mlsanityData to 7 Oct 2026

Learnable Path in Neural Controlled Differential Equations

arXiv 2301.04333 ↗First posted 11 Jan 2023cs.LG cs.AIcited by 8

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Abstract (arXiv)

Neural controlled differential equations (NCDEs), which are continuous analogues to recurrent neural networks (RNNs), are a specialized model in (irregular) time-series processing. In comparison with similar models, e.g., neural ordinary differential equations (NODEs), the key distinctive characteristics of NCDEs are i) the adoption of the continuous path created by an interpolation algorithm from each raw discrete time-series sample and ii) the adoption of the Riemann--Stieltjes integral. It is the continuous path which makes NCDEs be analogues to continuous RNNs. However, NCDEs use existing interpolation algorithms to create the path, which is unclear whether they can create an optimal path. To this end, we present a method to generate another latent path (rather than relying on existing interpolation algorithms), which is identical to learning an appropriate interpolation method. We design an encoder-decoder module based on NCDEs and NODEs, and a special training method for it. Our method shows the best performance in both time-series classification and forecasting.

Key facts. Cited by 8 papers in the map (data through 7 Oct 2026). Builds on 23 of its 54 references that are in the map. First posted on arXiv 11 Jan 2023.

Builds on

23 of 54 references.

References · 23

  1. 2018Neural Ordinary Differential Equationscited by 3,733
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11 more
  1. 2018The UEA multivariate time series classification archive, 2018cited by 330
  2. 2019GRU-ODE-Bayes: Continuous modeling of sporadically-observed time seriescited by 230
  3. 2021Spatial-Temporal Graph ODE Networks for Traffic Flow Forecastingcited by 209
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  5. 2021Graph Neural Controlled Differential Equations for Traffic Forecastingcited by 133
  6. 2021Z-GCNETs: Time Zigzags at Graph Convolutional Networks for Time Series Forecastingcited by 67
  7. 2021Neural Controlled Differential Equations for Online Prediction Taskscited by 46
  8. 2021Attentive Neural Controlled Differential Equations for Time-series Classification and Forecastingcited by 28
  9. 2021Climate Modeling with Neural Diffusion Equationscited by 20
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Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 1; 2024: 3; 2025: 3; 2026: 1.

8 papers.

  1. 2024Stable Neural Stochastic Differential Equations in Analyzing Irregular Time Series Datacited by 35
  2. 2025Comprehensive Review of Neural Differential Equations for Time Series Analysiscited by 20
  3. 2024Unleashing The Power of Pre-Trained Language Models for Irregularly Sampled Time Seriescited by 10
  4. 2024DualDynamics: Synergizing Implicit and Explicit Methods for Robust Irregular Time Series Analysiscited by 4
  5. 2025Forecasting Continuous Non-Conservative Dynamical Systems in SO(3)cited by 3
  6. 2023Long-term Time Series Forecasting based on Decomposition and Neural Ordinary Differential Equationscited by 1
  7. 2025TANDEM: Temporal Attention-guided Neural Differential Equations for Missingness in Time Series Classificationcited by 0
  8. 2026From Path Signatures to Sequential Modeling: Incremental Signature Contributions for Offline RLcited by 0