Dimensionality reduction can be used as a surrogate model for high-dimensional forward uncertainty quantification

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 predictive distribution is obtained by generating samples from a transition kernel that encodes the dimensionality reduction and a feature-space conditional distribution. The resulting surrogate model operates as 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 three uncertainty quantification problems characterized by high-dimensional input uncertainties.