Tools for the investigation of stochastic multiphysics models

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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.