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.

翻译：我们证明深层神经网络能够接近半线性科尔莫戈罗夫PDE的解决方案,以坡度独立、利普西茨持续的非线性为例,而网络中所需的参数数量最多以多元形式增长,两个方面都以美元计,并规定了对等精确度$\varepsilon$。以前,这只在半线性热方程式中得到证明。