Tools for the investigation of stochastic multiphysics models

现代社会以无数种方式受到复杂物理系统行为的影响，这些系统涉及多个物理过程在一系列尺度上的相互作用。飓风对海岸的影响、多孔介质中的污染流和铀燃料棒中的辐射损害只是许多例子中的几个。复杂系统的一个特点是，我们可以通过实验观察到某些尺度上行为的某些方面，并为某些尺度上的某些组成部分的行为构建经过良好验证的过程模型，但我们不能直接观察或模拟所有重要的行为和相互作用。因此，复杂系统的研究面临着巨大的挑战，至少需要整合所有可用的数据和模型。该项目的长期目标是开发强大的计算和统计工具，以探索复杂的多物理场系统的行为，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很大范围内变化时系统行为的变化。因为这些条件通常是未知的，或者很难量化，我们用概率来描述这些变化。我们还解决了相反的问题，即根据对其行为的观察来确定复杂系统的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。该研究具有很强的跨学科性，因为研究问题直接来自对科学和工程具有重要意义的复杂物理系统的研究。该项目将在海岸线的潮汐和风暴潮、通过地面的污染流动以及基于观察电磁辐射散射来探测物体的特性和几何形状等方面进行应用。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学领域的重大进展。

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.