How to get accurate estimates on Neural Networks Hessian?

I need to get not only accurate estimates on the neural network output itself but also on its second order derivatives in order to use the NN for optimization problems. With Adam optimizer I can’t get these accurate estimates. It seems that the neural network can’t get good estimates on its second order derivative beyond the domain it were trained getting erroneous erroneous in some particular data input. Is there any optimizer or regularization technique that can give me a better accuracy on the neural network derivative i.e get more information on it?