Before revision:  The developed neural network model and its simplified variations outperform the widely used surface stochastic volatility inspired (SSVI) model  on the mean average percentage error in both in-sample and out-of-sample datasets.
After revision:  The developed neural network model and its simplified variations outperform the widely used surface stochastic volatility inspired (SSVI) model and other benchmarked neural network models on the mean average percentage error in both in-sample and out-of-sample datasets.