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

## TL;DR

SpecFlu-Net is a new AI model that improves long-term predictions of seasonal influenza outbreaks by addressing data challenges like phase drift and peak asymmetry.

## Contribution

SpecFlu-Net introduces a frequency-aware neural architecture with a novel TDT loss to enhance long-term influenza forecasting accuracy and stability.

## Key findings

- SpecFlu-Net outperforms state-of-the-art models on three CDC datasets for up to 24 weeks ahead.
- The model's frequency-aware encoding and TDT loss improve peak timing and epidemic trajectory coherence.
- The framework is parameter-efficient and interpretable, suitable for public health applications.

## Abstract

•Influenza Burden Requires Long-Term Forecasts: Seasonal influenza causes millions of severe cases and up to 650,000 deaths annually, demanding reliable 3–6 month predictions for proactive interventions.•Four Data Challenges Identified: Quasi-periodicity with drifting phase, sharp asymmetric peaks, collinear seasonal drivers, and temporal inconsistency under NAR decoding hinder forecasting accuracy.•Frequency-Aware Spectral Encoding: SpecFlu-Net employs a learnable Fourier transform to preserve phase, compact energy, and denoise signals for improved epidemic peak timing.•Temporal-Dependency Optimised Loss: A novel TDT loss anchors first differences, balancing absolute accuracy with epidemic trajectory coherence in non-autoregressive decoding.•Consistent Outperformance Across Datasets: On three CDC datasets and horizons up to 24 weeks, SpecFlu-Net surpasses state-of-the-art baselines, achieving more stable long-term forecasts.•Interpretable and Efficient Framework: Complex-valued operations equate to global convolutions, ensuring parameter efficiency and theoretical interpretability for public health use.

Influenza Burden Requires Long-Term Forecasts: Seasonal influenza causes millions of severe cases and up to 650,000 deaths annually, demanding reliable 3–6 month predictions for proactive interventions.

Four Data Challenges Identified: Quasi-periodicity with drifting phase, sharp asymmetric peaks, collinear seasonal drivers, and temporal inconsistency under NAR decoding hinder forecasting accuracy.

Frequency-Aware Spectral Encoding: SpecFlu-Net employs a learnable Fourier transform to preserve phase, compact energy, and denoise signals for improved epidemic peak timing.

Temporal-Dependency Optimised Loss: A novel TDT loss anchors first differences, balancing absolute accuracy with epidemic trajectory coherence in non-autoregressive decoding.

Consistent Outperformance Across Datasets: On three CDC datasets and horizons up to 24 weeks, SpecFlu-Net surpasses state-of-the-art baselines, achieving more stable long-term forecasts.

Interpretable and Efficient Framework: Complex-valued operations equate to global convolutions, ensuring parameter efficiency and theoretical interpretability for public health use.

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.

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.

Evaluations on three real-world influenza datasets across 3–24 weeks horizons show SpecFlu-Net outperforms state-of-the-art baselines consistently.

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.

Image, graphical abstract