We investigate artificial neural networks as a parametrization tool for stochastic inputs in numerical simulations. We address parametrization from the point of view of emulating the data generating process, instead of explicitly constructing a parametric form to preserve predefined statistics of the data. This is done by training a neural network to generate samples from the data distribution using a recent deep learning technique called generative adversarial networks. By emulating the data generating process, the relevant statistics of the data are replicated. The method is assessed in subsurface flow problems, where effective parametrization of underground properties such as permeability is important due to the high dimensionality and presence of high spatial correlations. We experiment with realizations of binary channelized subsurface permeability and perform uncertainty quantification and parameter estimation. Results show that the parametrization using generative adversarial networks is very effective in preserving visual realism as well as high order statistics of the flow responses, while achieving a dimensionality reduction of two orders of magnitude.
翻译:我们调查人工神经网络,将其作为数字模拟中随机输入的准光化工具。我们从模拟数据生成过程的角度处理半光化问题,而不是明确构建一种参数形式,以保存预定义的数据统计数据。这是通过培训神经网络,利用最近一项称为基因对抗网络的深层学习技术,从数据分布中生成样本。通过模拟数据生成过程,数据的相关统计数据被复制。在地下流动问题中评估了该方法,由于高度的多维性和高度空间相关性的存在,地下水特性(如渗透性)的有效平衡十分重要。我们实验了二元信道子表层的可渗透性,并进行了不确定性的量化和参数估计。结果显示,使用基因对抗网络的配光化非常有效,既保存了视觉现实主义,也保存了流量反应的高顺序统计,同时实现了两个数量级的维度的减少。