  Parabolic partial differential equations (PDEs) and backward stochastic
differential equations (BSDEs) have a wide range of applications. In
particular, high-dimensional PDEs with gradient-dependent nonlinearities appear
often in the state-of-the-art pricing and hedging of financial derivatives. In
this article we prove that semilinear heat equations with gradient-dependent
nonlinearities can be approximated under suitable assumptions with
computational complexity that grows polynomially both in the dimension and the
reciprocal of the accuracy.
