Long-term time series forecasting (LTSF) provides longer insights into future trends and patterns. Over the past few years, deep learning models especially Transformers have achieved advanced performance in LTSF tasks. However, LTSF faces inherent challenges such as long-term dependencies capturing and sparse semantic characteristics. Recently, a new state space model (SSM) named Mamba is proposed. With the selective capability on input data and the hardware-aware parallel computing algorithm, Mamba has shown great potential in balancing predicting performance and computational efficiency compared to Transformers. To enhance Mamba's ability to preserve historical information in a longer range, we design a novel Mamba+ block by adding a forget gate inside Mamba to selectively combine the new features with the historical features in a complementary manner. Furthermore, we apply Mamba+ both forward and backward and propose Bi-Mamba+, aiming to promote the model's ability to capture interactions among time series elements. Additionally, multivariate time series data in different scenarios may exhibit varying emphasis on intra- or inter-series dependencies. Therefore, we propose a series-relation-aware decider that controls the utilization of channel-independent or channel-mixing tokenization strategy for specific datasets. Extensive experiments on 8 real-world datasets show that our model achieves more accurate predictions compared with state-of-the-art methods.

翻译：长期时间序列预测（LTSF）能够为未来趋势和模式提供更长远的洞察。过去几年中，深度学习模型尤其是Transformer在LTSF任务中取得了先进性能。然而，LTSF面临着长期依赖捕捉和稀疏语义特征等固有挑战。近期，一种名为Mamba的新型状态空间模型（SSM）被提出。凭借对输入数据的选择性能力和硬件感知并行计算算法，Mamba在平衡预测性能与计算效率方面展现出相较于Transformer的巨大潜力。为增强Mamba在更长时间范围内保留历史信息的能力，我们设计了一种新型Mamba+模块，通过在Mamba内部增加遗忘门，以互补方式选择性地将新特征与历史特征结合。此外，我们将Mamba+同时应用于前向和后向处理，提出了Bi-Mamba+，旨在提升模型捕捉时间序列元素间交互的能力。进一步地，不同场景下的多变量时间序列数据对序列内或序列间依赖关系的侧重可能有所不同。因此，我们提出了一种序列关系感知决策器，针对特定数据集控制采用通道独立或通道混合标记化策略。在8个真实世界数据集上的广泛实验表明，与现有最优方法相比，我们的模型实现了更精确的预测。