Process-aware physics-guided neural network framework for harmful algal bloom forecasting in lentic freshwater...

Harmful algal blooms (HABs) in lentic freshwater systems pose persistent challenges to water resource management, motivating the development of forecasting tools that combine physical rigor with data-driven flexibility. Although physics-informed neural networks (PINNs) are promising hybrid approaches, their application to HAB systems remains difficult because governing equations are hard to fully specify for bloom dynamics driven by partially observed, highly nonlinear, and site-specific ecological processes. To address this challenge, we developed a Transformer-based physics-guided neural network (T-PGNN) that embeds a simplified cyanobacterial net-growth mechanism, representing temperature-dependent growth, nutrient limitation, light limitation, and mortality, as a soft physical constraint. In contrast to conventional PINNs based on fully specified governing equations, the T-PGNN uses a finite difference-based residual derived from the simplified net-growth equation to flexibly guide learning in partially observed and nonlinear HAB systems. Model training was formulated as an inverse problem, enabling the joint inference of physical parameters alongside biomass forecasts. The framework was applied to forecast one-day-ahead Microcystis biomass at three HAB monitoring sites in Daecheong Lake, South Korea, using meteorological, water quality, and biological inputs. The T-PGNN generally outperformed the baseline models across the three sites (Nash-Sutcliffe efficiency = 0.763-0.926), with the largest improvement observed under highly variable bloom conditions. The inferred parameters reflected both lake-wide bloom-forming conditions and site-specific environmental characteristics, supporting ecologically plausible process-level parameterization. These results demonstrate that the T-PGNN provides not only accurate Microcystis forecasts but also interpretable process information to support proactive HAB management.