A physics-informed dual-branch fusion network for quantitative determination of total phosphorus in water using...

Quantitative determination of total phosphorus (TP), an indirectly absorbing aquatic indicator, using near-infrared (NIR) spectroscopy is challenged by high-dimensional, noisy, and nonlinear spectral data. Furthermore, traditional data-driven models tend to neglect underlying physical principles, resulting in overfitting and physically inconsistent predictions.

We propose PICSEN, a Physics-Informed Convolutional-Sequential Dual-Branch Fusion Network. Its architecture synergistically fuses global representations, extracted by a CNN from PCA features, with localized sequential dependencies captured by a GRU from key spectral sequences. To enhance physical consistency, a specialized regularization term is introduced. Unlike traditional methods, it learns an effective absorption proxy to reconstruct the original spectra, thereby embedding implicit physical constraints tailored for TP's indirect optical response within an end-to-end training framework.

Through rigorous repeated validation and statistical testing, PICSEN achieved an average R² of 0.9380 ± 0.0191, demonstrating competitive and robust performance across all benchmarks (p<0.05). Ablation studies confirmed the critical contributions of both the dual-branch architecture and the physics constraint, with the latter serving as a primary driver for model stability. The model demonstrated high stability across random seeds and enhanced resilience to Gaussian noise. SHAP analysis and saliency maps further validated that PICSEN aligns with known physicochemical absorption regions, indicating strong physical consistency within the studied aquatic matrix. While the current findings are based on a specific river basin (N=235), the adaptable nature of the effective absorption proxy provides a robust framework for regional water quality monitoring, with promising potential for recalibration across diverse hydrological environments.