用线性化与卡尔曼滤波提升长时序预测的准确性和效率
$K^2$VAE: A Koopman-Kalman Enhanced Variational AutoEncoder for Probabilistic Time Series Forecasting
- 通过KoopmanNet将非线性时序转为线性系统，降低建模复杂度
- 引入KalmanNet减少长期预测中的误差累积，显著提升长程精度
- 适合需要高精度长周期预测的金融、能源等场景
概率时间序列预测（PTSF）在经济、能源、交通等领域决策中至关重要。现有方法在短期预测表现优异，但面临长期预测难题。随着预测时域拉长，固有的非线性动态显著降低预测精度，且使生成模型每轮迭代成本上升。为此，我们提出K²VAE，一种基于变分自编码器的生成模型：利用KoopmanNet将非线性时序转换为线性动力系统，再通过KalmanNet对线性系统中的预测与不确定性进行优化，有效缓解长期预测中的误差累积。大量实验表明，K²VAE在短期和长期概率预测上均超越现有先进方法，提供更高效、更准确的解决方案。
原文摘要 · Abstract (English)
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.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。