$K^2$VAE: A Koopman-Kalman Enhanced Variational AutoEncoder for Probabilistic Time Series Forecasting
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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909705940500480 |
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| author | Wu, Xingjian Qiu, Xiangfei Gao, Hongfan Hu, Jilin Yang, Bin Guo, Chenjuan |
| author_facet | Wu, Xingjian Qiu, Xiangfei Gao, Hongfan Hu, Jilin Yang, Bin Guo, Chenjuan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_23017 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $K^2$VAE: A Koopman-Kalman Enhanced Variational AutoEncoder for Probabilistic Time Series Forecasting Wu, Xingjian Qiu, Xiangfei Gao, Hongfan Hu, Jilin Yang, Bin Guo, Chenjuan Machine Learning Artificial Intelligence 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. |
| title | $K^2$VAE: A Koopman-Kalman Enhanced Variational AutoEncoder for Probabilistic Time Series Forecasting |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2505.23017 |