  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-Loeve decomposition. The effectiveness of the
proposed dimension-reduction methodology is analyzed and demonstrated through a
multiphysics problem relevant to nuclear engineering.
