Koopman Neural Forecaster for Time Series with Temporal Distribution Shifts

TL;DR

This paper introduces the Koopman Neural Forecaster, a deep learning model that uses Koopman theory to improve time series forecasting under distributional shifts by learning linear representations and dynamically updating operators.

Contribution

The paper presents a novel Koopman-based neural network model with a feedback mechanism for robust forecasting amid temporal distribution shifts.

Findings

Outperforms existing methods on multiple datasets with distribution shifts.

Effectively captures changing dynamics through global and local operators.

Demonstrates robustness to temporal distributional shifts in real-world data.

Abstract

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.