Local Truncation Error-Guided Neural ODEs for Large Scale Traffic Forecasting

2026-05-05

AI Summary

Large-scale traffic forecasting requires simultaneous modeling of continuous macroscopic dynamics and discrete abrupt disturbances. Traditional neural ODEs, constrained by Lipschitz continuity, tend to oversmooth anomalous events, compromising both accuracy and robustness. This work proposes LTE-ODE, a novel framework that leverages local truncation error (LTE)—a concept from numerical integration—as an unsupervised inductive bias to dynamically generate spatial attention masks. During stable periods, the model maintains high-fidelity ODE evolution; at abrupt change points, it adaptively activates a discrete compensation branch. This approach circumvents gradient conflicts and attention collapse commonly observed in physics-informed models, unifying continuous evolution and discrete response without requiring manifold regularization. Experiments demonstrate that LTE-ODE achieves state-of-the-art performance across multiple traffic benchmarks, exhibits exceptional robustness to highly nonlinear fluctuations, and allows flexible adjustment of integration step sizes to accommodate varying hardware memory constraints.

Abstract

Spatiotemporal forecasting in physical systems, such as large-scale traffic networks, requires modeling a dual dynamic: continuous macroscopic rhythms and discrete, unpredictable microscopic shocks. While Neural Ordinary Differential Equations (ODEs) excel at capturing smooth evolution, their inherent Lipschitz continuity constraints inevitably cause severe over-smoothing when confronting abrupt anomalies. Recent physics-informed methods attempt to bypass this by penalizing numerical integration errors to enforce manifold smoothness. However, we mathematically reveal that such rigid regularization inherently triggers gradient conflicts and ``attention collapse,'' stripping the model of its sensitivity to anomalies. To resolve this continuity-shock dilemma, we propose Local Truncation Error-Guided Neural ODEs (LTE-ODE). Rather than treating numerical error as a nuisance to be eliminated, we innovatively repurpose the Local Truncation Error (LTE) as an unsupervised forward inductive bias. By mapping the LTE into a dynamic spatial attention mask, our architecture gracefully preserves high-precision continuous ODE evolution in stable regions, while adaptively triggering a discrete compensation branch exclusively at shock points. Trained purely end-to-end without manifold penalties, LTE-ODE achieves state-of-the-art performance on multiple large-scale benchmarks, exhibiting exceptional robustness against highly non-linear fluctuations. Furthermore, our ablation on integration steps demonstrates high deployment flexibility, allowing the model to seamlessly adapt to varying hardware memory constraints in real-world applications.

Problem

• Neural ODEs
• spatiotemporal forecasting
• local truncation error
• anomaly sensitivity
• over-smoothing

Innovation

• Local Truncation Error
• Neural ODEs
• Spatiotemporal Forecasting
• Dynamic Attention
• Anomaly Adaptation