Digital Commons Network^™

Interdisciplinary Studies Of Complex Network And Machine Learning And Its Applications, Shaojun Luo

Dissertations, Theses, and Capstone Projects

In this dissertation, we introduce the concept of network-based statistical inference methods of two types: network structure inference and variable inference. For network structure inference, we introduce correlation matrix, graphical Lasso, network clustering and identify the influencer in the network. For variable inference, we also introduce from Bayesian network, to Random Markov Field and Ising Model, Boltzmann and Restricted Boltzmann machine and the algorithm of Belief Propagation. Last but not the least, we introduce the most widely used neural network family and its two main types: Convolutional Neural Network and Recurrent Neural Network.

In Chapter 3 we provide an example …

A Study Of Neural Networks For The Quantum Many-Body Problem, Liam B. Schramm

Senior Projects Spring 2018

One of the fundamental problems in analytically approaching the quantum many-body problem is that the amount of information needed to describe a quantum state. As the number of particles in a system grows, the amount of information needed for a full description of the system increases exponentially. A great deal of work then has gone into finding efficient approximate representations of these systems. Among the most popular techniques are Tensor Networks and Quantum Monte Carlo methods. However, one new method with a number of promising theoretical guarantees is the Neural Quantum State. This method is an adaptation of the Restricted …