We propose a novel deep learning based surrogate model for solving high-dimensional uncertainty quantification and uncertainty propagation problems. The proposed deep learning architecture is developed by integrating the well-known U-net architecture with the Gaussian Gated Linear Network (GGLN) and referred to as the Gated Linear Network induced U-net or GLU-net. The proposed GLU-net treats the uncertainty propagation problem as an image to image regression and hence, is extremely data efficient. Additionally, it also provides estimates of the predictive uncertainty. The network architecture of GLU-net is less complex with 44\% fewer parameters than the contemporary works. We illustrate the performance of the proposed GLU-net in solving the Darcy flow problem under uncertainty under the sparse data scenario. We consider the stochastic input dimensionality to be up to 4225. Benchmark results are generated using the vanilla Monte Carlo simulation. We observe the proposed GLU-net to be accurate and extremely efficient even when no information about the structure of the inputs is provided to the network. Case studies are performed by varying the training sample size and stochastic input dimensionality to illustrate the robustness of the proposed approach.

翻译：我们提出一个新的深层次学习替代模型,以解决高层次不确定性量化和不确定性传播问题。拟议的深层次学习结构是通过将众所周知的U-net结构与Gaussian Gated Linear网络(GGLN)结合而开发的,称为Gated Linear网络引致U-net或GLU-net。拟议的GLU-net将不确定性传播问题视为图像回归的图像,因此极具数据效率。此外,它还提供了预测不确定性的估计。GLU-net的网络结构不那么复杂,其参数比当代工作少44 ⁇ 。我们用不同的培训样本大小和深度投入方式进行了案例研究,以说明在稀疏数据假设的不确定性下解决达西流动问题的情况。我们认为,Stochatical投入的维度最高可达4225年。使用vanilla Monte Carlo模拟得出基准结果。我们观察拟议的GLU-net是否准确和极有效,即使没有向网络提供有关投入结构的信息。案例研究是通过不同的培训样本和深度输入方式进行的。我们用不同的案例研究,以说明拟议的稳健的维度方法进行。