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Reduced chaos expansions with random coefficients in reduced-dimensional stochastic modeling of coupled problems

Coupled problems with various combinations of multiple physics, scales, and domains can be found in numerous areas of science and engineering. A key challenge in the formulation and implementation of corresponding coupled models is to facilitate communication of information across physics, scale, and domain interfaces, as well as between iterations of solvers used for response computations. In a probabilistic context, any information that is to be communicated between subproblems or iterations should be characterized by an appropriate probabilistic representation. In this work, we consider stochastic coupled problems whose subproblems involve only uncertainties that are statistically independent of one another; for these problems, we present a characterization of the exchanged information by using a reduced chaos expansion with random coefficients. This expansion provides a reduced-dimensional representation of the exchanged information, while maintaining segregation between sources of uncertainty that stem from different subproblems. Further, we present a measure transformation that allows stochastic expansion methods to exploit this dimension reduction to obtain an efficient solution of subproblems in a reduced-dimensional space. We show that owing to the uncertainty source segregation, requisite orthonormal polynomials and quadrature rules can be readily obtained by tensorization. Finally, the proposed methodology is demonstrated by applying it to a multiphysics problem in nuclear engineering.