Time series prediction plays a pivotal role across diverse domains such as finance, healthcare, energy systems, and environmental modeling. However, existing approaches often struggle to balance efficiency, scalability, and accuracy, particularly when handling long-range dependencies and irregularly sampled data. To address these challenges, we propose MODE, a unified framework that integrates Low-Rank Neural Ordinary Differential Equations (Neural ODEs) with an Enhanced Mamba architecture. As illustrated in our framework, the input sequence is first transformed by a Linear Tokenization Layer and then processed through multiple Mamba Encoder blocks, each equipped with an Enhanced Mamba Layer that employs Causal Convolution, SiLU activation, and a Low-Rank Neural ODE enhancement to efficiently capture temporal dynamics. This low-rank formulation reduces computational overhead while maintaining expressive power. Furthermore, a segmented selective scanning mechanism, inspired by pseudo-ODE dynamics, adaptively focuses on salient subsequences to improve scalability and long-range sequence modeling. Extensive experiments on benchmark datasets demonstrate that MODE surpasses existing baselines in both predictive accuracy and computational efficiency. Overall, our contributions include: (1) a unified and efficient architecture for long-term time series modeling, (2) integration of Mamba's selective scanning with low-rank Neural ODEs for enhanced temporal representation, and (3) substantial improvements in efficiency and scalability enabled by low-rank approximation and dynamic selective scanning.

翻译：时间序列预测在金融、医疗、能源系统和环境建模等多个领域具有关键作用。然而，现有方法往往难以在效率、可扩展性和准确性之间取得平衡，尤其是在处理长程依赖性和不规则采样数据时。为应对这些挑战，我们提出了MODE，一个将低秩神经常微分方程（Neural ODEs）与增强型Mamba架构相统一的框架。如框架所示，输入序列首先通过线性标记化层进行变换，随后经由多个Mamba编码器块处理，每个块均配备增强型Mamba层，该层采用因果卷积、SiLU激活函数以及低秩神经ODE增强机制，以高效捕捉时序动态。这种低秩形式在保持表达力的同时降低了计算开销。此外，受伪ODE动力学启发的分段选择性扫描机制，能够自适应地聚焦于关键子序列，从而提升可扩展性和长程序列建模能力。在基准数据集上的大量实验表明，MODE在预测准确性和计算效率方面均超越了现有基线方法。总体而言，我们的贡献包括：（1）一个统一且高效的长期时间序列建模架构；（2）将Mamba的选择性扫描与低秩神经ODE相结合以增强时序表示能力；（3）通过低秩近似和动态选择性扫描实现了效率与可扩展性的显著提升。