AI and Machine Learning for SNM detection and Solution of PDEs with Interface Conditions

Nuclear engineering hosts diverse domains including, but not limited to, power plant automation, human-machine interfacing, detection and identification of special nuclear materials, modeling of reactor kinetics and dynamics that most frequently are described by systems of differential equations (DEs), either ordinary (ODEs) or partial ones (PDEs). In this work we study multiple problems related to safety and Special Nuclear Material detection, and numerical solutions for partial differential equations using neural networks. More specifically, this work is divided in six chapters. Chapter 1 is the introduction, in Chapter

2 we discuss the development of a gamma-ray radionuclide library for the characterization

of gamma-spectra. In Chapter 3, we present a new approach, the ”Variance Counterbalancing”, for stochastic

large-scale learning. In Chapter 4, we introduce a systematic approach for constructing proper trial solutions to partial differential equations (PDEs) of up to second order, using neural forms that satisfy prescribed initial, boundary and interface conditions. Chapter 5 is about an alternative, less imposing development of neural-form trial solutions for PDEs, inside rectangular and non-rectangular convex boundaries. Chapter 6 presents an ensemble method that avoids the multicollinearity issue and provides

enhanced generalization performance that could be suitable for handling ”few-shots”- problems frequently appearing in nuclear engineering.