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Barium titanate (BaTiO3) is a class of ceramic multifunctional materials with unique thermal stability, prominent piezoelectricity constant, excellent dielectric constant, environmental friendliness, and excellent photocatalytic activities. These features have rendered barium titanate indispensable in many areas of applications such as electromechanical devices, thermistors, multilayer capacitors, and electrooptical devices. The photocatalytic activity of barium titanate semiconductor is hindered by its large band gap and high rate of charge recombination. Doping of the parent barium titanate compound for band gap tuning is challenging and consumes appreciable time and other valuable resources. This present work relates the influence of foreign material incorporation into the parent barium titanate with the corresponding energy band gap by developing extreme learning machine- (ELM-) based models and hybridization of support vector regression (SVR) with gravitational search algorithm (GSA) using the structural lattice distortion that emanated from doping as model descriptors. The developed gravitationally optimized SVR (GSVR) is characterized with a low value of mean absolute error (MAE), mean absolute percentage error (MAPE), and root mean square error (RMSE) of 0.036 ev, 1.145 ev, and 0.122 ev, respectively. The developed GSVR model outperforms ELM-Sine and ELM-Sig models using various performance evaluators. The developed GSVR model investigates the significance of iodine and samarium incorporation on the band gap of the parent barium titanate and the attained energy gaps conform excellently to the experimentally reported values. The demonstrated precision of the developed GSVR as measured from the closeness of its estimates with the measured values provides a quick and accurate method of energy gap characterization with circumvention of experimental stress and conservation of valuable time as well as other resources.

mathematical problems in engineering

Barium Titanate Semiconductor Band Gap Characterization through Gravitationally Optimized Support Vector Regression and Extreme Learning Machine Computational Methods