# Neural CDEs as Correctors for Learned Time Series Models

arXiv: https://arxiv.org/abs/2512.12116 · HTML: https://mlsanity.com/paper/2512.12116/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 57 references that are in the map.
- First posted on arXiv 13 Dec 2025.

## Builds on (most cited first, 30 of 33)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [Are Transformers Effective for Time Series Forecasting?](https://mlsanity.com/paper/2205.13504/) (2022)
- [On the Properties of Neural Machine Translation: Encoder-Decoder Approaches](https://mlsanity.com/paper/1409.1259/) (2014)
- [FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting](https://mlsanity.com/paper/2201.12740/) (2022)
- [Deep Reinforcement Learning in a Handful of Trials using Probabilistic Dynamics Models](https://mlsanity.com/paper/1805.12114/) (2018)
- [Offline Reinforcement Learning as One Big Sequence Modeling Problem](https://mlsanity.com/paper/2106.02039/) (2021)
- [Enhancing the Locality and Breaking the Memory Bottleneck of Transformer on Time Series Forecasting](https://mlsanity.com/paper/1907.00235/) (2019)
- [Recurrent Neural Networks for Multivariate Time Series with Missing Values](https://mlsanity.com/paper/1606.01865/) (2016)
- [Neural Controlled Differential Equations for Irregular Time Series](https://mlsanity.com/paper/2005.08926/) (2020)
- [UniPC: A Unified Predictor-Corrector Framework for Fast Sampling of Diffusion Models](https://mlsanity.com/paper/2302.04867/) (2023)
- [Anomaly Transformer: Time Series Anomaly Detection with Association Discrepancy](https://mlsanity.com/paper/2110.02642/) (2021)
- [BRITS: Bidirectional Recurrent Imputation for Time Series](https://mlsanity.com/paper/1805.10572/) (2018)
- [Scalable and accurate deep learning for electronic health records](https://mlsanity.com/paper/1801.07860/) (2018)
- [GRU-ODE-Bayes: Continuous modeling of sporadically-observed time series](https://mlsanity.com/paper/1905.12374/) (2019)
- [Deep Time Series Models: A Comprehensive Survey and Benchmark](https://mlsanity.com/paper/2407.13278/) (2024)
- [Disentangling Physical Dynamics from Unknown Factors for Unsupervised Video Prediction](https://mlsanity.com/paper/2003.01460/) (2020)
- [FourCastNet: Accelerating Global High-Resolution Weather Forecasting using Adaptive Fourier Neural Operators](https://mlsanity.com/paper/2208.05419/) (2022)
- [Latent ODEs for Irregularly-Sampled Time Series](https://mlsanity.com/paper/1907.03907/) (2019)
- [Neural Rough Differential Equations for Long Time Series](https://mlsanity.com/paper/2009.08295/) (2020)
- [KalmanNet: Neural Network Aided Kalman Filtering for Partially Known Dynamics](https://mlsanity.com/paper/2107.10043/) (2021)
- [Learning Long-Term Dependencies in Irregularly-Sampled Time Series](https://mlsanity.com/paper/2006.04418/) (2020)
- [Multi-Person Extreme Motion Prediction](https://mlsanity.com/paper/2105.08825/) (2021)
- [ContiFormer: Continuous-Time Transformer for Irregular Time Series Modeling](https://mlsanity.com/paper/2402.10635/) (2024)
- [Structured Linear CDEs: Maximally Expressive and Parallel-in-Time Sequence Models](https://mlsanity.com/paper/2505.17761/) (2025)
- [AutoHFormer: Efficient Hierarchical Autoregressive Transformer for Time Series Prediction](https://mlsanity.com/paper/2506.16001/) (2025)
- [Learning Semilinear Neural Operators : A Unified Recursive Framework For Prediction And Data Assimilation](https://mlsanity.com/paper/2402.15656/) (2024)
- [Predictor-Corrector Enhanced Transformers with Exponential Moving Average Coefficient Learning](https://mlsanity.com/paper/2411.03042/) (2024)

## Built on by (most cited first, 1 of 1)

- [Continuous-Time Probabilistic Correctors for Uncertainty-Aware Physics-Based Spacecraft Trajectory Forecasting](https://mlsanity.com/paper/2606.21021/) (2026)

## Abstract (arXiv)

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.