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 outperforms the widely used surface stochastic volatility inspired (SSVI) model on the mean average percentage error in both in-sample and out-of-sample datasets.