Adaptive Spectral-Spatial Regime Modeling for Non- Stationary Multivariate Time-Series Forecasting

Accurate forecasting of multivariate time series (MTS) is foundational across critical domains including high-frequency clinical monitoring, power grid operations, financial modeling, and distributed industrial telemetry. However, real-world MTS signals exhibit severe distribution shifts, complex cross-channel dependencies, and time-varying regime transitions that severely degrade the predictive power of conventional Transformer- and State-Space Model (SSM)-based architectures. Existing approaches predominantly decouple temporal feature extraction from cross-channel correlation modeling, overlooking the non-stationary frequency-domain shifts where regime drifts most prominently manifest. In this paper, we propose SpecRegNet (Adaptive Spectral-Spatial Regime Network), a novel end-to-end deep learning framework designed to jointly resolve spectral non-stationarity and dynamic inter-series dependencies. SpecRegNet introduces: (1) an Adaptive Spectral Gating Unit (ASGU) that dynamically isolates harmonic trends from non-stationary transient bursts via learnable orthogonal frequency-band filters; (2) a Regime-Guided Cross-Channel Attention (RGCA) module parameterized by dynamic latent regime routing matrices; and (3) an energy-constrained temporal continuity regularizer that penalizes abrupt high-order variance explosions. Extensive empirical evaluations across six real-world benchmark datasets (Electricity, Traffic, Weather, Exchange-Rate, and two clinical telemetry suites) demonstrate that SpecRegNet consistently outperforms state-of-the-art baselines (including PatchTST, iTransformer, TimeMixer, and TimesNet), achieving an average reduction of 14.8% in Mean Squared Error (MSE) and 12.3% in Mean Absolute Error (MAE) on long-horizon forecasting tasks while retaining computational efficiency.