论文标题
梯度增强的深神经网络近似
Gradient-enhanced deep neural network approximations
论文作者
论文摘要
我们在这项工作中提出了梯度增强的深神经网络（DNNS）方法，以进行功能近似和不确定性定量。更确切地说，所提出的方法同时采用功能评估和相关的梯度信息，以产生增强的近似精度。特别是，在梯度增强的DNN方法中，将梯度信息作为正规化项包括在内，为此，我们提供了类似的后验估计（通过两层神经网络）与路径 - 正常化DNNS近似值中的梯度估计值（通过两层神经网络）。我们还讨论了这种方法在梯度增强的不确定性量化中的应用，并提出了一些数值实验，以表明在许多兴趣情况下，所提出的方法可以胜过传统的DNN方法。
We propose in this work the gradient-enhanced deep neural networks (DNNs) approach for function approximations and uncertainty quantification. More precisely, the proposed approach adopts both the function evaluations and the associated gradient information to yield enhanced approximation accuracy. In particular, the gradient information is included as a regularization term in the gradient-enhanced DNNs approach, for which we present similar posterior estimates (by the two-layer neural networks) as those in the path-norm regularized DNNs approximations. We also discuss the application of this approach to gradient-enhanced uncertainty quantification, and present several numerical experiments to show that the proposed approach can outperform the traditional DNNs approach in many cases of interests.
