Cacuci, D.G. and Fang, R. (2023) Demonstrative Application to an OECD/NEA Reactor Physics Benchmark of the 2nd-BERRU-PM Method—I: Nominal Computations Consistent with Measurements. Energies, 16, Article No. 5552.
https://doi.org/10.3390/en16145552

has been cited by the following article:

• TITLE: Fourth-Order Predictive Modelling: I. General-Purpose Closed-Form Fourth-Order Moments-Constrained MaxEnt Distribution

  AUTHORS: Dan Gabriel Cacuci

  KEYWORDS: Maximum Entropy Principle, Fourth-Order Predictive Modeling, Data Assimilation, Data Adjustment, Reduced Predicted Uncertainties, Model Parameter Calibration

  JOURNAL NAME: American Journal of Computational Mathematics, Vol.13 No.4, October 16, 2023

  ABSTRACT: This work (in two parts) will present a novel predictive modeling methodology aimed at obtaining “best-estimate results with reduced uncertainties” for the first four moments (mean values, covariance, skewness and kurtosis) of the optimally predicted distribution of model results and calibrated model parameters, by combining fourth-order experimental and computational information, including fourth (and higher) order sensitivities of computed model responses to model parameters. Underlying the construction of this fourth-order predictive modeling methodology is the “maximum entropy principle” which is initially used to obtain a novel closed-form expression of the (moments-constrained) fourth-order Maximum Entropy (MaxEnt) probability distribution constructed from the first four moments (means, covariances, skewness, kurtosis), which are assumed to be known, of an otherwise unknown distribution of a high-dimensional multivariate uncertain quantity of interest. This fourth-order MaxEnt distribution provides optimal compatibility of the available information while simultaneously ensuring minimal spurious information content, yielding an estimate of a probability density with the highest uncertainty among all densities satisfying the known moment constraints. Since this novel generic fourth-order MaxEnt distribution is of interest in its own right for applications in addition to predictive modeling, its construction is presented separately, in this first part of a two-part work. The fourth-order predictive modeling methodology that will be constructed by particularizing this generic fourth-order MaxEnt distribution will be presented in the accompanying work (Part-2).