Neural Operators Simulate Toxic Bloom Dynamics in Freshwater Ecosystems at Scale

Toxic cyanobacterial harmful algal blooms (cyanoHABs) pose escalating threats to freshwater ecosystem integrity worldwide, driven by accelerating eutrophication and climate warming. Conventional simulation approaches, including process-based hydrodynamic models and shallow machine learning architectures, have struggled to generalize across spatially heterogeneous lake systems or to achieve the computational throughput required for operational forecasting at scale. This study investigates the application of neural operator (NO) frameworks, specifically the Fourier Neural Operator (FNO) and its extensions, to simulate spatiotemporal dynamics of cyanoHABs across multiple freshwater lakes simultaneously. Lake Erie served as the primary validation system given its well-documented history of recurring Microcystis-dominated bloom events. By learning solution operators of the partial differential equations (PDEs) governing bloom kinetics and nutrient cycling, the proposed NO architecture demonstrated superior cross-lake generalization over benchmarked deep learning baselines. Training incorporated multi-lake datasets encompassing water temperature, total phosphorus (TP), total nitrogen (TN), wind velocity, and chlorophyll-a (Chl-a) concentrations. Validation results showed a root mean square error (RMSE) reduction of 38.4% and a coefficient of determination (R²) exceeding 0.91 on four held-out lakes compared to a convolutional neural network baseline. The framework offers a scalable pathway toward real-time cyanoHAB early warning systems operable across diverse freshwater ecosystems.