Frequency-aligned loss and spectral filtering improve long-range influenza forecasting.

Background: Long-horizon forecasts of seasonal influenza remain limited by (i) rapid error growth beyond a few weeks, (ii) entanglement of persistent seasonal cycles with transient outbreaks, and (iii) training objectives that ignore strong autocorrelation in future incidence labels. Methods: We introduce a frequency-aware pipeline that couples a Spectral Adaptive Filtering Network with a Frequency-Aligned Direct Loss. The backbone first isolates stable global spectral bands and then builds window-specific cross-covariate filters to capture transient events; this convex loss function simultaneously supervises prediction results in both the time domain and the approximated decorrelated frequency domain, effectively reducing bias caused by autocorrelation without sacrificing point accuracy. Results: On 49 US states (2010-2020), 10 HHS and 9 Census regions (2002-2020), the proposed model lowers MSE by 6-15% and MAE by 2-20% at 24-week horizons vs. six recent baselines while maintaining interpretable band-pass responses that match annual and semi-annual epidemiological periodicities. Ablation and sensitivity analyses confirm that joint time-frequency supervision and dual static-dynamic filtering are both required for peak performance. Conclusions: Explicit spectral decomposition coupled with autocorrelation-aware training offers a principled route to stable, interpretable long-range influenza forecasting; the modular objective can be plugged into alternative architectures to gain similar error reductions.