$K^2$VAE: A Koopman-Kalman Enhanced Variational AutoEncoder for Probabilistic Time Series Forecasting
Xingjian Wu, Xiangfei Qiu, Hongfan Gao, Jilin Hu, Bin Yang, Chenjuan Guo
Abstract
Probabilistic Time Series Forecasting (PTSF) plays a crucial role in decision-making across various fields, including economics, energy, and transportation. Most existing methods excell at short-term forecasting, while overlooking the hurdles of Long-term Probabilistic Time Series Forecasting (LPTSF). As the forecast horizon extends, the inherent nonlinear dynamics have a significant adverse effect on prediction accuracy, and make generative models inefficient by increasing the cost of each iteration. To overcome these limitations, we introduce $K^2$VAE, an efficient VAE-based generative model that leverages a KoopmanNet to transform nonlinear time series into a linear dynamical system, and devises a KalmanNet to refine predictions and model uncertainty in such linear system, which reduces error accumulation in long-term forecasting. Extensive experiments demonstrate that $K^2$VAE outperforms state-of-the-art methods in both short- and long-term PTSF, providing a more efficient and accurate solution.
BibTeX
@inproceedings{
wu2025kvae,
title={\$K{\textasciicircum}2\${VAE}: A Koopman-Kalman Enhanced Variational AutoEncoder for Probabilistic Time Series Forecasting},
author={Xingjian Wu and Xiangfei Qiu and Hongfan Gao and Jilin Hu and Bin Yang and Chenjuan Guo},
booktitle={Forty-second International Conference on Machine Learning},
year={2025},
url={https://openreview.net/forum?id=71Mm8GDGYd}
}