  One of the most challenging problems in applied mathematics is the
approximate solution of nonlinear partial differential equations (PDEs) in high
dimensions. Standard deterministic approximation methods like finite
differences or finite elements suffer from the curse of dimensionality in the
sense that the computational effort grows exponentially in the dimension. In
this work we overcome this difficulty in the case of reaction-diffusion type
PDEs with a locally Lipschitz continuous coervice nonlinearity (such as
Allen-Cahn PDEs) by introducing and analyzing truncated variants of the
recently introduced full-history recursive multilevel Picard approximation
schemes.
