Neural forecasting of spatiotemporal time series drives both research and industrial innovation in several relevant application domains. Graph neural networks (GNNs) are often the core component of the forecasting architecture. However, in most spatiotemporal GNNs, the computational complexity scales up to a quadratic factor with the length of the sequence times the number of links in the graph, hence hindering the application of these models to large graphs and long temporal sequences. While methods to improve scalability have been proposed in the context of static graphs, few research efforts have been devoted to the spatiotemporal case. To fill this gap, we propose a scalable architecture that exploits an efficient encoding of both temporal and spatial dynamics. In particular, we use a randomized recurrent neural network to embed the history of the input time series into high-dimensional state representations encompassing multi-scale temporal dynamics. Such representations are then propagated along the spatial dimension using different powers of the graph adjacency matrix to generate node embeddings characterized by a rich pool of spatiotemporal features. The resulting node embeddings can be efficiently pre-computed in an unsupervised manner, before being fed to a feed-forward decoder that learns to map the multi-scale spatiotemporal representations to predictions. The training procedure can then be parallelized node-wise by sampling the node embeddings without breaking any dependency, thus enabling scalability to large networks. Empirical results on relevant datasets show that our approach achieves results competitive with the state of the art, while dramatically reducing the computational burden.

翻译：时空时间序列的神经预测驱动了多个相关应用领域的研究与工业创新。图神经网络（GNNs）通常是预测架构的核心组件。然而，在大多数时空GNN中，计算复杂度随序列长度与图中链接数量的乘积呈二次方增长，从而阻碍了这些模型在大型图与长时间序列上的应用。尽管在静态图场景下已有提升可扩展性的方法被提出，但针对时空案例的研究工作仍十分有限。为填补这一空白，我们提出了一种可扩展架构，该架构利用了时间与空间动态的高效编码。具体而言，我们采用随机循环神经网络将输入时间序列的历史嵌入到高维状态表示中，涵盖多尺度时间动态。随后，这些表示通过使用图邻接矩阵的不同幂次沿空间维度传播，生成富含丰富时空特征池的节点嵌入。所得节点嵌入可通过无监督方式高效预计算，之后输入到前馈解码器中，该解码器学习将多尺度时空表示映射为预测结果。训练过程可通过采样节点嵌入实现节点级并行化，且不破坏任何依赖性，从而支持大规模网络。在相关数据集上的实证结果表明，我们的方法在显著降低计算负担的同时，取得了与当前最优方法相竞争的结果。