Koopman operator theory, a powerful framework for discovering the underlying dynamics of
nonlinear dynamical systems, was recently shown to be intimately connected with neural …

Koopman operator theory is shown to be directly related to the renormalization group. This
observation allows us, with no assumption of translational invariance, to compute the critical …

This thesis delves into the intricate world of Deep Neural Networks (DNNs), focusing on the
exciting concept of the Lottery Ticket Hypothesis (LTH). The LTH posits that within extensive …

We motivate the use of neural networks for the construction of numerical solutions to
differential equations. We prove that there exists a feed-forward neural network that can …

This thesis explores the operations of Transformer blocks through the lens of Koopman
Operator theory, aiming to provide a deeper understanding of their inner dynamics …

Recurrent neural network (RNN) is a popular modeling choice for sequential data. However,
empirical experience shows RNNs are often difficult and time-consuming to tune and …

Many natural phenomenon such as human activities, wild species evolution and epidemic
spreading, man-made complex systems like the World Wide Web, the power grids and the …

Understanding and predicting states in dynamic systems is a core challenge in many areas
of study. This involves trying to estimate an evolving signal based on past observations or …

Neural Network Differential Equation (NN DE) solvers have surged in popularity due to a
combination of factors: computational advances making their optimization more tractable …

As discussed in Sec. 3 of the main text, the computational complexity of Koopman training is
dependent on the approach we take to estimate the action of the Koopman operator on the …