用神经控制微分方程修正预测误差，提升时序模型长期预测精度。
Neural CDEs as Correctors for Learned Time Series Models
- 构建预测-校正框架，用神经控制微分方程实时修正多步预测偏差。
- 在合成、物理系统和真实数据上，对多种预测器均实现稳定性能提升。
- 支持不规则采样数据，兼容连续与离散时间模型，适合高精度时序任务。
学习型时序模型在动态系统状态预测中广泛应用，但多步预测常面临误差累积问题。本文提出一种预测-校正框架：预测器采用学习型时序模型生成多步预测，校正器则为神经控制微分方程（Neural CDE），用于修正预测误差。该校正器可处理不规则采样数据，兼容连续与离散时间预测器。此外，引入两种正则化策略，提升校正器的外推能力并加速训练。理论分析提供了框架稳定性和收敛性的保证。在合成数据、物理系统及真实世界数据集上的实验表明，该框架在多种预测器（如神经微分方程、ContiFormer、DLinear）上均一致提升预测性能，验证了其预测器无关性。
原文摘要 · Abstract (English)
Learned time-series models, whether continuous or discrete, are widely used for forecasting the states of dynamical systems but suffer from error accumulation in multi-step forecasts. To address this issue, we propose a Predictor-Corrector framework in which the Predictor is a learned time-series model that generates multi-step forecasts and the Corrector is a neural controlled differential equation that corrects the forecast errors. The Corrector works with irregularly sampled time series and is compatible with both continuous- and discrete-time Predictors. We further introduce two regularization strategies that improve the Corrector's extrapolation performance and accelerate its training. We also provide theoretical guarantees on the stability and convergence of the proposed framework. Experiments on synthetic, physics-based, and real-world datasets show that the proposed framework consistently improves forecasting performance across diverse Predictors, including neural ordinary differential equations, ContiFormer, and DLinear, demonstrating its predictor-agnostic nature.
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