论文标题
参数双曲线保护法的深神网络近似的错误分析
Error analysis for deep neural network approximations of parametric hyperbolic conservation laws
论文作者
论文摘要
我们因与Relu神经网络的参数双曲标量保护定律的近似值所产生的误差得出了严格的界限。我们表明，通过克服维度诅咒的依赖神经网络，可以使近似误差尽可能小。此外，我们在训练错误，训练样本数量和神经网络大小方面提供了明确的上限。理论结果通过数值实验说明。
We derive rigorous bounds on the error resulting from the approximation of the solution of parametric hyperbolic scalar conservation laws with ReLU neural networks. We show that the approximation error can be made as small as desired with ReLU neural networks that overcome the curse of dimensionality. In addition, we provide an explicit upper bound on the generalization error in terms of the training error, number of training samples and the neural network size. The theoretical results are illustrated by numerical experiments.
