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Incorporating unmodeled dynamics into first-principles models through machine learning

Ward Quaghebeur (UGent) , Ingmar Nopens (UGent) and Bernard De Baets (UGent)
(2021) IEEE ACCESS. 9. p.22014-22022
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Abstract
First-principles modeling of dynamical systems is a cornerstone of science and engineering and has enabled rapid development and improvement of key technologies such as chemical reactors, electrical circuits, and communication networks. In various disciplines, scientists structure the available domain knowledge into a system of differential equations. When designed, calibrated, and validated appropriately, these equations are used to analyze and predict the dynamics of the system. However, perfect knowledge is usually not accessible in real-world problems. The incorporated knowledge thus is a simplification of the real system and is limited by the underlying assumptions. This limits the extent to which the model reflects reality. The resulting lack of predictive power severely hampers the application potential of such models. Here we introduce a framework that incorporates machine learning into existing first-principles modeling. The machine learning model fills in the knowledge gaps of the first-principles model, capturing the unmodeled dynamics and thus improving the representativeness of the model. Moreover, we show that this approach lowers the data requirements, both in quantity and quality, and improves the generalization ability in comparison with a purely data-driven approach. This approach can be applied to any first-principles model with sufficient data available and has tremendous potential in many fields.
Keywords
General Engineering, General Materials Science, General Computer Science, Mathematical model, Differential equations, Machine learning, Data models, Libraries, Training, Computational modeling, Differential equations, dynamical systems, first-principles modeling, hybrid modeling, machine learning

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MLA
Quaghebeur, Ward, et al. “Incorporating Unmodeled Dynamics into First-Principles Models through Machine Learning.” IEEE ACCESS, vol. 9, 2021, pp. 22014–22, doi:10.1109/access.2021.3055353.
APA
Quaghebeur, W., Nopens, I., & De Baets, B. (2021). Incorporating unmodeled dynamics into first-principles models through machine learning. IEEE ACCESS, 9, 22014–22022. https://doi.org/10.1109/access.2021.3055353
Chicago author-date
Quaghebeur, Ward, Ingmar Nopens, and Bernard De Baets. 2021. “Incorporating Unmodeled Dynamics into First-Principles Models through Machine Learning.” IEEE ACCESS 9: 22014–22. https://doi.org/10.1109/access.2021.3055353.
Chicago author-date (all authors)
Quaghebeur, Ward, Ingmar Nopens, and Bernard De Baets. 2021. “Incorporating Unmodeled Dynamics into First-Principles Models through Machine Learning.” IEEE ACCESS 9: 22014–22022. doi:10.1109/access.2021.3055353.
Vancouver
1.
Quaghebeur W, Nopens I, De Baets B. Incorporating unmodeled dynamics into first-principles models through machine learning. IEEE ACCESS. 2021;9:22014–22.
IEEE
[1]
W. Quaghebeur, I. Nopens, and B. De Baets, “Incorporating unmodeled dynamics into first-principles models through machine learning,” IEEE ACCESS, vol. 9, pp. 22014–22022, 2021.
@article{8692515,
  abstract     = {{First-principles modeling of dynamical systems is a cornerstone of science and engineering and has enabled rapid development and improvement of key technologies such as chemical reactors, electrical circuits, and communication networks. In various disciplines, scientists structure the available domain knowledge into a system of differential equations. When designed, calibrated, and validated appropriately, these equations are used to analyze and predict the dynamics of the system. However, perfect knowledge is usually not accessible in real-world problems. The incorporated knowledge thus is a simplification of the real system and is limited by the underlying assumptions. This limits the extent to which the model reflects reality. The resulting lack of predictive power severely hampers the application potential of such models. Here we introduce a framework that incorporates machine learning into existing first-principles modeling. The machine learning model fills in the knowledge gaps of the first-principles model, capturing the unmodeled dynamics and thus improving the representativeness of the model. Moreover, we show that this approach lowers the data requirements, both in quantity and quality, and improves the generalization ability in comparison with a purely data-driven approach. This approach can be applied to any first-principles model with sufficient data available and has tremendous potential in many fields.}},
  author       = {{Quaghebeur, Ward and Nopens, Ingmar and De Baets, Bernard}},
  issn         = {{2169-3536}},
  journal      = {{IEEE ACCESS}},
  keywords     = {{General Engineering,General Materials Science,General Computer Science,Mathematical model,Differential equations,Machine learning,Data models,Libraries,Training,Computational modeling,Differential equations,dynamical systems,first-principles modeling,hybrid modeling,machine learning}},
  language     = {{eng}},
  pages        = {{22014--22022}},
  title        = {{Incorporating unmodeled dynamics into first-principles models through machine learning}},
  url          = {{http://doi.org/10.1109/access.2021.3055353}},
  volume       = {{9}},
  year         = {{2021}},
}

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