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

• URL: http://arxiv.org/abs/2605.03386v1
• Date: Tue, 05 May 2026 05:46:00 GMT
• Title: Local Truncation Error-Guided Neural ODEs for Large Scale Traffic Forecasting
• Abstract summary: Local Truncation Error-Guided Neural ODEs (LTE-ODE)<n>Our architecture gracefully preserves high-precision continuous ODE evolution in stable regions.<n>LTE-ODE achieves state-of-the-art performance on multiple large-scale benchmarks.
• Score: 26.116856080963966
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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