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

研究者和他的同事们开发了多孔介质中流动的新的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是完全病态的。可靠和相关的额外数据来源很少。这个问题是多尺度的，因为定义参数的细尺度变化可以产生关键的大尺度效应。因此，本项目将在一个层次的尺度上发展模型和数值方法。然而，不同尺度子模型之间的关系不仅仅是简单的平均。研究人员开发统计模型，方法和计算数据合成和高维推理和预测。流体流动的计算包括自适应网格细化和流管方法的分层模拟。大规模的计算需要分布式计算和构建运行定制软件的工作站网络。针对随机偏微分方程的新解析工作，验证了方法的有效性。最后，将所得方法应用于涉及表面活性剂的污染物清除和石油生产问题的现场研究。多孔流体的不确定性对社会经济产生了重大影响。例如，石油的发现和有效生产的成本影响着运输和能源生产的成本。此外，从地下水中定位和清除污染物的费用也影响到安全水资源的成本和质量。该项目的目标之一是开发新的统计和计算方法来评估和减少多孔介质中流动建模的不确定性。这一目标需要对建模、不确定性、计算和数据测量进行新的研究。为了解决这些广泛的问题，该项目涉及应用数学家、统计学家和工程师的合作。因此，该项目是针对NSF感兴趣的知识和分布式智能领域，特别是该计划的新计算挑战方面。为了给计算机模拟分配信心，这个项目中的统计学家开发了概念、模型和方法来整合数据，并纳入和测量不确定性。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。工程师们将所得到的方法应用于各种实地研究，并将结果传达给他们的工业分支机构。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。应用数学家们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指导。

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.