Loss Terms and Operator Forms of Koopman Autoencoders

TL;DR

This paper systematically studies the loss functions and operator forms in Koopman autoencoders, introduces new loss terms, and clarifies their impact on operator learning.

Contribution

It provides a comprehensive analysis of existing loss functions and operator forms, and proposes novel loss terms for improved Koopman autoencoder performance.

Findings

New loss terms improve learning stability

Operator form choices significantly affect model accuracy

Systematic comparison clarifies best practices

Abstract

Koopman autoencoders are a prevalent architecture in operator learning. But, the loss functions and the form of the operator vary significantly in the literature. This paper presents a fair and systemic study of these options. Furthermore, it introduces novel loss terms.