This paper presents a neural network-based calibration method for stochastic volatility models, particularly rough Bergomi (rBergomi) and rough Heston (rHeston). The authors combine the pointwise approach of Bayer et al. (2018) and Liu et al. (2019) with the grid-based approach of Horvath et al. (2021) by training a neural network on implied volatility surfaces generated on random grids. This hybrid method inherits the robustness of grid-based training while avoiding interpolation/extrapolation steps, as the network directly outputs implied volatility for any strike-maturity pair. The training data consists of quadruplets (model parameters, strike, maturity, implied volatility) derived from random grids, where maturities are drawn from intervals covering short to long expirations and strikes are adapted to each maturity. The network is small (4 hidden layers of 30-50 nodes) and trained offline, enabling calibration in under one second via gradient-based optimization.

The authors also propose a simple parametrization of the forward variance curve, reducing the number of calibrated parameters and improving efficiency. Numerical experiments demonstrate the method's effectiveness for both rBergomi (using Monte Carlo simulation) and rHeston (using Fourier-based pricing with the SINC method). Key findings include: (1) random grids improve out-of-sample accuracy compared to fixed or adaptive grids; (2) including very short maturities (e.g., 0.003 years) is essential for accurate estimation of the roughness parameter H; (3) the simple forward variance parametrization fits market data well. The method is validated on real market volatility surfaces, showing fast and accurate calibration. This work paves the way for applications in local stochastic volatility models and path-dependent volatility models.