  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 $d \in \mathbb{N}$ and
prescribed reciprocal accuracy $\varepsilon$. Previously, this has only been
proven in the case of semilinear heat equations.
