We prove that deep neural networks with ReLU activation function are capable of approximating solutions of semilinear partial integro-differential equations in the case of gradient-independent and Lipschitz-continuous nonlinearities, while the required number of parameters in the neural networks grows at most polynomially in both the dimension $ d\in\mathbb{N} $ and the reciprocal of the prescribed accuracy $ \epsilon $.

翻译：本文证明，在非线性项梯度无关且满足Lipschitz连续条件下，使用ReLU激活函数的深度神经网络能够逼近半线性偏积分微分方程的解，且神经网络所需参数个数在维数$ d\in\mathbb{N} $与给定精度倒数$ \epsilon $上至多以多项式形式增长。