# Prediction of Band Gap Energy of Doped Graphitic Carbon Nitride Using Genetic Algorithm-Based Support Vector Regression and Extreme Learning Machine

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## Abstract

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_{2}, water splitting and other photocatalytic applications. Efficient utilization of this material is hampered by the nature of its band gap and the rapid recombination of electron-hole pairs. Heteroatom incorporation due to doping alters the symmetry of the semiconductor and has been among the adopted strategies to tailor the band gap for enhancing the visible-light harvesting capacity of the material. Electron modulation and enhancement of reaction active sites due to doping as evident from the change in specific surface area of doped graphitic carbon nitride is employed in this work for modeling the associated band gap using hybrid genetic algorithm-based support vector regression (GSVR) and extreme learning machine (ELM). The developed GSVR performs better than ELM-SINE (with sine activation function), ELM-TRANBAS (with triangular basis activation function) and ELM-SIG (with sigmoid activation function) model with performance enhancement of 69.92%, 73.59% and 73.67%, respectively, on the basis of root mean square error as a measure of performance. The four developed models are also compared using correlation coefficient and mean absolute error while the developed GSVR demonstrates a high degree of precision and robustness. The excellent generalization and predictive strength of the developed models would ultimately facilitate quick determination of the band gap of doped graphitic carbon nitride and enhance its visible-light harvesting capacity for various photocatalytic applications.

## 1. Introduction

## 2. Mathematical Formulation of the Proposed Hybrid Algorithms

#### 2.1. Support Vector Regression Machine Learning Algorithm

#### 2.2. Brief Description of Genetic Population-Based Optimization Algorithm

#### 2.3. Extreme Learning Machine

## 3. Computational Methodology of the Proposed Hybrid GSVR and ELM

#### 3.1. Dataset Acquisition and Description

#### 3.2. Support Vector Regression and Genetic Algorithm Hybridization

- Kernel function selection: choose a function from Gaussian, Sigmoid or Polynomial that serves as the kernel function.
- Each chromosome that depicts hyperparameters (in a known and defined order) goes into the chosen kernel function and SVR algorithm is trained using the training set of data. RMSE-training value corresponding to each of the trained models is recorded while the support vectors acquired during the training are saved.
- The support vectors saved in (ii) are employed in further evaluation of each of the trained SVR algorithm using testing dataset. The associated RMSE-testing for each of the chromosome is saved
- Each of the developed models is evaluated using RMSE-testing obtained in (iii). The model characterized with the lowest value of RMSE-testing is regarded as the best model, while the model with largest value of RMSE-testing is the worst of the models.

#### 3.3. Computational Implementation of Extreme Learning Machine-Based Model

## 4. Results and Discussion

#### 4.1. Number of Population in Genetic Algorithm and Model Convergence

#### 4.2. Performance Comparison and Evaluation of the Developed Models

#### 4.3. Effect of Experimental Preparation Conditions on the Band Gap of GCN Using the Developed GSVR Model

#### 4.4. Photocatalytic Effect of Sulfur Dopant and Temperature Treatment on GCN

#### 4.5. Significance of Oxygen Incorporation on the Band Gap of GCN

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Flow chart of the computational strategies employed for extreme learning machine (ELM)-based model development.

**Figure 2.**Model (genetic algorithm-based support vector regression; GSVR) convergence with the number of population.

**Figure 8.**Correlation cross-plot between the estimated and measured band gaps using the developed models.

Mean | Maximum | Minimum | Correlation Coefficient | |
---|---|---|---|---|

Surface area | 49.36926 | 210.1 | 5.6 | −0.03 |

Band gap | 2.650952 | 2.93 | 1.68 |

**Table 2.**Optimum obtained values of support vector regression (SVR) parameters using genetic algorithm (GA).

HyperParameters (GSVR) | Optimum Value |
---|---|

C | 1 |

N | 200 |

Gaussian kernel option | 0.001099 |

Epsilon | 0.002 |

Hyperparameter lambda | 10^{−7} |

Coefficient of Correlation | RMSE (ev) | MAE (ev) | |
---|---|---|---|

GSVR | 0.9680 | 0.0490 | 0.0245 |

ELM-SINE | 0.6134 | 0.1631 | 0.1219 |

ELM-TRANBAS | 0.2811 | 0.1857 | 0.1252 |

ELM-SIG | 0.2720 | 0.1863 | 0.1274 |

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**MDPI and ACS Style**

Owolabi, T.O.; Abd Rahman, M.A.
Prediction of Band Gap Energy of Doped Graphitic Carbon Nitride Using Genetic Algorithm-Based Support Vector Regression and Extreme Learning Machine. *Symmetry* **2021**, *13*, 411.
https://doi.org/10.3390/sym13030411

**AMA Style**

Owolabi TO, Abd Rahman MA.
Prediction of Band Gap Energy of Doped Graphitic Carbon Nitride Using Genetic Algorithm-Based Support Vector Regression and Extreme Learning Machine. *Symmetry*. 2021; 13(3):411.
https://doi.org/10.3390/sym13030411

**Chicago/Turabian Style**

Owolabi, Taoreed O., and Mohd Amiruddin Abd Rahman.
2021. "Prediction of Band Gap Energy of Doped Graphitic Carbon Nitride Using Genetic Algorithm-Based Support Vector Regression and Extreme Learning Machine" *Symmetry* 13, no. 3: 411.
https://doi.org/10.3390/sym13030411