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：在领域泛化领域，构建能够在无目标域数据的情况下泛化至目标域的预测模型仍是一项挑战。当考虑域间动态演化时，该问题更为复杂。尽管已有多种方法被提出以解决此问题，但对底层泛化理论的全面理解仍存在不足。在本研究中，我们提出了新颖的理论结果：对齐条件分布可降低泛化边界。该分析为通过库普曼神经算子解决时间域泛化问题提供了关键动机，进而构建了时间库普曼网络。通过运用库普曼算子，我们基于库普曼理论有效处理了时间域泛化中随时间演化的分布——该理论通过寻找测量函数来建立演化域之间的线性转移关系。通过在合成数据集与真实世界数据集上的实证评估，我们验证了所提方法的有效性。