$K^2$VAE: A Koopman-Kalman Enhanced Variational AutoEncoder for Probabilistic Time Series Forecasting

Xingjian Wu, Xiangfei Qiu, Hongfan Gao, Jilin Hu, Bin Yang, Chenjuan Guo
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:67562-67583, 2025.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-wu25w, title = {$K^2${VAE}: A Koopman-Kalman Enhanced Variational {A}uto{E}ncoder for Probabilistic Time Series Forecasting}, author = {Wu, Xingjian and Qiu, Xiangfei and Gao, Hongfan and Hu, Jilin and Yang, Bin and Guo, Chenjuan}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {67562--67583}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/wu25w/wu25w.pdf}, url = {https://proceedings.mlr.press/v267/wu25w.html}, 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.} }
Endnote
%0 Conference Paper %T $K^2$VAE: A Koopman-Kalman Enhanced Variational AutoEncoder for Probabilistic Time Series Forecasting %A Xingjian Wu %A Xiangfei Qiu %A Hongfan Gao %A Jilin Hu %A Bin Yang %A Chenjuan Guo %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-wu25w %I PMLR %P 67562--67583 %U https://proceedings.mlr.press/v267/wu25w.html %V 267 %X 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.
APA
Wu, X., Qiu, X., Gao, H., Hu, J., Yang, B. & Guo, C.. (2025). $K^2$VAE: A Koopman-Kalman Enhanced Variational AutoEncoder for Probabilistic Time Series Forecasting. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:67562-67583 Available from https://proceedings.mlr.press/v267/wu25w.html.

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