Advances in High-Order Predictive Modeling: Methodologies and Illustrative Problems (Advances in Applied Mathematics)

Continuing the author’s previous work on modeling, this book presents the most recent advances in high-order predictive modeling. The author begins with the mathematical framework of the 2nd-BERRU-PM methodology, an acronym that designates the “second-order best-estimate with reduced uncertainties (2nd-BERRU) predictive modeling (PM).” The 2nd-BERRU-PM methodology is fundamentally anchored in physics-based principles stemming from thermodynamics (maximum entropy principle) and information theory, being formulated in the most inclusive possible phase-space, namely the combined phase-space of computed and measured parameters and responses.

The 2nd-BERRU-PM methodology provides second-order output (means and variances) but can incorporate, as input, arbitrarily high-order sensitivities of responses with respect to model parameters, as well as arbitrarily high-order moments of the initial distribution of uncertain model parameters, in order to predict best-estimate mean values for the model responses (i.e., results of interest) and calibrated model parameters, along with reduced predicted variances and covariances for these predicted responses and parameters.

Dan Gabriel Cacuci is a Distinguished Professor Emeritus in the Department of Mechanical Engineering at the University of South Carolina and the Karlsruhe Institute of Technology, Germany. He received his PhD in applied physics, mechanical and nuclear engineering from Columbia University. He is also the recipient of many awards including four honorary doctorates, the Ernest Orlando Lawrence Memorial award from the U.S. Deptartment of Energy and the Arthur Holly Compton, Eugene P. Wigner and the Glenn Seaborg Awards from the American Nuclear Society. He was named an “Inaugural Highly Ranked Scholar” by Scholar GPS, being ranked #2 in the world in the field of Uncertainty Analysis, #5 in the world in the field of Sensitivity Analysis, and ranked in the top 0.05% of all scholars worldwide.

This is Dr. Cacuci’s fifth book for CRC Press. The others include, The Second-Order Adjoint Sensitivity Analysis Methodology (2018); Computational Methods for Data Evaluation and Assimilation with Ionel Michael Navon and Mihaela Ionescu-Bujor (2013); Sensitivity and Uncertainty Analysis, Volume I Applications to Large-Scale Systems (2003) and Volume II (2005) also with Mihaela Ionescu-Bujor and Michael Navon.

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