MULTI-PRED: A Software Module for Predictive Modeling of Coupled Multi-Physics Systems

摘要

The software module MULTI-PRED implements the methodology for predictive modeling of coupled multi-physics systems (PM-CMPS) formulated by Cacuci [Ann. Nucl. Energy, Vol. 70, p, 266 (2014)]. This methodology fully takes into account the coupling terms between the systems but requires only the computational resources that would be needed to perform predictive modeling on each system separately. The PM-CMPS methodology uses the maximum entropy principle to construct an optimal approximation of the unknown a priori distribution based on a priori known mean values and uncertainties characterizing the experimental and computational parameters and results of interest responses called for the multi-physics models under consideration. This maximum entropy a priori distribution is combined, using Bayes' theorem, with the likelihood provided by the multi-physics simulation models to obtain a formal posterior distribution. Subsequently, the posterior distribution thus obtained is evaluated using the saddle-point method to obtain analytical expressions for the optimally predicted values for the multi-physics model parameters and responses along with corresponding reduced uncertainties. Noteworthy, the predictive modeling methodology for the coupled systems is constructed such that the systems can be considered sequentially rather than simultaneously, while preserving exactly the same results as if the systems were treated simultaneously. Consequently, very large coupled systems, which could perhaps exceed available computational resources if treated simultaneously, can be treated with the PM-CMPS methodology presented in this work sequentially and without any loss of generality or information, requiring just the resources that would be needed if the systems were treated sequentially.