A general theorem shows that neural networks inherit the absence of the curse of dimensionality from any discrete Monte Carlo scheme they can emulate, with applications to Kolmogorov PDEs.
Machine Learning Approximation Algorithms for High-Dimensional Fully Nonlinear Partial Differential Eq uations and Second-order Backward Stochastic Differential Equations
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Deep neural network approximations for Monte Carlo algorithms
A general theorem shows that neural networks inherit the absence of the curse of dimensionality from any discrete Monte Carlo scheme they can emulate, with applications to Kolmogorov PDEs.