Some Studies in Operator Learning for Solving Differential Equations

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