Tools for the investigation of stochastic multiphysics models

现代社会以各种方式受到复杂物理系统行为的影响，复杂的物理系统涉及通过一系列尺度作用的多个物理过程的相互作用。飓风对海岸的影响、多孔介质中的污染流动以及铀燃料棒的辐射损害只是众多例子中的一小部分。复杂系统的一个特征是可以通过实验观察某些尺度上的行为的某些方面，并在某些尺度上构建经过良好验证的某些组件行为的过程模型，但我们不能直接观察或模拟所有重要的行为和交互作用。因此，复杂系统的研究面临着巨大的挑战，这至少需要整合所有可用的数据和模型。拟议项目的长期目标是开发强大的计算和统计工具，以探索复杂多物理系统的行为，预测其行为，并量化结果中的不确定性。这包括描述当物理条件在大范围内变化时系统行为的变化。因为条件通常是未知的，或者量化得很差，所以我们用概率来描述变化。我们还解决了相反的问题，即根据对复杂系统行为的观察来确定其各种物理条件的概率。研究范围包括计算方法的发展、理论分析和软件开发。这项研究具有很强的跨学科性质，因为研究问题直接源于对科学和工程具有重要意义的复杂物理系统的研究。该项目将在海岸线上的潮汐和风暴潮、地面污染流动以及基于观测电磁辐射散射的物体属性和几何检测方面继续应用。该项目将支持培训高素质的人员和公开可用的软件，使科学家和工程师能够获得研究成果。这项研究还将导致数学和统计领域的重大进步。

Modern society is affected in myriad ways by the behavior of complex physical systems involving the interaction of multiple physical processes acting through a range of scales. The impact of hurricanes on coasts, pollution flow in porous media, and radiation damage in uranium fuel rods are just a few of many examples. A characteristic of complex systems is that it is possible to observe certain aspects of behavior at some scales experimentally and to construct well-validated process models of some component behavior at some scales, but we cannot directly observe or model all important behaviors and interactions. Thus, the study of complex systems faces significant challenges that require, at a minimum, integrating all available data and models. The long-term goal of the proposed project is to develop powerful computational and statistical tools to explore the behavior of complex multiphysics systems, predict their behavior, and quantify uncertainties in the results. This involves describing the variation in the behavior of the system as physical conditions change over a wide range. Because the conditions are often unknown, or poorly quantified, we describe the variations using probability. We also tackle the reverse problem, which is to determine the probability of various physical conditions of a complex system based on observations of its behavior. The research scope includes development of computational methods, theoretical analysis, and software development. The research is strongly interdisciplinary because the research questions arise directly from the study of complex physical systems of importance for science and engineering. The project will pursue applications in tidal and storm surges along coastlines, the flow of pollution through the ground, and the detection of properties and geometries of an object based on observing scattering of electromagnetic radiation. The project will support the training of highly qualified personnel and publicly available software that will make the research results accessible to scientists and engineers. The research will also lead to significant advances in the fields of mathematics and statistics.