  Temporal Domain Generalization (TDG) addresses the challenge of training
predictive models under temporally varying data distributions. Traditional TDG
approaches typically focus on domain data collected at fixed, discrete time
intervals, which limits their capability to capture the inherent dynamics
within continuous-evolving and irregularly-observed temporal domains. To
overcome this, this work formalizes the concept of Continuous Temporal Domain
Generalization (CTDG), where domain data are derived from continuous times and
are collected at arbitrary times. CTDG tackles critical challenges including:
1) Characterizing the continuous dynamics of both data and models, 2) Learning
complex high-dimensional nonlinear dynamics, and 3) Optimizing and controlling
the generalization across continuous temporal domains. To address them, we
propose a Koopman operator-driven continuous temporal domain generalization
(Koodos) framework. We formulate the problem within a continuous dynamic system
and leverage the Koopman theory to learn the underlying dynamics; the framework
is further enhanced with a comprehensive optimization strategy equipped with
analysis and control driven by prior knowledge of the dynamics patterns.
Extensive experiments demonstrate the effectiveness and efficiency of our
approach.
