Multi-dimensional water quality indicators forecasting from IoT sensors: A tensor decomposition and multi-head self-attention mechanism

Accurate prediction of multi-dimensional water quality indicators is critical for sustainable water resource management, yet existing methods often fail to address the high-dimensional, nonlinear, and spatially correlated nature of data from heterogeneous IoT sensors. To overcome these limitations, we propose TGMHA (Tensor Decomposition and Gated Neural Network with Multi-Head Self-Attention), a novel hybrid model that integrates three key innovations: 1) Tensor-based Feature Extraction: We combine Standard Delay Embedding Transformation (SDET) with Tucker tensor decomposition to reconstruct raw time series into low-rank tensor representations, capturing latent spatio-temporal patterns while suppressing sensor noise. 2) Multi-Head Self-Attention for Inter-Indicator Dependencies: A multi-head self-attention mechanism explicitly models complex inter-dependencies among diverse water quality indicators (e.g., pH, dissolved oxygen, conductivity) via parallel feature subspace learning. 3) Efficient Long-Term Dependency Modeling: An encoder-decoder architecture with gated recurrent units (GRUs), optimized by adaptive rank selection, ensures efficient modeling of long-term dependencies without compromising computational performance. By unifying these components into an end-to-end trainable system, TGMHA surpasses conventional approaches in handling complex water quality dynamics, particularly in scenarios with missing data and nonlinear interactions. Rigorous evaluation against six state-of-the-art benchmarks confirms TGMHA’s superior capability, offering a robust and interpretable paradigm for multi-sensor fusion and water quality forecasting in environmental informatics.