Neural CDEs as Correctors for Learned Time Series Models

2025-12-12

AI Summary

Temporal forecasting models—whether continuous/discrete or regularly/irregularly sampled—commonly suffer from error accumulation in multi-step-ahead prediction. This paper proposes a generic prediction-correction framework that, for the first time, employs Neural Controlled Differential Equations (Neural CDEs) to dynamically model and correct multi-step residual errors of arbitrary predictors. The framework supports plug-and-play integration of heterogeneous predictors and introduces two novel regularization strategies—CDE-L2 and TrajReg—that substantially improve extrapolation robustness and training efficiency. Evaluated on synthetic data, physics-based simulations, and multiple real-world benchmarks—including electricity, traffic, and meteorological datasets—the framework consistently enhances the performance of state-of-the-art models such as Neural Differential Equations (NDE), Contiformer, and DLinear, achieving average multi-step prediction error reductions of 12.7%–28.4%.

Technology Category

• Intelligent Robots: State Estimation
• Planning, Routing, and Scheduling: Temporal Planning
• Humans and AI: Human-Aware Planning and Behavior Prediction

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

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.

Problem

• Improving multi-step forecast accuracy in learned time-series models
• Correcting errors in continuous- and discrete-time model predictions
• Enhancing irregularly sampled time series forecasting performance

Innovation

• Neural CDE corrector predicts forecast errors
• Works with irregular time series and diverse predictors
• Uses regularization for improved extrapolation and training