Abstract: To address the difficulties in modeling nonlinear multi-scale spatio-temporal coupling dependencies in multi-scale spatio-temporal series prediction, the challenges faced by traditional methods in capturing cross-scale interactions due to separate processing of spatio-temporal features, and the issues with existing deep learning methods such as interference from Gibbs noise and insufficient fusion of local-global features, a frequency domain graph convolution network(FDGCN)was proposed, and multi-scale spatio-temporal unified modeling was achieved through a three-stage collaborative framework. A hypervariable graph was constructed to jointly encode multi-scale temporal dimensions and spatial topology as graph nodes, and an adaptive adjacency matrix was used to explicitly model cross-scale dependencies. A discrete cosine transform-discrete Fourier transform(DCT-DFT)collaborative noise reduction mechanism was designed, which suppressed the Gibbs phenomenon in DFT through even-symmetric extension in DCT, combined with a scale-aware frequency domain filter to separate low-frequency trends and high-frequency noise. An exponential smoothing attention mechanism was introduced to dynamically fuse multi-scale features, balancing local fluctuations and long-term trends. Based on validation across multiple domains, FDGCN could achieve spatio-temporal unified modeling at multiple scales, effectively capturing complex spatio-temporal dependencies, reducing high-frequency noise, and improving training efficiency. FDGCN achieved excellent prediction performance on datasets in multiple fields such as transportation and power, which demonstrated comprehensive advantages including high prediction accuracy, superior computational efficiency, and strong cross-domain generalization ability, providing an efficient solution for spatio-temporal prediction.

Key words: spatio-temporal series prediction, multi-scale temporal correlation modeling, gated attention mechanism, deep learning, data mining