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.

翻译：在域泛化领域，构建能够在无目标数据情况下推广至目标域的预测模型仍具挑战性。当考虑域间动态演变时，该问题更为复杂。尽管已有多种方法被提出，但对底层泛化理论的全面理解尚不充分。本研究提出了新颖的理论结果：对齐条件分布可降低泛化上界。该分析为通过应用Koopman神经算子解决时间域泛化（TDG）问题提供了关键动机，由此产生时间Koopman网络（TKNets）。我们利用Koopman算子原理有效处理TDG中随时间演变的分布，通过寻找测量函数建立演化域之间的线性转移关系。在合成数据集与真实数据集上的实证评估验证了所提方法的有效性。