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.

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.

Although tokamaks are one of the most promising devices for realizing nuclear fusion as an energy source, there are still key obstacles when it comes to understanding the dynamics of the plasma and controlling it. As such, it is crucial that high quality models are developed to assist in overcoming these obstacles. In this work, we take an entirely data driven approach to learn such a model. In particular, we use historical data from the DIII-D tokamak to train a deep recurrent network that is able to predict the full time evolution of plasma discharges (or "shots"). Following this, we investigate how different training and inference procedures affect the quality and calibration of the shot predictions.