Abstract: Existing time series prediction methods fail to fully account for the spatiotemporal dependencies among variables, which limits the improvement of prediction accuracy. The spatial modeling methods based on graph neural networks also face limitations in graph structure construction: 1) Statically predefined graphs struggle to capture the dynamic interaction characteristics between variables; 2) Adaptive graph structure learning is highly sensitive to parameter initialization and may easily fall into local optima. To address these issues, this paper proposes a multivariate time series prediction model that combines spatiotemporal and Kolmogorov-Arnold networks. In the spatial dimension, a graph structure learning module uses the pearson correlation coefficient to establish an initial adjacency matrix for variables. Learnable parameters are introduced to dynamically adjust and optimize the graph structure. By stacking multiple layers of graph convolutional networks, the model effectively captures the spatial dependencies between variables. In the temporal dimension, the multi-head self-attention mechanism combined with gated recurrent units extracts time dependencies in different subspaces, capturing both local temporal patterns and global key information simultaneously. In order to further improve the representation ability of the model, the Kolmogorov-Arnold networks are used to replace the traditional multilayer perceptron, and the nonlinear fusion of spatiotemporal features is realized through the learnable activation functions. Experimental results show that this proposed model achieves average reductions of 36.9 percentage points in mean squared error and 24.8 percentage points in mean absolute error across seven benchmark datasets. The generalization performance of the model is verified by using the Australian electricity load dataset for testing. Compared with other mainstream models, the proposed model can accurately capture the dependencies between variables and effectively integrate spatiotemporal features, which improves the accuracy and robustness of prediction.

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。基于图神经网络的空间建模方法在图结构的构建上也存在局限：1)静态预定义图难以捕捉变量间的动态交互特性；2)自适应图结构学习易受参数初始化影响陷入局部最优。为解决上述问题，提出结合时空和Kolmogorov-Arnold网络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Kolmogorov-Arnold网络替代传统的多层感知机，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，所提出模型在七个基准数据集上的均方误差和平均绝对误差分别平均下降了36.9和24.8个百分点。并利用澳大利亚电力负荷数据集进行测试，验证了模型的泛化性能。相比其他主流模型，该模型能够精确捕捉变量间依赖关系并有效融合时空特征，提升了预测的准确性和鲁棒性。