Measure transformation and efficient quadrature in reduced-dimensional stochastic modeling of coupled problems

TL;DR

This paper introduces a measure-transformation and dimension-reduction technique to improve computational efficiency in probabilistic coupled problems involving multiple physics and scales.

Contribution

It proposes a novel measure-transformation approach that leverages lower-dimensional probabilistic representations to enhance efficiency in coupled stochastic modeling.

Findings

Effective dimension reduction in probabilistic information exchange

Significant computational gains demonstrated in nuclear engineering problem

Method applicable to various multiphysics coupled problems

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. In this work, we thus use a dimension-reduction technique for obtaining the representation of the exchanged information. The main subject of this work is the investigation of a measure-transformation technique that allows 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.