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

TL;DR

This paper introduces LTE-ODE, a novel neural ODE framework that uses local truncation error as an adaptive bias to improve large-scale traffic forecasting by effectively handling both smooth and shock dynamics.

Contribution

It proposes LTE-ODE, which leverages local truncation error for adaptive attention, overcoming over-smoothing and sensitivity issues in neural ODEs for traffic prediction.

Findings

Achieves state-of-the-art results on large-scale traffic benchmarks.

Demonstrates robustness against highly non-linear fluctuations.

Flexible to different hardware constraints through adjustable integration steps.

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.