Tackling complexity and nonlinearity in plasmas and networks using artificial intelligence and analytical methods

Abstract

Nonlinear interactions of a large number of components are a core aspect of many phenomena in the physical, biological, and social sciences. In this thesis, we tackle such complexity in plasmas and networks using analytical, computational, and data-driven methods. In Chapter 1, we study the impact of key features of social network structure — including sparsity, community structure, and degree distributions — on the spread of nonlinear contagions. By developing effective diffusion models with reduced degrees of freedom, we obtain closed form and numerical predictions for the contagion dynamics and identify phase transitions demarcating structural regimes where global cascades become possible. In Chapter 2, we consider a model of reputation spread on networks, and use it to quantify the impact of indirect reciprocity as a function of local network structure. We use these insights to motivate a new network growth mechanism – trust based attachment – which generates networks that match key quantitative characteristics of real world social networks. In Chapter 3, we present a deep learning approach for forecasting disruptive instabilities in tokamak fusion reactors based on scalar and multi-dimensional data from past experimental runs. The approach is able to successfully predict disruptions on machines unseen during training.