Continuous Temporal Domain Generalization

TL;DR

This paper introduces a novel framework called Koodos for continuous temporal domain generalization, leveraging Koopman theory to model and control complex dynamics in temporally evolving data, outperforming traditional fixed-interval methods.

Contribution

It formalizes the concept of continuous temporal domain generalization and proposes a Koopman operator-based approach to learn and optimize the dynamics across continuous time.

Findings

Effective modeling of continuous temporal dynamics.

Improved generalization across irregular time observations.

Demonstrated efficiency and effectiveness in experiments.

Abstract

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. The code can be found at: https://github.com/Zekun-Cai/Koodos.