  We present a multidimensional deep learning implementation of a stochastic
branching algorithm for the numerical solution of fully nonlinear PDEs. This
approach is designed to tackle functional nonlinearities involving gradient
terms of any orders, by combining the use of neural networks with a Monte Carlo
branching algorithm. In comparison with other deep learning PDE solvers, it
also allows us to check the consistency of the learned neural network function.
Numerical experiments presented show that this algorithm can outperform deep
learning approaches based on backward stochastic differential equations or the
Galerkin method, and provide solution estimates that are not obtained by those
methods in fully nonlinear examples.
