Neural CDEs as Correctors for Learned Time Series Models

Learned time-series models, whether continuous-or discrete-time, are widely used to forecast the states of a dynamical system. Such models generate multi-step forecasts either directly, by predicting the full horizon at once, or iteratively, by feeding back their own predictions at each step. In both cases, the multi-step forecasts are prone to errors. To address this, we propose a Predictor-Corrector mechanism where the Predictor is any learned time-series model and the Corrector is a neural controlled differential equation. The Predictor forecasts, and the Corrector predicts the errors of the forecasts. Adding these errors to the forecasts improves forecast performance. The proposed Corrector works with irregularly sampled time series and continuous-and discrete-time Predictors. Additionally, we introduce two regularization strategies to improve the extrapolation performance of the Corrector with accelerated training. We evaluate our Corrector with diverse Predictors, e.g., neural ordinary differential equations, Contiformer, and DLinear, on synthetic, physics simulation, and real-world forecasting datasets. The experiments demonstrate that the Predictor-Corrector mechanism consistently improves the performance compared to Predictor alone. Learning time-series models from such datasets has applications ranging from energy demand forecasting, traffic and mobility prediction, weather prediction, anomaly detection, and decision-making in robotics (Zeng et al., 2022; Li et al., 2017; Stankeviciute et al., 2021; Xu et al., 2021; Chua et al., 2018). Several works focused on learning time-series models from data. There are at least two ways to train such models. Early studies focused on training the model to predict one step ahead (Basharat & Shah, 2009; Khansari-Zadeh & Billard, 2011).