Weformer: Adaptive spectral cross-variable transformer for long-horizon weather forecasting

Accurate long-term weather forecasting from multivariate sensor time series remains challenging due to the inherent non-stationarity of atmospheric observations acquired by heterogeneous environmental sensors and the complex physical coupling among meteorological variables. Existing general-purpose deep forecasting models, while successful on idealized benchmarks, suffer notable performance degradation on raw ground-station sensor data because they lack domain-specific mechanisms for cross-variable interaction and noise resistance. We propose Weformer, a Transformer-based architecture purpose-built for sensor-derived weather time series. Weformer introduces two core innovations: (1) a Frequency-driven Cross-Variable Rotary Position Embedding (CrossVarRoPE) that extracts dominant spectral patterns via the Fourier transform and injects adaptive, cross-variable-aware positional encoding into the attention mechanism, and (2) a Global Token mechanism that distills macroscopic environmental context through cross-attention, preventing overfitting to local high-frequency sensor noise. We provide rigorous theoretical analysis, including a noise-suppression bound, a capacity bound for the global token, and a forecasting error decomposition, to justify the design. To bridge the evaluation gap in current benchmarks, we curate seven new real-world datasets sourced from ground-station sensor networks and energy-grid monitoring systems, spanning diverse climate zones and temporal resolutions. Extensive experiments on eight datasets demonstrate that Weformer achieves the best overall performance among seven competitive baselines—the lowest global average MSE and MAE and the largest number of first-place results—under both standard and long-horizon settings (up to 2,880 steps, i.e., 20–120 days depending on the sampling resolution), while CrossVarRoPE serves as a portable plug-in that improves standard Transformer architectures in most evaluated settings. Code and data are available at https://github.com/sekiro1211/Weformer .