The Seven-League Scheme: Deep learning for large time step Monte Carlo simulations of stochastic differential equations

Understand

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.