  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.
