The development of a reliable and robust surrogate model is often constrained by the dimensionality of the problem. For a system with high‐dimensional inputs/outputs (I/O), conventional approaches usually use a low‐dimensional manifold to describe the high‐dimensional system, where the I/O data are first reduced to more manageable dimensions and then the condensed representation is used for surrogate modeling. In this study, a new solution scheme for this type of problem based on a deep learning approach is presented. The proposed surrogate is based on a particular network architecture, that is, convolutional neural networks. The surrogate architecture is designed in a hierarchical style containing three different levels of model structures, advancing the efficiency and effectiveness of the model in the aspect of training. To assess the model performance, uncertainty quantification is carried out in a continuum mechanics benchmark problem. Numerical results suggest the proposed model is capable of directly inferring a wide variety of I/O mapping relationships. Uncertainty analysis results obtained via the proposed surrogate have successfully characterized the statistical properties of the output fields compared to the Monte Carlo estimates.

中文翻译：

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深度卷积神经网络用于不确定场中的不确定性传播

可靠且健壮的替代模型的开发通常受问题的维度限制。对于具有高维输入/输出（I / O）的系统，常规方法通常使用低维流形来描述高维系统，在该系统中，首先将I / O数据缩减为更易于管理的维，然后将其压缩制图表达用于代理建模。在这项研究中，提出了一种基于深度学习方法的此类问题的新解决方案。提出的代理基于特定的网络体系结构，即卷积神经网络。代理体系结构以分层样式设计，其中包含三个不同级别的模型结构，从而在训练方面提高了模型的效率和有效性。为了评估模型性能，在连续力学基准问题中进行了不确定性量化。数值结果表明，所提出的模型能够直接推断出各种I / O映射关系。与蒙特卡洛估计相比，通过提议的替代方法获得的不确定性分析结果已成功表征了输出字段的统计属性。