INDEQS: Informed Neural controlled Differential EQuationS

2026-06-18 · Source: stat.ML updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Data Science & Analytics, Mathematics & Computational Sciences · Depth: Expert, quick

Summary

INDEQS (Informed Neural controlled Differential EQuationS) is a novel graph-based Neural Controlled Differential Equation (NCDE) method for time series forecasting. Submitted on 17 Jun 2026, INDEQS integrates prior knowledge of directed graph structures into its architecture, a departure from standard graph-based NCDEs that learn spatial structure purely from data. The method distinguishes between inner mixing of hidden states across graph nodes and outer mixing between the vector field and control. It offers both a lightweight, graph-constrained variant and a more expressive version that learns additional graph connections via adaptive graph convolutions. Evaluated on a synthetic continuous advection simulation, river discharge forecasting, and traffic flow prediction on PeMS08, INDEQS demonstrates that "outer informedness" consistently improves mean absolute error (MAE) compared to uninformed NCDEs, particularly on larger graphs. "Inner informedness" provides a parameter-efficient alternative when strict adherence to a known adjacency is desired. Furthermore, continuous decoders showed superior accuracy and temporal flexibility on real-world tasks over discrete convolutional decoders.

Key takeaway

For Machine Learning Engineers developing time series forecasting models on graph-structured data, you should consider INDEQS to leverage known directed graph structures. Implementing "outer informedness" can significantly improve forecasting accuracy, especially on larger graphs, by directly integrating prior knowledge. If parameter efficiency or strict adherence to a known adjacency is critical, opt for "inner informedness." This approach offers superior performance and temporal flexibility compared to uninformed NCDEs and discrete decoders.

Key insights

Incorporating known graph structures into NCDEs improves time series forecasting accuracy and efficiency.

Principles

• Prior graph knowledge enhances NCDE forecasting.
• Outer informedness improves MAE on larger graphs.
• Inner informedness offers parameter efficiency.

Method

INDEQS integrates prior directed graph knowledge into NCDEs by separating inner and outer mixing, offering graph-constrained or adaptive graph convolution variants for time series forecasting.

In practice

• Use INDEQS for directed graph time series.
• Prioritize outer informedness for larger graphs.
• Consider inner informedness for strict graph adherence.

Topics

• Neural Controlled Differential Equations
• Time Series Forecasting
• Graph Neural Networks
• Directed Graphs
• Spatio-temporal Data
• PeMS08

Code references

• Mitchi1/indeqs

Best for: AI Scientist, Machine Learning Engineer, Research Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.