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Coupled problems with various combinations of multiple physics, scales, and domains are found in numerous areas of science and engineering. A key challenge in the formulation and implementation of corresponding coupled numerical models is to facilitate the communication of information across physics, scale, and domain interfaces, as well as between the 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. Although the number of sources of uncertainty can be expected to be large in most coupled problems, our contention is that exchanged probabilistic information often resides in a considerably lower-dimensional space than the sources themselves. In this work, we thus propose to use a dimension reduction technique for obtaining the representation of the exchanged information, and we propose a measure transformation technique that allows subproblem implementations to exploit this dimension reduction to achieve computational gains. The effectiveness of the proposed dimension reduction and measure transformation methodology is demonstrated through a multiphysics problem relevant to nuclear engineering. 1045 which include Monte Carlo sampling techniques [3] and stochastic expansion methods. The latter typically involve the computation of a representation of the predictions as a polynomial chaos (PC) expansion. Several approaches, such as embedded projection [4,5], nonintrusive projection [5], and collocation [6][7][8][9][10], are available to calculate the coefficients in this expansion.A key challenge in the formulation and implementation of a coupled model is to facilitate the communication of information across physics, scale, and domain interfaces, as well as between the iterations of solvers used for response computations. This information can comprise physical properties, energetic quantities, or solution patches, among other quantities. Although the number of sources of uncertainty can be expected to be large in most coupled problems, we believe that the exchanged information often resides in a considerably lower dimensional space than the sources themselves. Exchanged information can be expected to have a low effective stochastic dimension in multiphysics problems when this information consists of a solution field that has been smoothed by a forward operator and in multiscale problems when this information is obtained by summarizing fine-scale quantities into a coarse-scale representation.In a previous paper [11], we had proposed the use of a dimension reduction technique to represent the exchanged information: we proposed to represent the exchanged information by an adaptation of the Karhunen-Loève (KL) decomposition as this information passes from subproblem to subproblem and from iteration to iteration. The main objective of this paper is to complement this dimension reduction technique by a measure transformation technique that allow...

SUMMARY Coupled problems with various combinations of multiple physics, scales, and domains are found in numerous areas of science and engineering. A key challenge in the formulation and implementation of corresponding coupled numerical models is to facilitate the communication of information across physics, scale, and domain interfaces, as well as between the 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. Although the number of sources of uncertainty can be expected to be large in most coupled problems, our contention is that exchanged probabilistic information often resides in a considerably lower dimensional space than the sources themselves. This work thus presents an investigation into the characterization of the exchanged information by a reduced‐dimensional representation and in particular by an adaptation of the Karhunen‐Loève decomposition. The effectiveness of the proposed dimension–reduction methodology is analyzed and demonstrated through a multiphysics problem relevant to nuclear engineering. Copyright © 2012 John Wiley & Sons, Ltd.

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