale effects. Hence this project will develop models and numerical methods on a hierarchy of scales. However, the relationship between different scale sub-models goes beyond simple averaging. The investigators develop statistical models, methodology and computation for data synthesis and high-dimensional inference and predictions. Computations for fluid flow incorporate hierarchical simulation involving adaptive mesh refinement and streamtube methods. The large size of the computations requires distributed computing and the construction of a network of workstations running custom software. The methods are validated against new analytical work in stochastic partial differential equations. Finally, the resulting methodology is applied to field studies of contaminant cleanup involving surfactants and to oil production problems.Uncertainty in porous flow has a large impact on society and the economy. For example, the cost of discovery and efficient production of petroleum affects the cost of transportation and energy production. Also the cost of location and removal of contaminants from ground water affects the cost and quality of safe water resources. One goal of this project is to develop new statistical and computational methods to assess and reduce the uncertainty in modeling flow in porous media. This goal requires new research into modeling, uncertainty, computation and data measurement. To address this wide range of issues, this project involves a collaboration of applied mathematicians, statisticians and engineers. As a result, this project is directed toward the Knowledge and Distributed Intelligence area of interest at NSF, and especially the New Computational Challenges aspect of this initiative. In order to assign confidence to computer simulations, the statisticians in this project develop concepts, models and methods to integrate data and to incorporate and measure uncertainty. Together, the statisticians, applied mathematicians and engineers use a variety of sophisticated analytical and numerical techniques to reduce the size and cost of the computations. The engineers apply the resulting methods to various field studies, and communicate the results to their industrial affiliates. Even with these new concepts and algorithms, the size of the computations is so large that many computers have to work on the problem simultaneously. The applied mathematicians build a network of workstations using fast communication boards to perform these large calculations, and dedicate this machine to these calculations and to student instruction.