Temporal distributional shifts, with underlying dynamics changing over time, frequently occur in real-world time series and pose a fundamental challenge for deep neural networks (DNNs). In this paper, we propose a novel deep sequence model based on the Koopman theory for time series forecasting: Koopman Neural Forecaster (KNF) which leverages DNNs to learn the linear Koopman space and the coefficients of chosen measurement functions. KNF imposes appropriate inductive biases for improved robustness against distributional shifts, employing both a global operator to learn shared characteristics and a local operator to capture changing dynamics, as well as a specially-designed feedback loop to continuously update the learned operators over time for rapidly varying behaviors. We demonstrate that \ours{} achieves superior performance compared to the alternatives, on multiple time series datasets that are shown to suffer from distribution shifts.

翻译：时间分布偏移（其底层动力学随时间变化）在真实世界时间序列中频繁出现，并对深度神经网络构成根本性挑战。本文提出一种基于库普曼理论的新型深度序列模型用于时间序列预测：Koopman神经预测器（KNF），该模型利用深度神经网络学习线性库普曼空间及所选测量函数的系数。KNF通过施加适当的归纳偏置来增强对分布偏移的鲁棒性：采用全局算子学习共享特征、局部算子捕捉动态变化，并设计专用反馈回路持续更新学习算子以应对快速变化行为。我们证明，在多个存在分布偏移的时间序列数据集上，本方法相较现有替代方案实现了更优性能。