A multi-scale trend–fluctuation dual-branch model for multi-step influent ammonia nitrogen forecasting

Accurate multi-step forecasting of influent ammonia nitrogen (NH 3 N) is important for warning of influent NH 3 N concentration changes and operational decision support in municipal wastewater treatment plants. However, influent NH 3 N sequences exhibit nonlinear, non-stationary, and multi-scale dynamics, where slowly varying NH 3 N concentration trends are coupled with short-term fluctuations associated with discharge variability, hydraulic loading, rainfall, and meteorological conditions. Existing generic time-series forecasting models often represent these patterns within a unified temporal space, which may obscure the distinct roles of trend and fluctuation components. To address this issue, this study proposes a trend–fluctuation-aware multi-scale dual-branch framework for multi-step influent NH 3 N forecasting. The framework builds multi-resolution representations, decomposes each scale-specific sequence into trend and fluctuation components, and performs component-specific cross-scale fusion to preserve their distinct temporal characteristics. The fused trend representation is modeled by a Mamba-based branch for long-range trend evolution, whereas the fused fluctuation representation is modeled by a local-window Transformer branch for abrupt local variations. Scale-gated prediction integrates multi-scale outputs, and a fast Fourier transform (FFT)-based auxiliary loss is introduced to reduce over-smoothed forecasts and preserve fluctuation-structure consistency. Experiments using real-world influent water-quality and meteorological data aligned at 30-min intervals from a municipal wastewater treatment plant in Yan’an, China, provide single-plant case-study evidence that the proposed model achieves lower prediction errors than representative linear, Transformer-based, Mamba-based, and hybrid baselines across 3–24 h forecasting horizons. Ablation results further support the effectiveness of the main architectural designs.