Frequency-Aligned Loss and Spectral Filtering Improve Long-Range Influenza Forecasting

Tianyi Feng^1*Chunyan Luo²Yu Huang¹

• ¹Department of Rehabilitation, West China Hospital Sichuan University JinTang Hospital. Jintang First People's Hospital, Chengdu, China
• ²Jilin Sport University, Changchun, China

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 versus 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.