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Hybrid differential equations : integrating mechanistic and data-driven techniques for modelling of water systems

Ward Quaghebeur (UGent) , Elena Torfs (UGent) , Bernard De Baets (UGent) and Ingmar Nopens (UGent)
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Abstract
Mathematical modelling is increasingly used to improve the design, understanding, and operation of water systems. Two modelling paradigms, i.e., mechanistic and data-driven modelling, are dominant in the water sector, both with their advantages and drawbacks. Hybrid modelling aims to combine the strengths of both paradigms. Here, we introduce a novel framework that incorporates a data-driven component into an existing activated sludge model of a water resource recovery facility. In contrast to previous efforts, we tightly integrate both models by incorporating a neural differential equation into an existing mechanistic ODE model. This machine learning component fills in the knowledge gaps of the mechanistic model. We show that this approach improves the predictive capabilities of the mechanistic model and is able to extrapolate to unseen conditions, a problematic task for data-driven models. This approach holds tremendous potential for systems that are difficult to model using the mechanistic paradigm only.
Keywords
Hybrid models, Data-driven models, Mechanistic models, Neural differential equations, Machine learning, Water systems, PRACTICAL IDENTIFIABILITY, NEURAL-NETWORKS, APPROXIMATION, IDENTIFICATION, PARAMETERS, DYNAMICS

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MLA
Quaghebeur, Ward, et al. “Hybrid Differential Equations : Integrating Mechanistic and Data-Driven Techniques for Modelling of Water Systems.” WATER RESEARCH, vol. 213, 2022, doi:10.1016/j.watres.2022.118166.
APA
Quaghebeur, W., Torfs, E., De Baets, B., & Nopens, I. (2022). Hybrid differential equations : integrating mechanistic and data-driven techniques for modelling of water systems. WATER RESEARCH, 213. https://doi.org/10.1016/j.watres.2022.118166
Chicago author-date
Quaghebeur, Ward, Elena Torfs, Bernard De Baets, and Ingmar Nopens. 2022. “Hybrid Differential Equations : Integrating Mechanistic and Data-Driven Techniques for Modelling of Water Systems.” WATER RESEARCH 213. https://doi.org/10.1016/j.watres.2022.118166.
Chicago author-date (all authors)
Quaghebeur, Ward, Elena Torfs, Bernard De Baets, and Ingmar Nopens. 2022. “Hybrid Differential Equations : Integrating Mechanistic and Data-Driven Techniques for Modelling of Water Systems.” WATER RESEARCH 213. doi:10.1016/j.watres.2022.118166.
Vancouver
1.
Quaghebeur W, Torfs E, De Baets B, Nopens I. Hybrid differential equations : integrating mechanistic and data-driven techniques for modelling of water systems. WATER RESEARCH. 2022;213.
IEEE
[1]
W. Quaghebeur, E. Torfs, B. De Baets, and I. Nopens, “Hybrid differential equations : integrating mechanistic and data-driven techniques for modelling of water systems,” WATER RESEARCH, vol. 213, 2022.
@article{8741782,
  abstract     = {{Mathematical modelling is increasingly used to improve the design, understanding, and operation of water systems. Two modelling paradigms, i.e., mechanistic and data-driven modelling, are dominant in the water sector, both with their advantages and drawbacks. Hybrid modelling aims to combine the strengths of both paradigms. Here, we introduce a novel framework that incorporates a data-driven component into an existing activated sludge model of a water resource recovery facility. In contrast to previous efforts, we tightly integrate both models by incorporating a neural differential equation into an existing mechanistic ODE model. This machine learning component fills in the knowledge gaps of the mechanistic model. We show that this approach improves the predictive capabilities of the mechanistic model and is able to extrapolate to unseen conditions, a problematic task for data-driven models. This approach holds tremendous potential for systems that are difficult to model using the mechanistic paradigm only.}},
  articleno    = {{118166}},
  author       = {{Quaghebeur, Ward and Torfs, Elena and De Baets, Bernard and Nopens, Ingmar}},
  issn         = {{0043-1354}},
  journal      = {{WATER RESEARCH}},
  keywords     = {{Hybrid models,Data-driven models,Mechanistic models,Neural differential equations,Machine learning,Water systems,PRACTICAL IDENTIFIABILITY,NEURAL-NETWORKS,APPROXIMATION,IDENTIFICATION,PARAMETERS,DYNAMICS}},
  language     = {{eng}},
  pages        = {{11}},
  title        = {{Hybrid differential equations : integrating mechanistic and data-driven techniques for modelling of water systems}},
  url          = {{http://doi.org/10.1016/j.watres.2022.118166}},
  volume       = {{213}},
  year         = {{2022}},
}

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