An entropy-based debiasing approach to quantifying experimental coverage for novel applications of interest in the nuclear community

This manuscript proposes a novel information-theoretic approach to the quantification of experimental relevance, i.e., coverage, to achieve optimal data assimilation results for nuclear engineering applications. Specifically, this work posits the need for a new metric, called coverage ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m1"> <mml:mrow> <mml:msub> <mml:mi>q</mml:mi> <mml:mi>C</mml:mi> </mml:msub> </mml:mrow> </mml:math> ) of an application’s quantity of interest, i.e., eigenvalue or power peaking for an advanced reactor concept, defined herein as the theoretically maximum achievable reduction in the quantity’s uncertainty given measurements from a pool of experiments in a manner that is independent of the data assimilation procedure employed. Currently, reduction in a quantity’s uncertainty is strongly biased by the underlying assumptions of the assimilation procedure to account for the under-determined nature of such problems and the similarity criterion employed to identify relevant experiments. To address this challenge, this work has developed a coverage metric, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m2"> <mml:mrow> <mml:msub> <mml:mi>q</mml:mi> <mml:mi>C</mml:mi> </mml:msub> </mml:mrow> </mml:math> , based on mutual information, which establishes a new conceptual framework for assessing coverage, one that is independent of the model parameters and responses degree of variations in both the experimental and application domains, i.e., linear vs non-linear, and their prior uncertainty distributions, i.e., Gaussian vs. non-Gaussian. The <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m3"> <mml:mrow> <mml:msub> <mml:mi>q</mml:mi> <mml:mi>C</mml:mi> </mml:msub> </mml:mrow> </mml:math> is an entropic measure capable of addressing coverage for general nonlinear problems with non-Gaussian uncertainties and inclusive of the measurement uncertainties from multiple experiments. Numerical experiments from manufactured analytical problems as well as a set of benchmarks from the ICSBEP handbook are employed to demonstrate its theoretical and practical performance as compared to the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m4"> <mml:mrow> <mml:msub> <mml:mi>c</mml:mi> <mml:mi>k</mml:mi> </mml:msub> </mml:mrow> </mml:math> -based experiment selection methodology, commonly employed in the neutronic community. The manuscript then employs other well-known adaptations to existing data assimilation methodologies for nonlinear and non-Gaussian problems capable of achieving the coverage posited by <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m5"> <mml:mrow> <mml:msub> <mml:mi>q</mml:mi> <mml:mi>C</mml:mi> </mml:msub> </mml:mrow> </mml:math> .