Yue Song

This book introduces approaches to generalize the benefits of equivariant deep learning to a broader set of learned structures through learned homomorphisms. In the field of machine learning, the idea of incorporating knowledge of data symmetries into artificial neural networks is known as equivariant deep learning and has led to the development of cutting edge architectures for image and physical data processing. The power of these models originates from data-specific structures ingrained in them through careful engineering. To-date however, the ability for practitioners to build such a structure into models is limited to situations where the data must exactly obey specific mathematical symmetries. The authors discuss naturally inspired inductive biases, specifically those which may provide types of efficiency and generalization benefits through what are known as homomorphic representations, a new general type of structured representation inspired from techniques in physics and neuroscience. A review of some of the first attempts at building models with learned homomorphic representations are introduced. The authors demonstrate that these inductive biases improve the ability of models to represent natural transformations and ultimately pave the way to the future of efficient and effective artificial neural networks.

Rotor angle stability is a topic of fundamental importance in electric power systems. Traditionally, rotor angle stability analysis is oriented to node dynamics, especially the impact of generator modeling and parameters. On the other hand, the power network structural information is simply treated as some coefficients in the system dynamical models, which have been paid less attention. This monograph surveys the network-based theories of rotor angle stability that elaborate the role of power network structure, including the results developed in early years as well as in recent years that are facilitated by the new progress on graph theory. It focuses on the connections between power network structures and system dynamic behaviors, and those graph theoretic tools tailored for power system analysis.This publication provides new insights into some important problems in rotor angle stability that have not been well addressed by the traditional node-based approaches. Network-Based Analysis of Rotor Angle Stability of Power Systems is a must-read for all students and researchers working on the cutting edge of electric power systems.