Gamma Enrichment Analysis Algorithm Based on
Physics-Informed Neural Networks

A gamma enrichment analysis is presented that utilises physics-informed neural networks (PINN). Such networks exploit existing mathematical formulas and analytic transformations, to provide the best possible starting for a machine learning training - they hybridise the machine learning perspective with established analytic relationships. Autoregressive-PINN structures are presented. They are a tool for nonlinear preparation of the spectral data and are used for extracting characteristic enrichment features. Primary reason for using a physics-informed approach was the reduced amount of training data needed by this learning method, which de-facto yields good results even on sparse data sets. Tests of the algorithm were performed with Sodium Iodide (NaI:Tl), Lanthanum Bromide (LaBr3:Ce,Sr) and Cadmium Zinc Telluride (CZT) spectra. The algorithm was applied to measurement data from real sources and to simulated data conducted with GEANT4. The results for the different detectors are compared. The physics-informed approach yields advantages, because it can include complex peak shapes and the variation of the shape during the training. Interpreting the peak shape as probability distribution, the variational autoencoding represents an effective uncertainty quantification of the moments of this distribution. This includes kurtosis and skewness in the context of asymmetrical CZT peak structures. The tested PINN is studied by sensitivity analysis methods. It allows us to quantify the influence of each input data contribution: scattering, background, spectrum content in specific regions-of-interest or temperature.