In this paper we consider PIDEs with gradient-independent Lipschitz continuous nonlinearities and prove that deep neural networks with ReLU activation function can approximate solutions of such semilinear PIDEs without curse of dimensionality in the sense that the required number of parameters in the deep neural networks increases at most polynomially in both the dimension $ d $ of the corresponding PIDE and the reciprocal of the prescribed accuracy $\epsilon $.

翻译：本文考虑具有梯度无关Lipschitz连续非线性的偏积分-微分方程(PIDEs)，证明采用ReLU激活函数的深度神经网络可在无维度灾难意义下逼近此类半线性PIDEs的解，即深度神经网络所需参数数量在对应PIDE的维度$d$和预设精度$\epsilon$的倒数上至多以多项式形式增长。