  In the field of domain generalization, the task of constructing a predictive
model capable of generalizing to a target domain without access to target data
remains challenging. This problem becomes further complicated when considering
evolving dynamics between domains. While various approaches have been proposed
to address this issue, a comprehensive understanding of the underlying
generalization theory is still lacking. In this study, we contribute novel
theoretic results that aligning conditional distribution leads to the reduction
of generalization bounds. Our analysis serves as a key motivation for solving
the Temporal Domain Generalization (TDG) problem through the application of
Koopman Neural Operators, resulting in Temporal Koopman Networks (TKNets). By
employing Koopman Operators, we effectively address the time-evolving
distributions encountered in TDG using the principles of Koopman theory, where
measurement functions are sought to establish linear transition relations
between evolving domains. Through empirical evaluations conducted on synthetic
and real-world datasets, we validate the effectiveness of our proposed
approach.
