Deep neural network discretization of the Wong-Zakai approximation of...

In recent years, deepneural networks (DNNs) have been successfully used in many computationalproblems including, for example, fraud detection or pattern recognition. DNNalgorithms have been also proven to be enormously successful in overcoming thecurse of dimensionality, in particular for solving Kolmogorov-type partialdifferential equations in hundreds of dimensions in reasonable computationtime. Nothing is known until now on using neural networks in connection withthe so-called Wong-Zakai method that approximates stochastic differentialequations by suitable random ordinary differential equations. We are exploringwhether neural networks are numerically beneficial in this context and providean algorithm for that. This is joint work with Andreas Neuenkirch (Universityof Mannheim) and Michaela Szölgyenyi (University of Klagenfurt).