Loss Terms and Operator Forms of Koopman Autoencoders

A neural operator is a neural network that is intended to approximate an operator between function spaces [1-3]. An example of an output function for a neural operator is a solution to a differential equation. Examples of input functions for a neural operator are the initial conditions or the boundary conditions for the differential equation. The study of neural operators is called operator learning. This paper is about Koopman autoencoders, which is a prevalent neural operator architecture to to learn the time evolution of differential equations [4-7].