  Real-world time series are characterized by intrinsic non-stationarity that
poses a principal challenge for deep forecasting models. While previous models
suffer from complicated series variations induced by changing temporal
distribution, we tackle non-stationary time series with modern Koopman theory
that fundamentally considers the underlying time-variant dynamics. Inspired by
Koopman theory of portraying complex dynamical systems, we disentangle
time-variant and time-invariant components from intricate non-stationary series
by Fourier Filter and design Koopman Predictor to advance respective dynamics
forward. Technically, we propose Koopa as a novel Koopman forecaster composed
of stackable blocks that learn hierarchical dynamics. Koopa seeks measurement
functions for Koopman embedding and utilizes Koopman operators as linear
portraits of implicit transition. To cope with time-variant dynamics that
exhibits strong locality, Koopa calculates context-aware operators in the
temporal neighborhood and is able to utilize incoming ground truth to scale up
forecast horizon. Besides, by integrating Koopman Predictors into deep residual
structure, we ravel out the binding reconstruction loss in previous Koopman
forecasters and achieve end-to-end forecasting objective optimization. Compared
with the state-of-the-art model, Koopa achieves competitive performance while
saving 77.3% training time and 76.0% memory.
