Modelling N2O and NH+ 4 in a Full-scale Wastewater Treatment Plant with NeuralODE
Resumo
Previsão precisa das emissões de óxido nitroso (N2O) em estações de tratamento de águas residuais é essencial para esforços de mitigação. Como sua produção está ligada à nitrificação, prever amônio (NH+4 ) ajuda capturar condições precursoras. Este estudo avalia um modelo de Equação Diferencial Ordinária Neural em tempo contínuo (NODE) para prever N2O e NH+4 usando dados em escala real, comparando com modelos NARX e LSTM. Resultados preliminares mostram que, frente a modelos discretos, NODE captura a variabilidade de curto prazo e explica a fração da variância observada em N2O e NH+4, destacando potencial de modelos neurais em tempo contínuo para previsão de curto prazo para apoiar estratégias avançadas de controle de aeração.
Referências
Billings, S. A. (2013). Nonlinear system identification: NARMAX methods in the time, frequency, and spatio-temporal domains. John Wiley & Sons.
Chen, R. T., Rubanova, Y., Bettencourt, J., and Duvenaud, D. K. (2018). Neural ordinary differential equations. Advances in neural information processing systems, 31.
Debel, L., Stentoft, P. A., Stokholm-Bjerregaard, M. A., Ortiz-Arroyo, D., and Durdevic, P. (2025). Grey-box model of N2O and NH+ 4 for predictive control in the activated sludge process. Journal of Water Process Engineering, 72:107503.
Dormand, J. R. and Prince, P. J. (1980). A family of embedded runge-kutta formulae. Journal of computational and applied mathematics, 6(1):19–26.
Finlay, C., Jacobsen, J.-H., Nurbekyan, L., and Oberman, A. (2020). How to train your neural ODE: The world of jacobian and kinetic regularization. In International conference on machine learning, pages 3154–3164. PMLR.
Hansen, L. D. (2025). Data-driven Modeling and Predictive Control for N2O Mitigation in Wastewater Treatment Processes. PhD thesis, Aalborg University, Denmark.
Hansen, L. D., Rani, A., Stokholm-Bjerregaard, M. A., Stentoft, P. A., Ortiz Arroyo, D., and Durdevic, P. (2024a). Time series dataset for modeling and forecasting of N2O in wastewater treatment. arXiv preprint and associated dataset. Version 4 of the dataset available at Mendeley Data.
Hansen, L. D., Stentoft, P. A., Ortiz-Arroyo, D., and Durdevic, P. (2024b). Black-box modelling of non-stationary N2O dynamics in a full-scale wastewater treatment plant. IFAC-PapersOnLine, 58(28):714–719. The 4th Modeling, Estimation, and Control Conference 2024.
Hansen, L. D., Stentoft, P. A., Ortiz-Arroyo, D., and Durdevic, P. (2024c). Exploring data quality and seasonal variations of N2O in wastewater treatment: a modeling perspective. Water Practice & Technology, 19(3):1016–1031.
Hochreiter, S. and Schmidhuber, J. (1997). Long short-term memory. Neural computation, 9(8):1735–1780.
Huang, X., Kandris, K., and Katsou, E. (2025). Training stiff neural ordinary differential equations in data-driven wastewater process modelling. Journal of Environmental Management, 373:123870.
Khalil, M., AlSayed, A., Liu, Y., and Vanrolleghem, P. A. (2023). Machine learning for modeling N2O emissions from wastewater treatment plants: Aligning model performance, complexity, and interpretability. Water Research, 245:120667.
Leontaritis, I. J. and Billings, S. A. (1985). Input-output parametric models for non-linear systems part i: deterministic non-linear systems. International journal of control, 41(2):303–328.
Li, K., Duan, H., Liu, L., Qiu, R., van den Akker, B., Ni, B.-J., Chen, T., Yin, H., Yuan, Z., and Ye, L. (2022). An integrated first principal and deep learning approach for modeling nitrous oxide emissions from wastewater treatment plants. Environmental Science & Technology, 56(4):2816–2826.
Loshchilov, I. and Hutter, F. (2019). Decoupled weight decay regularization.
Massara, T. M., Solís, B., Guisasola, A., Katsou, E., and Baeza, J. A. (2018). Development of an ASM2d-N2O model to describe nitrous oxide emissions in municipal WWTPs under dynamic conditions. Chemical Engineering Journal, 335:185–196.
Masson-Delmotte, V. and et. al, editors (2021). Climate Change 2021: The Physical Science Basis. Contribution of Working Group I to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change. Cambridge University Press.
Szelag, B., Zaborowska, E., and Makinia, J. (2023). An algorithm for selecting a machine learning method for predicting nitrous oxide emissions in municipal wastewater treatment plants. Journal of Water Process Engineering, 54:103939.
Vasilaki, V., Massara, T., Stanchev, P., Fatone, F., and Katsou, E. (2019). A decade of nitrous oxide (N2O) monitoring in full-scale wastewater treatment processes: A critical review. Water Research, 161:392–412.
Chen, R. T., Rubanova, Y., Bettencourt, J., and Duvenaud, D. K. (2018). Neural ordinary differential equations. Advances in neural information processing systems, 31.
Debel, L., Stentoft, P. A., Stokholm-Bjerregaard, M. A., Ortiz-Arroyo, D., and Durdevic, P. (2025). Grey-box model of N2O and NH+ 4 for predictive control in the activated sludge process. Journal of Water Process Engineering, 72:107503.
Dormand, J. R. and Prince, P. J. (1980). A family of embedded runge-kutta formulae. Journal of computational and applied mathematics, 6(1):19–26.
Finlay, C., Jacobsen, J.-H., Nurbekyan, L., and Oberman, A. (2020). How to train your neural ODE: The world of jacobian and kinetic regularization. In International conference on machine learning, pages 3154–3164. PMLR.
Hansen, L. D. (2025). Data-driven Modeling and Predictive Control for N2O Mitigation in Wastewater Treatment Processes. PhD thesis, Aalborg University, Denmark.
Hansen, L. D., Rani, A., Stokholm-Bjerregaard, M. A., Stentoft, P. A., Ortiz Arroyo, D., and Durdevic, P. (2024a). Time series dataset for modeling and forecasting of N2O in wastewater treatment. arXiv preprint and associated dataset. Version 4 of the dataset available at Mendeley Data.
Hansen, L. D., Stentoft, P. A., Ortiz-Arroyo, D., and Durdevic, P. (2024b). Black-box modelling of non-stationary N2O dynamics in a full-scale wastewater treatment plant. IFAC-PapersOnLine, 58(28):714–719. The 4th Modeling, Estimation, and Control Conference 2024.
Hansen, L. D., Stentoft, P. A., Ortiz-Arroyo, D., and Durdevic, P. (2024c). Exploring data quality and seasonal variations of N2O in wastewater treatment: a modeling perspective. Water Practice & Technology, 19(3):1016–1031.
Hochreiter, S. and Schmidhuber, J. (1997). Long short-term memory. Neural computation, 9(8):1735–1780.
Huang, X., Kandris, K., and Katsou, E. (2025). Training stiff neural ordinary differential equations in data-driven wastewater process modelling. Journal of Environmental Management, 373:123870.
Khalil, M., AlSayed, A., Liu, Y., and Vanrolleghem, P. A. (2023). Machine learning for modeling N2O emissions from wastewater treatment plants: Aligning model performance, complexity, and interpretability. Water Research, 245:120667.
Leontaritis, I. J. and Billings, S. A. (1985). Input-output parametric models for non-linear systems part i: deterministic non-linear systems. International journal of control, 41(2):303–328.
Li, K., Duan, H., Liu, L., Qiu, R., van den Akker, B., Ni, B.-J., Chen, T., Yin, H., Yuan, Z., and Ye, L. (2022). An integrated first principal and deep learning approach for modeling nitrous oxide emissions from wastewater treatment plants. Environmental Science & Technology, 56(4):2816–2826.
Loshchilov, I. and Hutter, F. (2019). Decoupled weight decay regularization.
Massara, T. M., Solís, B., Guisasola, A., Katsou, E., and Baeza, J. A. (2018). Development of an ASM2d-N2O model to describe nitrous oxide emissions in municipal WWTPs under dynamic conditions. Chemical Engineering Journal, 335:185–196.
Masson-Delmotte, V. and et. al, editors (2021). Climate Change 2021: The Physical Science Basis. Contribution of Working Group I to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change. Cambridge University Press.
Szelag, B., Zaborowska, E., and Makinia, J. (2023). An algorithm for selecting a machine learning method for predicting nitrous oxide emissions in municipal wastewater treatment plants. Journal of Water Process Engineering, 54:103939.
Vasilaki, V., Massara, T., Stanchev, P., Fatone, F., and Katsou, E. (2019). A decade of nitrous oxide (N2O) monitoring in full-scale wastewater treatment processes: A critical review. Water Research, 161:392–412.
Publicado
19/07/2026
Como Citar
NOGUEIRA FILHO, Francisco José Matos; MULAS, Michela.
Modelling N2O and NH+ 4 in a Full-scale Wastewater Treatment Plant with NeuralODE. In: WORKSHOP DE COMPUTAÇÃO APLICADA À GESTÃO DO MEIO AMBIENTE E RECURSOS NATURAIS (WCAMA), 17. , 2026, Gramado/RS.
Anais [...].
Porto Alegre: Sociedade Brasileira de Computação,
2026
.
p. 205-214.
ISSN 2595-6124.
DOI: https://doi.org/10.5753/wcama.2026.20802.
