Hybrid neural network models for environmental process control (The 1998 Hunter Lecture)

Veaux, Richard D. De; Bain, Rod; Ungar, Lyle H.

doi:10.1002/(sici)1099-095x(199905/06)10:3<225::aid-env356>3.0.co;2-1

Cited by 9 publications

(1 citation statement)

References 17 publications

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“…The work of Psichogios and Ungar was continued by Hagge et al [27] with use of modern machine learning techniques on the same physical problem as Psichogios. The fed-batch bioreactor problem was further addressed in [28][29][30]. Many more researchers attempted to solve the problem in a similar manner-identify the difficult to model parts in first principles and substitute them with machine learning techniques: Cubillos et al [31] in solid drying process, Piron et al in crossflow microfiltration process [32], Oliveira in fed-batch bioreactor and bakers' yeast production [30], Vieira and Mota in water gas heater system [33], Romijn et al in energy balance for a glass melting process [34] and Chaffart and Ricardez-Sandoval in thin film growth process [35].…”

Section: Literature Reviewmentioning

confidence: 99%

Integration of Classical Mathematical Modeling with an Artificial Neural Network for the Problems with Limited Dataset

2021

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One of the most common problems in science is to investigate a function describing a system. When the estimate is made based on a classical mathematical model (white-box), the function is obtained throughout solving a differential equation. Alternatively, the prediction can be made by an artificial neural network (black-box) based on trends found in past data. Both approaches have their advantages and disadvantages. Mathematical models were seen as more trustworthy as their prediction is based on the laws of physics expressed in the form of mathematical equations. However, the majority of existing mathematical models include different empirical parameters, and both approaches inherit inevitable experimental errors. Simultaneously, the approximation of neural networks can reproduce the solution exceptionally well if fed sufficient data. The difference is that an artificial neural network requires big data to build its accurate approximation, whereas a typical mathematical model needs several data points to estimate an empirical constant. Therefore, the common problem that developers meet is the inaccuracy of mathematical models and artificial neural networks. Another common challenge is the mathematical models’ computational complexity or lack of data for a sufficient precision of the artificial neural networks. Here we analyze a grey-box solution in which an artificial neural network predicts just a part of the mathematical model, and its weights are adjusted based on the mathematical model’s output using the evolutionary approach to avoid overfitting. The performance of the grey-box model is statistically compared to a Dense Neural Network on benchmarking functions. With the use of Shaffer procedure, it was shown that the grey-box approach performs exceptionally well when the overall complexity of a problem is properly distributed with the mathematical model and the Artificial Neural Network. The obtained calculation results indicate that such an approach could increase precision and limit the dataset required for learning. To show the applicability of the presented approach, it was employed in modeling of the electrochemical reaction in the Solid Oxide Fuel Cell’s anode. Implementation of a grey-box model improved the prediction in comparison to the typically used methodology.

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Section: Literature Reviewmentioning

confidence: 99%

Integration of Classical Mathematical Modeling with an Artificial Neural Network for the Problems with Limited Dataset

2021

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Smoothing

Kafadar¹,

Horn²

2001

Encyclopedia of Environmetrics

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We describe smoothing as an exploratory tool in data analysis, including an underlying model that motivates the need for smoothing, the goals and characteristics of good smoothers, and general classes of smoothers (linear and nonlinear). We also relate smoothing to the concepts of general fitting, parametric and nonparametric regression, and illustrate the use of smoothers on both one‐ and two‐dimensional data sets.

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Smoothing

Kafadar¹

2012

Encyclopedia of Environmetrics

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This article describes smoothing as an exploratory tool in data analysis, including an underlying model that motivates the need for smoothing, the goals and characteristics of good smoothers, general classes of smoothers (linear and nonlinear), and illustrations of the value of smoothing. Smoothing is related to the concepts of general fitting, parametric regression, and nonparametric regression, and the smoothers are illustrated as both one‐ and two‐dimensional data sets. Some insight is offered on choosing smoothing parameters, and some resources for computing smoothers and further references are also provided.

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Hybrid neural network models for environmental process control (The 1998 Hunter Lecture)

Cited by 9 publications

References 17 publications

Integration of Classical Mathematical Modeling with an Artificial Neural Network for the Problems with Limited Dataset

Integration of Classical Mathematical Modeling with an Artificial Neural Network for the Problems with Limited Dataset

Smoothing

Smoothing

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