Robust Spatiotemporal Forecasting Using Adaptive Deep-Unfolded Variational Mode Decomposition

Abstract

Accurate spatiotemporal forecasting is critical for numerous complex systems but remains challenging due to complex volatility patterns and spectral entanglement in conventional graph neural networks (GNNs). While decomposition-integrated approaches like variational mode graph convolutional network (VMGCN) improve accuracy through signal decomposition, they suffer from computational inefficiency and manual hyperparameter tuning. To address these limitations, we propose the mode adaptive graph network (MAGN) that transforms iterative variational mode decomposition (VMD) into a trainable neural module. Our key innovations include (1) an unfolded VMD (UVMD) module that replaces iterative optimization with a fixed-depth network to reduce the decomposition time (by 250x for the LargeST benchmark), and (2) mode-specific learnable bandwidth constraints (αk ) adapt spatial heterogeneity and eliminate manual tuning while preventing spectral overlap. Evaluated on the LargeST benchmark (6,902 sensors, 241M observations), MAGN achieves an 85-95% reduction in the prediction error over VMGCN and outperforms state-of-the-art baselines.