Neural Differential Equations for Continuous-Time Analysis

Oh, Y., Lim, D.-Y., & Kim, S. (2025). Neural Differential Equations for Continuous-Time Analysis. In Proceedings of the 34th ACM International Conference on Information and Knowledge Management (CIKM ‘25) (pp. 6837–6840). Association for Computing Machinery. https://doi.org/10.1145/3746252.3761447 [paper]

Overview

Modeling complex, irregular time series is a common challenge in knowledge discovery and data mining. This tutorial introduces Neural Differential Equations (NDEs) as a continuous-time modeling framework for non-uniform sampling and missing observations. It reviews the theory and practical application of Neural Ordinary (NODEs), Controlled (NCDEs), and Stochastic (NSDEs) Differential Equations. The tutorial also covers robustness and stability, then uses open-source libraries for tasks such as interpolation and classification.

Learning Goals

By the end of this resource, you will:

Understand why continuous-time modeling is beneficial for irregular and multi-resolution time series.
Know the differences between NODEs, NCDEs, and NSDEs — their assumptions, strengths, and limitations.
Be able to train and evaluate NDE-based models with attention to solver choice, stability, and computational cost.
Recognize strategies for assessing robustness, interpretability, and reliability in sensitive domains.

Target Audience

Graduate students entering time series modeling research.
Applied researchers in domains with irregular or sparse observations.
Practitioners studying forecasting or classification under dataset shift and uncertainty.

Prerequisites:

Working knowledge of calculus, linear algebra, and probability.
Familiarity with deep learning fundamentals and PyTorch.

Tutorial Outline and Structure

Session I: Foundations of Continuous-Time Modeling [link]

Overview & Motivation (10 min) Why continuous-time? Challenges of irregular data.
Neural Ordinary Differential Equations (35 min) Theory, core concepts, and the adjoint method for training.
Hands-on: Part I [link] (30 min) Implementing Neural Ordinary Differential Equations and Latent ODEs.

Session II: Advanced Models and Applications [link]

Neural Controlled Differential Equations (25 min) Handling irregular data as a continuous path.
Neural Stochastic Differential Equations (20 min) Modeling uncertainty; focus on Stable SDEs.
Hands-on: Part II [link] (20 min) Implementing and comparing advanced models.
Summary & Future Directions (10 min) Recap of the NDE family, applications, and conclusion.