Physics Informed Bayesian Machine Learning of Sparse and Imperfect Nuclear Data

TL;DR

This work implements the physics-model informed prior into Bayesian machine learning to evaluate the energy dependence of independent fission product yields, which are crucial for advanced nuclear energy applications but only sparse and imperfect experimental data are available.

Abstract

The prevailing data-driven machine learning has been plagued by the absence of physics knowledge and the scarcity of data. We implement the physics-model informed prior into Bayesian machine learning to evaluate the energy dependence of independent fission product yields, which are crucial for advanced nuclear energy applications but only sparse and imperfect experimental data are available. The informative prior is the posterior after learning the generated data from fission models. Furthermore, cumulative fission yields are included as a physical constraint via a conversion matrix to provide augmented energy dependence. Our work demonstrated a truly Bayesian machine learning by incorporating comprehensive physics knowledges as a powerful tool to exploit the sparse but expensive nuclear data.

Figures (4)

• Figure 1: Illustration of the physics model informed Bayesian machine learning for evaluations of independent fission yields, with and without physics constraints. The physics model generated data are used to train the informed priors for evaluation of measured data. The heterogenous cumulative yields are employed to provide additional constraints on energy dependencies via a conversion matrix. See details in the text.
• Figure 2: The inferences of neutron induced fission yields of $^{235}$U at different incident energies. (a) mass yields with uninformed learning; (b) charge yields with uninformed learning; (c) mass yields with informed learning; (d) charge yields with informed learning. The evaluated JENDL data (black lines) at 0.0253 eV and 14 MeV are also shown for comparison.
• Figure 3: (a) The loss values with and without informed priors as a function of learning steps; (b) the loss values of informed learning with and without constraints with respect to the target cumulative yields. The loss values are displayed in every 3 steps for smoothing results. The shadow region denotes the distribution of data points associated with a polynomial fitting curve. The loss values are given in units of particles per 100 fissions (PC/FIS).
• Figure 4: (a, b) The independent yields of $Z$=53 isotopes at 3 and 8 MeV, respectively, in which different approaches, such as the uninformed learning, informed learning, the informed learning with constraints, the GEF results, are employed. (c, d) The energy dependent yields of $^{135, 136}$I with different approaches. The experiment data and different evaluation data are also shown.