Some Studies in Operator Learning for Solving Differential Equations

Operator learning has the potential to supplement traditional numerical methods, especially when speed is desired more than accuracy. 
This includes the architectures DeepONets, Fourier neural operators and Koopman autoencoders.
First, this dissertation provides the background material for operator learning. 
Then, it studies some general best practices for operator learning.
Then, it studies the loss functions and operator forms for Koopman autoencoders. 
Finally, it studies the use of an adversarial addition to neural operators that have an autoencoder structure.