To address this issue, we propose using probabilistic reparameterization ( PR).

UML is known to be challenging: Even learning linear mixtures requires highly nontrivial analytical tools, e.g., independent component analysis or nonnegative matrix factorization.

Artificial Intelligence is rapidly embedding itself within militaries, economies, and societies, reshaping their very foundations. Given the depth and breadth of its consequences, it has never been more pressing to understand how to ensure that AI systems are safe, ethical, and have a positive societal impact. This book aims to provide a comprehensive approach to understanding AI risk. Our primary goals include consolidating fragmented knowledge on AI risk, increasing the precision of core ideas, and reducing barriers to entry by making content simpler and more comprehensible. The book has been designed to be accessible to readers from diverse backgrounds. You do not need to have studied AI, philosophy, or other such topics. The content is skimmable and somewhat modular, so that you can choose which chapters to read. We introduce mathematical formulas in a few places to specify claims more precisely, but readers should be able to understand the main points without these.

Accurately capturing the three dimensional power distribution within a reactor core is vital for ensuring the safe and economical operation of the reactor, compliance with Technical Specifications, and fuel cycle planning (safety, control, and performance evaluation). Offline (that is, during cycle planning and core design), a three dimensional neutronics simulator is used to estimate the reactor's power, moderator, void, and flow distributions, from which margin to thermal limits and fuel exposures can be approximated. Online, this is accomplished with a system of local power range monitors (LPRMs) designed to capture enough neutron flux information to infer the full nodal power distribution. Certain problems with this process, ranging from measurement and calibration to the power adaption process, pose challenges to operators and limit the ability to design reload cores economically (e.g., engineering in insufficient margin or more margin than required). Artificial intelligence (AI) and machine learning (ML) are being used to solve the problems to reduce maintenance costs, improve the accuracy of online local power measurements, and decrease the bias between offline and online power distributions, thereby leading to a greater ability to design safe and economical reload cores. We present ML models trained from two deep neural network (DNN) architectures, SurrogateNet and LPRMNet, that demonstrate a testing error of 1 percent and 3 percent, respectively. Applications of these models can include virtual sensing capability for bypassed or malfunctioning LPRMs, on demand virtual calibration of detectors between successive calibrations, highly accurate nuclear end of life determinations for LPRMs, and reduced bias between measured and predicted power distributions within the core.

The domain of laser fusion presents a unique and challenging predictive modeling application landscape for machine learning methods due to high problem complexity and limited training data. Data-driven approaches utilizing prescribed functional forms, inductive biases and physics-informed learning (PIL) schemes have been successful in the past for achieving desired generalization ability and model interpretation that aligns with physics expectations. In complex multi-physics application domains, however, it is not always obvious how architectural biases or discriminative penalties can be formulated. In this work, focusing on nuclear fusion energy using high powered lasers, we present the use of Kolmogorov-Arnold Networks (KANs) as an alternative to PIL for developing a new type of data-driven predictive model which is able to achieve high prediction accuracy and physics interpretability. A KAN based model, a MLP with PIL, and a baseline MLP model are compared in generalization ability and interpretation with a domain expert-derived symbolic regression model. Through empirical studies in this high physics complexity domain, we show that KANs can potentially provide benefits when developing predictive models for data-starved physics applications.