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Multi-View Neural Differential Equations for Continuous-Time Stream Data in Long-Term Traffic Forecasting

Zibo Liu, Zhe Jiang, Shigang Chen

TL;DR

This work tackles long-term traffic forecasting on continuous-time data by introducing MNDE, a multi-view neural differential equation framework. It combines CNDE for current dynamics, DNDE for delayed propagation, and DM for local gradient-based differentiation, followed by a learned aggregation to produce $l'$-step forecasts from past $l$ steps. Across multiple public datasets, MNDE achieves state-of-the-art accuracy and robustness to missing or noisy inputs, outperforming strong baselines and demonstrating stability across input lengths and flow-rate ranges. The approach offers a scalable, continuous-time modeling paradigm with practical potential for real-time traffic management and intelligent transportation systems.

Abstract

Long-term traffic flow forecasting plays a crucial role in intelligent transportation as it allows traffic managers to adjust their decisions in advance. However, the problem is challenging due to spatio-temporal correlations and complex dynamic patterns in continuous-time stream data. Neural Differential Equations (NDEs) are among the state-of-the-art methods for learning continuous-time traffic dynamics. However, the traditional NDE models face issues in long-term traffic forecasting due to failures in capturing delayed traffic patterns, dynamic edge (location-to-location correlation) patterns, and abrupt trend patterns. To fill this gap, we propose a new NDE architecture called Multi-View Neural Differential Equations. Our model captures current states, delayed states, and trends in different state variables (views) by learning latent multiple representations within Neural Differential Equations. Extensive experiments conducted on several real-world traffic datasets demonstrate that our proposed method outperforms the state-of-the-art and achieves superior prediction accuracy for long-term forecasting and robustness with noisy or missing inputs.

Multi-View Neural Differential Equations for Continuous-Time Stream Data in Long-Term Traffic Forecasting

TL;DR

This work tackles long-term traffic forecasting on continuous-time data by introducing MNDE, a multi-view neural differential equation framework. It combines CNDE for current dynamics, DNDE for delayed propagation, and DM for local gradient-based differentiation, followed by a learned aggregation to produce -step forecasts from past steps. Across multiple public datasets, MNDE achieves state-of-the-art accuracy and robustness to missing or noisy inputs, outperforming strong baselines and demonstrating stability across input lengths and flow-rate ranges. The approach offers a scalable, continuous-time modeling paradigm with practical potential for real-time traffic management and intelligent transportation systems.

Abstract

Long-term traffic flow forecasting plays a crucial role in intelligent transportation as it allows traffic managers to adjust their decisions in advance. However, the problem is challenging due to spatio-temporal correlations and complex dynamic patterns in continuous-time stream data. Neural Differential Equations (NDEs) are among the state-of-the-art methods for learning continuous-time traffic dynamics. However, the traditional NDE models face issues in long-term traffic forecasting due to failures in capturing delayed traffic patterns, dynamic edge (location-to-location correlation) patterns, and abrupt trend patterns. To fill this gap, we propose a new NDE architecture called Multi-View Neural Differential Equations. Our model captures current states, delayed states, and trends in different state variables (views) by learning latent multiple representations within Neural Differential Equations. Extensive experiments conducted on several real-world traffic datasets demonstrate that our proposed method outperforms the state-of-the-art and achieves superior prediction accuracy for long-term forecasting and robustness with noisy or missing inputs.
Paper Structure (30 sections, 12 equations, 8 figures, 7 tables)

This paper contains 30 sections, 12 equations, 8 figures, 7 tables.

Table of Contents

  1. Introduction
  2. Preliminaries and Problem Statement
  3. Preliminaries
  4. Problem Statement
  5. Related Works on Traffic Forecasting
  6. Statistics and Machine Learning Approaches
  7. Deep Learning Approaches
  8. Neural Differential Equation Methods
  9. Proposed Approach
  10. Temporal Interpolation and Latent Embeddings
  11. Current Neural Differential Equations (CNDE) Module
  12. Delayed Neural Differential Equations Module
  13. Differentiation Module
  14. Aggregation Module
  15. Loss Function
  16. ...and 15 more sections

Figures (8)

  • Figure 1: An overview of the Multi-View Neural Differential Equation (MNDE) framework, which comprises four distinct modules. (A) Current Neural Differential Equations (CNDE) Module, (B) Delayed Neural Differential Equations (DNDE) Module, (C) Differentiation Module (DM), and (D) Aggregation Module.
  • Figure 2: Ablation study, 8th hour time interval, PEMS08 dataset
  • Figure 3: Comparison of traffic flow forecasting between our proposed MNDE and STGNCDE on PEMS04 dataset.
  • Figure 4: Performance comparison of four models with different length of input data on PEMS04 dataset.
  • Figure 5: (a) Embedding visualization. (b) Embedding visualization (DNDE shifted to the right)
  • ...and 3 more figures