  The rough Bergomi (rBergomi) model can accurately describe the historical and
implied volatilities, and has gained much attention in the past few years.
However, there are many hidden unknown parameters or even functions in the
model. In this work, we investigate the potential of learning the forward
variance curve in the rBergomi model using a neural SDE. To construct an
efficient solver for the neural SDE, we propose a novel numerical scheme for
simulating the volatility process using the modified summation of exponentials.
Using the Wasserstein 1-distance to define the loss function, we show that the
learned forward variance curve is capable of calibrating the price process of
the underlying asset and the price of the European-style options
simultaneously. Several numerical tests are provided to demonstrate its
performance.
