Neural CDEs as Correctors for Learned Time Series Models

TL;DR

This paper introduces a predictor-corrector framework using neural controlled differential equations to enhance multi-step time series forecasting accuracy, especially with irregular sampling.

Contribution

It presents a novel predictor-corrector approach with regularization strategies, providing theoretical guarantees and demonstrating predictor-agnostic improvements across datasets.

Findings

Consistent forecasting improvements across diverse datasets.

Effective correction of multi-step forecast errors.

Compatibility with various neural time series models.

Abstract

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.