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

- Author(s): Cacuci, Dan G
- Fang, Ruixian
- Badea, Madalina C
- et al.

## Abstract

This User’s Manual describes the code module MULTI-PRED, written in FORTRAN which implements the methodology for “predictive modeling of coupled multi-physics systems (PM-CMPS)” formulated by Cacuci (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 models 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. Three illustrative demonstration problems are also provided. The first problem presents the application of the PM-CMPS methodology to a simple particle diffusion problem which admits a closed-form analytical solution which facilitates a rapid understanding of this methodology and its predicted results. The second demonstration problem presents the application of the PM-CMPS methodology to the problem of inverse prediction, from detector responses in the presence of counting uncertainties, of the thickness of a homogeneous slab of material containing uniformly distributed gamma-emitting sources, for optically thin and thick slabs. This problem highlights the essential role played by the relative uncertainties (or, conversely, accuracies) of measured and computed responses. The third demonstration problem presents the application of the PM-CMPS methodology to the F-area cooling towers at the Savannah River National Lab. This problem demonstrates that the PM-CMPS methodology reduces the predicted response uncertainties not only at locations where measurements are available, but also at locations where measurements are not available.