We introduce a method to construct a stochastic surrogate model from the results of dimensionality reduction in forward uncertainty quantification. The hypothesis is that the high-dimensional input augmented by the output of a computational model admits a low-dimensional representation. This assumption can be met by numerous uncertainty quantification applications with physics-based computational models. The proposed approach differs from a sequential application of dimensionality reduction followed by surrogate modeling, as we "extract" a surrogate model from the results of dimensionality reduction in the input-output space. This feature becomes desirable when the input space is genuinely high-dimensional. The proposed method also diverges from the Probabilistic Learning on Manifold, as a reconstruction mapping from the feature space to the input-output space is circumvented. The final product of the proposed method is a stochastic simulator that propagates a deterministic input into a stochastic output, preserving the convenience of a sequential "dimensionality reduction + Gaussian process regression" approach while overcoming some of its limitations. The proposed method is demonstrated through two uncertainty quantification problems characterized by high-dimensional input uncertainties.

翻译：我们提出了一种方法，通过前向不确定性量化中降维的结果构建随机替代模型。其假设在于：通过计算模型输出的高维输入增强数据具有低维表示。这一假设适用于众多基于物理计算模型的不确定性量化应用。所提方法与先降维后替代建模的序贯应用不同，因为我们在输入-输出空间的降维结果中"提取"替代模型。当输入空间真正高维时，这一特性尤为理想。所提方法也与流形概率学习不同，因为它规避了从特征空间到输入-输出空间的重构映射。该方法的最终产物是一个随机模拟器，能将确定性输入传播为随机输出，既保持了序贯"降维+高斯过程回归"方法的便捷性，又克服了其部分局限性。通过两个以高维输入不确定性为特征的不确定性量化问题，对所提方法进行了验证。