  Techniques from deep learning play a more and more important role for the
important task of calibration of financial models. The pioneering paper by
Hernandez [Risk, 2017] was a catalyst for resurfacing interest in research in
this area. In this paper we advocate an alternative (two-step) approach using
deep learning techniques solely to learn the pricing map -- from model
parameters to prices or implied volatilities -- rather than directly the
calibrated model parameters as a function of observed market data. Having a
fast and accurate neural-network-based approximating pricing map (first step),
we can then (second step) use traditional model calibration algorithms. In this
work we showcase a direct comparison of different potential approaches to the
learning stage and present algorithms that provide a suffcient accuracy for
practical use. We provide a first neural network-based calibration method for
rough volatility models for which calibration can be done on the y. We
demonstrate the method via a hands-on calibration engine on the rough Bergomi
model, for which classical calibration techniques are diffcult to apply due to
the high cost of all known numerical pricing methods. Furthermore, we display
and compare different types of sampling and training methods and elaborate on
their advantages under different objectives. As a further application we use
the fast pricing method for a Bayesian analysis of the calibrated model.
