Neural Operators Simulate Toxic Bloom Dynamics in Freshwater Ecosystems at Scale
DOI:
https://doi.org/10.66238/fsrma57Keywords:
neural operators, cyanobacterial harmful algal blooms, Fourier Neural Operator, bloom dynamics, water quality forecasting, Lake Erie, scalable simulationAbstract
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.
References
Moreira, C., Vasconcelos, V., & Antunes, A. (2022). Cyanobacterial blooms: Current knowledge and new perspectives. Earth, 3(1), 127-135.
Paerl, H. W., Havens, K. E., Hall, N. S., Otten, T. G., Zhu, M., Xu, H., ... & Qin, B. (2020). Mitigating a global expansion of toxic cyanobacterial blooms: confounding effects and challenges posed by climate change. Marine and Freshwater Research, 71(5), 579-592.
Zhang, X., Li, P., Han, X., Yang, Y., & Cui, Y. (2024). Enhancing time series product demand forecasting with hybrid attention-based deep learning models. IEEE Access, 12, 190079-190091.
Yuan, S., Chen, X., Xing, S., Li, J., Chen, H., Liu, Z., & Guo, S. (2025). Transformer-Based Scalable Multi-Agent Reinforcement Learning for Joint Resource Optimization in Cloud–Edge–End Video Streaming Systems. IEEE Transactions on Cognitive Communications and Networking.
Zhang, S., Qiu, L., & Zeng, Z. (2026). Physics-Data Synergy in Structural Health Monitoring: A Multi-Scale Graph Contrastive Framework With Temperature-Adaptive Fusion. IEEE Access.
Shen, Z., Zhao, W., Wang, B., Wang, Z. and Shang, W. (2026). CAGR: A Cross-Accelerator Graph Optimization Framework for Efficient Recommender System Inference. IEEE Access.
Sun, T., Yang, J., Li, J., Chen, J., Liu, M., Fan, L., & Wang, X. (2024). Enhancing auto insurance risk evaluation with transformer and SHAP. IEEE Access, 12, 116546-116557.
Li, J., Fan, L., Wang, X., Sun, T., & Zhou, M. (2024). Product demand prediction with spatial graph neural networks. Applied Sciences, 14(16), 6989.
Xing, S., & Wang, Y. (2025). Proactive data placement in heterogeneous storage systems via predictive multi-objective reinforcement learning. IEEE Access.
Liu, Y., Ren, S., Wang, X., & Zhou, M. (2024). Temporal logical attention network for log-based anomaly detection in distributed systems. Sensors, 24(24), 7949.
Zhao, X., Sun, T., Ren, S., Yang, J., & Liu, Y. (2025). RAG-Based AI Agents for Enterprise Software Development: Implementation Patterns and Production Deployment. Frontiers in Artificial Intelligence Research, 2(3), 501-520.
Fang, Q., & Liu, W. (2025). HARLA-ED: Resolving Information Asymmetry and Enhancing Algorithmic Symmetry in Intelligent Educational Assessment via Hybrid Reinforcement Learning. Symmetry, 18(1), 58.
Mai, N. T., Cao, W., & Fang, Q. (2025). A study on how LLMs (eg GPT-4, chatbots) are being integrated to support tutoring, essay feedback and content generation. Journal of Computing and Electronic Information Management, 18(3), 43-52.
Jiang, B., Wu, B., Cao, J., & Tan, Y. (2025). Interpretable Fair Value Hierarchy Classification via Hybrid Transformer-GNN Architecture. IEEE Access, 13, 198142-198163.
Chen, J., Cui, Y., Zhang, X., Yang, J., & Zhou, M. (2024). Temporal convolutional network for carbon tax projection: A data-driven approach. Applied Sciences, 14(20), 9213.
Chen, J., Liu, J., Liang, Y., & Zhou, M. (2026). KE-MLLM: A Knowledge-Enhanced Multi-Sensor Learning Framework for Explainable Fake Review Detection. Applied Sciences, 16(6), 2909.
Liu, J., Wang, J., Chen, H., Guinness, J., Martin, R., & Kulkarni, C. S. (2019). Optimal Level Crossing Predictions for Electronic Prognostics. In AIAA Scitech 2019 Forum (p. 1962).
Xing, S., Wang, Y., & Liu, W. (2025). Self-adapting CPU scheduling for mixed database workloads via hierarchical deep reinforcement learning. Symmetry, 17(7), 1109.
Liu, C. L., Tseng, C. J., Huang, T. H., Yang, J. S., & Huang, K. B. (2023). A multi-task learning model for building electrical load prediction. Energy and Buildings, 278, 112601.
Liu, C. L., Chang, T. Y., Yang, J. S., & Huang, K. B. (2023). A deep learning sequence model based on self-attention and convolution for wind power prediction. Renewable Energy, 219, 119399.
Ding, G., Yang, S., Lin, H., Chen, Z., & Yang, J. S. (2026). LLM-Driven Adaptive Cloud Resource Scheduling: Bridging Reasoning Intelligence with Optimization Guarantees. IEEE Open Journal of the Computer Society.
Wang, X., Zhang, X., Hoo, V., Shao, Z., & Zhang, X. (2024). Legalreasoner: A multi-stage framework for legal judgment prediction via large language models and knowledge integration. Ieee Access, 12, 166843-166854.
Qiu, L. (2024). Deep learning approaches for building energy consumption prediction. Frontiers in Environmental Research, 2(3), 11-17.
Wang, M. (2024). AI technologies in modern taxation: Applications, challenges, and strategic directions. International Journal of Finance and Investment, 1(1), 42-46.
Mai, N. T., Fang, Q., & Cao, W. (2025). Measuring student trust and over-reliance on AI tutors: Implications for STEM learning outcomes. International Journal of Social Sciences and English Literature, 9(12), 11-17.
Li, P., Ren, S., Zhang, Q., Wang, X., & Liu, Y. (2024). Think4SCND: Reinforcement learning with thinking model for dynamic supply chain network design. IEEE Access, 12, 195974-195985.
Smith, B., Pahlevan, N., Schalles, J., Ruberg, S., Errera, R., Ma, R., ... & Kangro, K. (2021). A chlorophyll-a algorithm for Landsat-8 based on mixture density networks. Frontiers in Remote Sensing, 1, 623678.
Woolway, R. I., & Merchant, C. J. (2019). Worldwide alteration of lake mixing regimes in response to climate change. Nature Geoscience, 12(4), 271-276.
Recknagel, F., Shan, K., Adrian, R., & Köhler, J. (2025). Early warning of harmful cyanobacteria blooms based on high frequency in situ monitoring and intelligible machine learning modelling: The case study of Lake Müggelsee (Germany). Water Research, 124514.
Ahmad, N. R. (2025). Monetary policy, inflation and unemployment: The interactions and their economic impacts in Pakistan. Pakistan Journal of Economics and Public Policy, 5(1), 66–81.
Ahmad, N. R. (2025). Leadership ethics in practice: Employees’ experiences of integrity and hypocrisy in public-sector organizations in Pakistan. Journal of Applied Leadership and Transparency. https://doi.org/10.63878/jalt874
Ahmad, N. R. (2025). Blockchain beyond buzzwords: Evaluating its practical application in Pakistan’s supply chain systems. Quarterly Review Journal of Social Sciences. https://doi.org/10.63878/qrjs253
Safdar, M. R. (2025). Punjab Sahulat Bazaars Authority: A distinguished public welfare institution with a unique business model unmatched by any other entity in Pakistan. Contemporary Journal of Social Sciences and Research, 3(3). https://doi.org/10.63878/cjssr.v3i3.1311
Toor, M. J., Shabbir, S., Rauf, A., Nisar, A., Safdar, S., & Zaib-Un-Nisa. (n.d.). The role of structured-communication-technique in developing pragmatic language capability among ASD-children. https://doi.org/10.63878/cjssr.v3i2.785
Toor, M. J., Mehmood, H., Yasmeen, A., Honey, Q., Waseem, M., & Wasif, M. (n.d.). Exploring the effect of verbal encouraging phrases (VEP) on Chinese language learners’ academic achievement at university level.
Toor, M. J., Arafat, M., Ayoub, M., Ali, M., & Alessi Longa, F. E. (n.d.). From coherent self to fragmented persona: Digital identity fragmentation and academic self-concept among Generation Z, with comparative insights from Generation Alpha. https://doi.org/10.63878/cjssr.v4i2.2318
Katsitadze, N., Kharadze, N., & Pirtskhalaishvili, D. (2025). The impact of social media on students’ effective time management. Baltic Journal of Economic Studies, 11(1), 200–210. https://doi.org/10.30525/2256-0742/2025-11-1-200-210
Toor, M. J., Zafar, S., Omer, F., Sarwar, M., & Hussain, A. K. (n.d.). Teachers’ perspectives on effectiveness of translanguaging in enhancing English language learning at secondary school level.
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