Generalizing across Temporal Domains with Koopman Operators
This addresses the challenge of building predictive models that generalize across time-evolving domains without access to target data, representing an incremental advance in domain generalization theory.
The paper tackles the Temporal Domain Generalization problem where models must generalize across domains with evolving dynamics, proposing Temporal Koopman Networks that apply Koopman theory to align conditional distributions and reduce generalization bounds, with empirical validation on synthetic and real-world datasets.
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.