SpecFlu-Net: A frequency-aware neural architecture with temporal-dependency optimization for long-term seasonal influenza transmission forecasting.

Background: Seasonal influenza poses severe global health and economic burdens, demanding reliable long-term (3-6 months) forecasts for proactive public-health interventions. However, influenza surveillance data exhibits four key idiosyncrasies-quasi-periodicity with drifting phase, sharp asymmetric peaks, collinear seasonal exogenous drivers, and temporal inconsistency in non-autoregressive (NAR) decoding-that existing methods address in isolation, lacking a unified solution. Methods: We propose SpecFlu-Net, a lightweight frequency-aware neural architecture for long-term influenza transmission forecasting. It integrates two core components: (1) a frequency-domain encoder, which lifts historical incidence data to the complex frequency domain via learnable discrete Fourier transform (DFT) to preserve phase information (critical for peak timing) and denoise signals through energy compaction; (2) an NAR decoding framework enhanced by temporal-dependency tuning (TDT) loss, which penalizes deviations between predicted and ground-truth first differences and adaptively balances training focus between absolute accuracy and epidemic shape. Theoretically, the complex-valued multi-layer perceptron (MLP) layer in SpecFlu-Net equals a time-domain global convolution (ensuring interpretability and parameter efficiency), and TDT loss prevents gradient flow into historical data for stable training. Results: Evaluations on three real-world influenza datasets across 3-24 weeks horizons show SpecFlu-Net outperforms state-of-the-art baselines consistently. Conclusions: SpecFlu-Net provides a unified solution to influenza data challenges, delivering epidemiologically coherent long-term forecasts to support proactive public health, and is adaptable to other seasonal infectious diseases.