Machine Learning to Select Experiments Driven by Fundamental Science and Applications for Targeted Nuclear Data Improvement

This work describes a blueprint for a process that accelerates progress in science by quantitatively answering the following question: What is the optimal combination of fundamental-science and application-driven experiments to maximally reduce pertinent data uncertainties? Answering this question entails solving a high-dimensional and complex optimization problem that is best solved with advanced statistic techniques often classified as machine learning. We apply this process within the framework of nuclear data with the aim to select an experiment combination that will reduce uncertainties in <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mmultiscripts><a:mrow><a:mi>Pu</a:mi></a:mrow><a:mprescripts/><a:none/><a:mrow><a:mn>239</a:mn></a:mrow></a:mmultiscripts></a:mrow></a:math> nuclear data for neutron energies between 1 and 600 keV. In this field, fundamental-physics driven data, called , look at one nuclear physics observable at a time. They are contrasted to application-driven, , data where one or few resulting values inform a broad set of nuclear data across several nuclides and energies. The candidates for integral experiments are criticality measurements that were refined by a genetic algorithm to be maximally sensitive to <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mrow><c:mmultiscripts><c:mrow><c:mi>Pu</c:mi></c:mrow><c:mprescripts/><c:none/><c:mrow><c:mn>239</c:mn></c:mrow></c:mmultiscripts></c:mrow></c:math> fission cross sections in the desired energy range. Twenty-three candidate differential experiments were investigated and span multiple nuclear physics observables (e.g., total, capture cross sections) for isotopes appearing in the integral experiments. The optimal combination among these candidate experiments was investigated via generalized least squares fitting, augmented with Gaussian processes to ameliorate statistical irregularities in data, and the D-optimality criterion. The latter evaluates for each pair of candidates the joint reduction in uncertainties of all 12200 nuclear data appearing in the integral experiments compared to the knowledge we have from 168 past experiments, theory, and nuclear data. We chose as differential measurements those that investigate <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mrow><e:mmultiscripts><e:mrow><e:mi>Cu</e:mi></e:mrow><e:mprescripts/><e:none/><e:mrow><e:mn>63</e:mn></e:mrow></e:mmultiscripts></e:mrow></e:math> and <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mrow><g:mmultiscripts><g:mrow><g:mi>Pu</g:mi></g:mrow><g:mprescripts/><g:none/><g:mrow><g:mn>239</g:mn></g:mrow></g:mmultiscripts></g:mrow></g:math> total cross sections, based on D-optimality rank and feasibility constraints. Two integral (criticality) experiments were selected: An experiment with <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:msub><i:mi>Al</i:mi><i:mn>2</i:mn></i:msub><i:msub><i:mi mathvariant="normal">O</i:mi><i:mn>3</i:mn></i:msub></i:math> and graphite interleaved with Pu and a thick Cu reflector explores 1–30 keV, while we target the 30–600 keV range with an experiment that swaps boron in place of graphite with a different geometry.