Abstract: Firstly,  we used the original dual active set method to solve the forward problem of option pricing, with the corresponding numerical solutions as the output for supervised learning, and then replaced the  forward problem model of option pricing with a well-trained neural network. Secondly, we combined Bayesian inference with neural networks for Metropolis-Hastings sampling  to solve the inverse problem of implied volatility. This method reduced the problem of large computational complexity  of the forward problem during the sampling process, thereby accelerating the solution process for the inverse problem.

Key words: implied volatility, Bayesian inference, neural network, surrogated model