Deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear partial differential equations

05/28/2022

∙

by   Petru A. Cioica-Licht, et al.

∙

0

∙

share

We prove that deep neural networks are capable of approximating solutions of semilinear Kolmogorov PDE in the case of gradient-independent, Lipschitz-continuous nonlinearities, while the required number of parameters in the networks grow at most polynomially in both dimension d ∈ℕ and prescribed reciprocal accuracy ε. Previously, this has only been proven in the case of semilinear heat equations.