  We propose an accurate data-driven numerical scheme to solve Stochastic
Differential Equations (SDEs), by taking large time steps. The SDE
discretization is built up by means of a polynomial chaos expansion method, on
the basis of accurately determined stochastic collocation (SC) points. By
employing an artificial neural network to learn these SC points, we can perform
Monte Carlo simulations with large time steps. Error analysis confirms that
this data-driven scheme results in accurate SDE solutions in the sense of
strong convergence, provided the learning methodology is robust and accurate.
With a method variant called the compression-decompression collocation and
interpolation technique, we can drastically reduce the number of neural network
functions that have to be learned, so that computational speed is enhanced.
Numerical experiments confirm a high-quality strong convergence error when
using large time steps, and the novel scheme outperforms some classical
numerical SDE discretizations. Some applications, here in financial option
valuation, are also presented.
