Dimension reduction in stochastic modeling of coupled problems

TL;DR

This paper explores a dimension reduction technique using Karhunen-Loeve decomposition to efficiently represent probabilistic information exchanged in coupled multiphysics problems, improving computational efficiency.

Contribution

It introduces a novel application of dimension reduction to probabilistic information exchange in coupled problems, enhancing modeling efficiency.

Findings

Reduced-dimensional probabilistic representations are effective.

The methodology improves computational efficiency in multiphysics simulations.

Demonstrated on a nuclear engineering problem.

Abstract

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.