Abstract:

Existing time series forecasting methods fail to fully consider the spatiotemporal dependencies among variables, which hinders the improvement of forecasting accuracy. Spatial modeling methods based on Graph Neural Networks (GNN) also have limitations in graph structure construction. Specifically, static predefined graphs struggle to capture the dynamic interaction characteristics among variables, and adaptive graph structure learning is influenced by parameter initialization, rendering the method prone to being trapped in local optima. To address these issues, a multivariate time series forecasting method that combines spatiotemporal information and the Kolmogorov—Arnold Networks (KAN) is proposed. In the spatial dimension, a graph structure learning module is designed. It utilizes the Pearson correlation coefficient to establish the initial adjacency matrix of variables, introduces learnable parameters to dynamically adjust and optimize the graph structure, and effectively captures the spatial dependencies among variables by stacking multiple layers of graph convolutions. In the temporal dimension, the method combines the multi-head self-attention mechanism and Gated Recurrent Unit (GRU) to extract temporal dependencies in different subspaces, while capturing both local temporal patterns and global key information. To further enhance the representational capacity of the model, the KAN is used instead of the traditional Multi-Layer Perceptron (MLP), enabling nonlinear fusion of spatiotemporal features through learnable activation functions. Experimental results on seven benchmark datasets demonstrate that the proposed model achieves an average reduction of 36.9 percentage points in Mean Squared Error (MSE) and 24.8 percentage points in Mean Absolute Error (MAE). The generalization performance of the model is validated via testing using the Australian electricity load dataset. Compared with other mainstream models, this model can accurately capture the dependencies among variables and effectively fuse spatiotemporal features, thereby improving forecasting accuracy and robustness.

Key words: multivariate, spatiotemporal features, graph structure learning, Graph Convolutional Network (GCN), feature fusion

摘要：

现有的时间序列预测方法未能充分考虑变量间的时空依赖关系, 影响了预测精度的提升。基于图神经网络(GNN)的空间建模方法在图结构的构建上也存在局限性, 即静态预定义图难以捕捉变量间的动态交互特性, 且自适应图结构学习受参数初始化影响, 易陷入局部最优。为解决上述问题, 提出结合时空和Kolmogorov-Arnold网络(KAN)的多变量时间序列预测方法。在空间维度上, 设计图结构学习模块, 利用皮尔逊相关系数建立变量的初始邻接矩阵, 引入可学习参数动态调整和优化图结构, 并通过堆叠多层图卷积, 有效捕捉变量间的空间依赖关系。在时间维度上, 结合多头自注意力机制和门控循环单元(GRU)提取不同子空间下的时间依赖关系, 同时捕捉局部时间模式和全局关键信息。为进一步提升模型的表征能力, 使用KAN代替传统的多层感知机(MLP), 通过可学习的激活函数实现时空特征的非线性融合。实验结果表明, 在7个基准数据集上, 所提模型的均方误差(MSE)和平均绝对误差(MAE)分别平均下降36.9和24.8百分点。利用澳大利亚电力负荷数据集进行测试, 结果验证了所提模型的泛化性能。相比其他主流模型, 该模型能够精确捕捉变量间的依赖关系并有效融合时空特征, 提升预测的准确性和鲁棒性。

关键词: 多变量, 时空特征, 图结构学习, 图卷积网络, 特征融合