arXiv:2605.03386cs.LGcs.AI2026-05

用局部截断误差引导神经微分方程,提升交通预测对突发异常的敏感度。

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

论文配图:Local Truncation Error-Guided Neural ODEs for Large Scale Traffic Forecasting
图 1 · 摘自论文原文
  • 将数值误差转为动态注意力掩码,区分平滑区与突变点
  • 在多个大规模数据集上达到最优性能,对非线性波动鲁棒
  • 无需额外正则化,适配不同硬件内存限制,部署灵活

大规模交通网络的时空预测需同时建模连续的宏观演化和离散的突发异常。传统神经微分方程因李普希茨连续性约束,在面对突发扰动时会产生严重过平滑。现有物理信息方法通过惩罚数值积分误差来强制流形平滑,但数学分析表明这会引发梯度冲突与“注意力坍缩”,削弱对异常的感知能力。为此,本文提出局部截断误差引导的神经微分方程(LTE-ODE)。不将数值误差视为需消除的噪声,而是将其重构为无监督前向归纳偏置,映射为动态空间注意力掩码。该架构在稳定区域保持高精度连续演化,仅在异常点激活离散补偿分支。模型端到端训练,无需流形正则化,在多个大规模基准上实现当前最优性能,对高度非线性波动具有极强鲁棒性。消融实验显示其对积分步数具有高适应性,可无缝适配实际应用中的异构硬件内存约束。

原文摘要 · Abstract (English)

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.

神经微分方程交通预测异常检测自适应建模

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