In this paper we prove that rectified deep neural networks do not suffer from the curse of dimensionality when approximating McKean--Vlasov SDEs in the sense that the number of parameters in the deep neural networks only grows polynomially in the space dimension $d$ of the SDE and the reciprocal of the accuracy $\epsilon$.

翻译：本文证明，整流深度神经网络在逼近McKean-Vlasov随机微分方程时不会遭受维数灾难，其意义在于：深度神经网络的参数数量仅随随机微分方程的空间维度$d$和精度倒数$\epsilon$的多项式阶次增长。