Perspective on Predictive Modeling: Current Status, New High-Order Methodology and Outlook for Energy Systems

Abstract

This work presents a perspective on deterministic predictive modeling methodologies, which aim at extracting best-estimate values for model responses and parameters along with reduced predicted uncertainties for these best-estimate values. The two oldest such methodologies are the data-adjustment method, which stems from the nuclear energy field, and the data-assimilation method, which is implemented in the geophysical sciences. Both of these methodologies attempt to minimize, in the least-square sense, a user-defined functional that represents the discrepancies between computed and measured model responses. These two methodologies were briefly reviewed and shown to be inconsistent even to first-order in the sensitivities of the response to the model parameters. In contrast to these methodologies, it was shown that the “maximum entropy”-based predictive modeling methodology (called BERRU-PM) that was developed by the author not only dispenses with the subjective “user-chosen functional to be minimized” but is also inherently amenable to high-order formulations. This inherent potential was illustrated by presenting a novel, higher-order, MaxEnt-based predictive modeling methodology, labelled BERRU-PM-2+, which is complete and exact to second-order sensitivities and moments of both the a priori and posterior distributions of responses and parameters, while explicitly including third- and fourth-order sensitivities and correlations, thus indicating the mechanism for incorporating information of orders higher than second in predictive modeling. The presentation of this new predictive modeling methodology also aims at motivating a widespread application of predictive modeling principles and methodologies in the energy sciences for obtaining best-estimate results with reduced uncertainties.